This document provides an overview and objectives of a modular workbook on decimal numbers for grade 6 students. It includes lessons on reading, writing, naming, comparing, ordering, rounding decimals, as well as lessons on equivalent fractions and decimals and the four fundamental operations of addition, subtraction, multiplication and division of decimal numbers. The workbook aims to help students understand the language and concepts of decimal numbers through exercises and examples.
This document provides information about reading, writing, and understanding decimal numbers. It begins with definitions of decimals and discusses how to read and write decimals with one, two, three, or more decimal places according to standard rules. It also covers how to read and write mixed decimal numbers. The document aims to teach learners the "language of decimal numbers" through examples and exercises so they can competently work with decimals in technical and scientific contexts.
This document provides an overview and objectives of a modular workbook on learning decimal numbers for 6th grade students. It covers reading, writing, naming, comparing, ordering, and rounding decimal numbers. It also includes lessons on equivalent fractions and decimals, and the four arithmetic operations of addition, subtraction, multiplication and division of decimal numbers. The workbook aims to help students understand and work with decimal numbers in a fun and engaging way through various exercises and activities.
This document provides an overview of a modular workbook for teaching fundamental math operations and integers to 1st year high school students. The workbook is divided into two units: Unit I focuses on the four basic operations (addition, subtraction, multiplication, division) using whole numbers. Unit II applies these operations to integers. Each unit includes multiple chapters with lessons explaining concepts and providing exercises for students to practice skills and problem-solving. The overall goal is to help students master the foundational math operations and feel that exploring mathematics is interesting.
This document contains a daily lesson log for a 4th grade math class. It outlines the objectives, content, learning resources, procedures, and evaluation for lessons on numbers and number sense from 10,001 to 100,000. Key concepts covered include visualizing large numbers with place value models, determining the place value and value of digits, and reading and writing numbers in symbols and words. Activities include drills, group work, and word problems to reinforce understanding of large numbers.
Here are the answers to the questions in the "What I Know" section:
1. D
2. D
3. B
4. A
5. A
6. C
7. Graph C
8. y = (x + 3)(x - 1)
9. A
10. A
11. Graph B
12. C
13. a = 2, n = 2
14. B
15. B
16. A
17. B
18. A
19. B
20. C
21. B
22. B
23. C
24. A
Here are a few key points about using an addition table:
- The addition table lists the possible sums for adding any two single-digit numbers. This makes it easy to look up the answer rather than calculating it.
- To use it, find the number you're adding in the left column, and the number you're adding to in the top row. Their sum is where their rows and columns intersect.
- Memorizing the addition table is very helpful for quickly and accurately adding single-digit numbers. It builds addition fact fluency.
- You can also use it to double check your work. If you calculate 4 + 5 and get 9, look it up - it matches!
- As you get
Students will learn about decimals including:
- Understanding place value of decimals and comparing decimal values
- Performing computations of addition, subtraction, multiplication and division of decimals
- Solving problems involving combined operations with decimals
Key points include representing decimals on a number line, using calculators to explore decimals, and limiting operations to no more than three decimal numbers. Students will be able to perform calculations and solve real-world problems involving decimals.
This document is a mathematics module that focuses on relationships between chords, arcs, central angles, and inscribed angles of circles. It begins with an introduction activity where students identify and define terms related to circles like radius, diameter, chord, semicircle, arc, and angles. The module is divided into four lessons that examine central angles, arcs and chords, theorems about these concepts, intercepted arcs and inscribed angles, and theorems about them. The goal is for students to understand these geometric relationships and be able to use them to solve real-world problems.
This document provides information about reading, writing, and understanding decimal numbers. It begins with definitions of decimals and discusses how to read and write decimals with one, two, three, or more decimal places according to standard rules. It also covers how to read and write mixed decimal numbers. The document aims to teach learners the "language of decimal numbers" through examples and exercises so they can competently work with decimals in technical and scientific contexts.
This document provides an overview and objectives of a modular workbook on learning decimal numbers for 6th grade students. It covers reading, writing, naming, comparing, ordering, and rounding decimal numbers. It also includes lessons on equivalent fractions and decimals, and the four arithmetic operations of addition, subtraction, multiplication and division of decimal numbers. The workbook aims to help students understand and work with decimal numbers in a fun and engaging way through various exercises and activities.
This document provides an overview of a modular workbook for teaching fundamental math operations and integers to 1st year high school students. The workbook is divided into two units: Unit I focuses on the four basic operations (addition, subtraction, multiplication, division) using whole numbers. Unit II applies these operations to integers. Each unit includes multiple chapters with lessons explaining concepts and providing exercises for students to practice skills and problem-solving. The overall goal is to help students master the foundational math operations and feel that exploring mathematics is interesting.
This document contains a daily lesson log for a 4th grade math class. It outlines the objectives, content, learning resources, procedures, and evaluation for lessons on numbers and number sense from 10,001 to 100,000. Key concepts covered include visualizing large numbers with place value models, determining the place value and value of digits, and reading and writing numbers in symbols and words. Activities include drills, group work, and word problems to reinforce understanding of large numbers.
Here are the answers to the questions in the "What I Know" section:
1. D
2. D
3. B
4. A
5. A
6. C
7. Graph C
8. y = (x + 3)(x - 1)
9. A
10. A
11. Graph B
12. C
13. a = 2, n = 2
14. B
15. B
16. A
17. B
18. A
19. B
20. C
21. B
22. B
23. C
24. A
Here are a few key points about using an addition table:
- The addition table lists the possible sums for adding any two single-digit numbers. This makes it easy to look up the answer rather than calculating it.
- To use it, find the number you're adding in the left column, and the number you're adding to in the top row. Their sum is where their rows and columns intersect.
- Memorizing the addition table is very helpful for quickly and accurately adding single-digit numbers. It builds addition fact fluency.
- You can also use it to double check your work. If you calculate 4 + 5 and get 9, look it up - it matches!
- As you get
Students will learn about decimals including:
- Understanding place value of decimals and comparing decimal values
- Performing computations of addition, subtraction, multiplication and division of decimals
- Solving problems involving combined operations with decimals
Key points include representing decimals on a number line, using calculators to explore decimals, and limiting operations to no more than three decimal numbers. Students will be able to perform calculations and solve real-world problems involving decimals.
This document is a mathematics module that focuses on relationships between chords, arcs, central angles, and inscribed angles of circles. It begins with an introduction activity where students identify and define terms related to circles like radius, diameter, chord, semicircle, arc, and angles. The module is divided into four lessons that examine central angles, arcs and chords, theorems about these concepts, intercepted arcs and inscribed angles, and theorems about them. The goal is for students to understand these geometric relationships and be able to use them to solve real-world problems.
Lesson guide gr. 3 chapter i -comprehension of whole numbers v1.0EDITHA HONRADEZ
Here are the answers to the matching activity:
A B
a 1) 10 bundles of 1000 straws a. 10 000
b 2) 7 bundles of 1000 straws and 1 bundle of 100 straws b. 7 500
This document provides an overview of a modular workbook on mastering fundamental math operations and integers. It contains two units: [1] Mastering basic fundamental operations with whole numbers, covering addition, subtraction, multiplication and division, and [2] Working with integers. The goal is for students to understand the concepts and master skills in performing the four operations on whole numbers and integers through lessons, exercises and word problems. It was created by education students and their advisers to serve as a supplementary reference for teachers and students.
The document is a curriculum guide for 4th grade mathematics that outlines the key concepts and standards for Unit 1 on factors, multiples, and arrays involving multiplication and division. The unit focuses on helping students understand relationships between multiplication and division and strategies for solving word problems using the four operations. It provides examples of how students can find factor pairs, determine if numbers are multiples, and identify prime and composite numbers between 1-100. The unit aims to build students' abstract reasoning skills and ability to model mathematical concepts.
The document provides an overview of the fourth grade mathematics curriculum for Unit 3 on multiplication and division. It includes the big ideas, essential questions, unit vocabulary, and Arizona state standards addressed. It also provides explanations and examples for key concepts around multiplicative comparisons, solving multi-step word problems using the four operations, and interpreting remainders. Students will learn to represent word problems algebraically and assess the reasonableness of their answers.
Lesson plan for x and dividing by 10, 100, 1000Angela Phillips
1) The lesson objective was to teach students to multiply whole numbers by 10, 100, and 1000 at levels 3 and 4. A card sorting activity was used as an entry task to review basic math skills.
2) Students used whiteboards to practice multiplying numbers by 10, 100, and 1000 with teacher demonstration. They showed their understanding using RAG cards.
3) An activity with correct and incorrect examples was completed, followed by demonstration on the interactive board. Students came up to show their work.
4) Students demonstrated understanding of multiples using whiteboards and did a poster activity in pairs to identify multiples of 10, 100, and 1000.
The document provides an overview of Unit 5 of the 4th grade mathematics curriculum for the Isaac School District. The unit focuses on addition, subtraction, and place value with large numbers up to 1,000,000. It includes 27 instructional sessions covering key concepts like using place value to represent numbers in expanded form and standard algorithms for addition and subtraction. Students are expected to fluently perform multi-digit calculations and explain their work by referring to place value. The unit vocabulary and Arizona state math standards addressed are also outlined.
1) The document provides a lesson plan for teaching trainees about shift registers. It includes information on the trainees, classroom, college, curriculum, content, methodology, and objectives of the lesson.
2) The lesson plan uses various teaching methods like lecture, classroom discussion, individual work, partner work and group work. Videos and handouts will also be used.
3) The lesson objectives are for trainees to understand what a shift register is, its types, how it works in serial in/serial out and serial in/parallel out modes, and design simple shift register circuits.
Slide Show Exploring The Numbers By Number Senses And NumerationHoneylay P. Royo
This document provides an overview of a teacher's guide workbook for exploring numbers through numeration for 4th grade students. It includes sections on place value, expanded form, comparing and ordering numbers, rounding numbers, and Roman numerals. The objectives are to help students develop skills and understanding of mathematical concepts related to everyday activities. The workbook is meant to engage students through clear lessons and activities while meeting curriculum requirements. The author acknowledges those who provided support and guidance in creating the workbook.
Higher modern studies extended responses inductionmrmarr
This document provides information about the Higher Modern Studies course in Scotland. It outlines the course content, which is divided into three subject areas: political issues in Scotland and the UK, social issues in the UK, and international issues focusing on poverty. It describes the skills developed in the course, such as writing extended responses and conclusions. Students must pass internal assessments, an added value assignment, and an external exam to complete the course successfully. The document provides examples of PEEL and PEEREEL paragraphs for analyzing issues, and explains how to structure extended response answers for the exam.
1. The document outlines a mathematics curriculum covering the real number system over 20 days. It focuses on helping students understand key concepts like rational and irrational numbers through hands-on activities and solving real-life problems.
2. The curriculum is divided into three stages: exploring real numbers through number lines and games, having students firmly grasp operations and order axioms through investigations, and applying the concepts to daily life problems.
3. Student understanding and performance will be assessed through problems they formulate involving real numbers and multiple solution strategies.
This document outlines a mathematics curriculum guide for 4th grade students in the Isaac School District. Specifically, it details a 22-session unit on size, shape, and symmetry that focuses on 2-D geometry and measurement. The unit aims to teach students about appropriate units of measurement, classifying geometric figures by their attributes, and relationships between geometric attributes such as perimeter and area. It provides learning objectives, essential questions, and examples for helping students learn concepts related to addition, subtraction, measurement, geometry, angles, and classifying shapes.
This document provides an overview of the fourth grade mathematics curriculum for Unit 6 on fractions and decimals. The unit focuses on problem solving strategies, representing fractions and decimals, and understanding that fractions represent parts of a whole. Key concepts covered include equivalent fractions, comparing fractions, and adding/subtracting fractions. Students will represent fractions using visual models and explore strategies like finding common denominators. The unit aims to develop students' conceptual understanding of fractions and decimals through exploration of essential questions.
This document discusses quadratic equations and complex numbers. It begins with an introduction to quadratic equations, their standard form, and examples of writing equations in standard form. It then covers complex numbers, defining them as numbers with real and imaginary parts, and explores the imaginary unit i and complex arithmetic operations. Finally, it discusses various methods for solving quadratic equations, such as factoring, completing the square, using the quadratic formula, and graphing.
Modeling and Simulation - An Interdisciplinary, Project-Based First Year CourseMark Somerville
This is a description of an interdisciplinary first year course at Olin College. The course uses a series of projects to introduce students to major concepts in modeling and simulation.
The document outlines strategies to improve mathematics results for Class X students. It analyzes factors responsible for poor mathematics performance, such as phobia of the subject, lack of practice, and faulty teaching methods. Steps for improvement include focusing on mental math skills, introducing short courses, encouraging more practice, and improving teacher accountability by analyzing results by teacher. Sample questions are provided covering topics like algebra, arithmetic progressions, and quadratic equations at varying difficulty levels. Common student mistakes and ways to emphasize key points for each topic are also discussed.
1. The document discusses multiplying decimal numbers, including multiplying decimals by whole numbers, decimals by decimals, and decimals by 10, 100, and 1,000.
2. Key rules covered are counting decimal places to determine the product's decimal placement and moving the decimal over when multiplying by powers of 10.
3. Examples provide step-by-step workings of multiplying decimals using partial products and placing the decimal point correctly in the final product.
The document is about algebra and graphing. It contains 7 lessons: negative numbers, finding points on a grid, graphing ordered pairs, problem-solving strategies using logical reasoning, functions, graphing functions, and a problem-solving investigation. Each lesson contains examples and practice problems to teach the concepts and standards covered in that lesson.
This document contains an overview of Chapter 10 from a geometry textbook. It covers the following topics across 10 lessons: solid figures, plane figures, problem-solving strategies like looking for patterns, lines/segments/rays, angles, and problem-solving investigations. The chapter introduces key concepts, provides examples, and aligns topics to state math standards. It aims to teach students to identify, describe, classify and solve problems involving various geometric shapes and their properties.
This document provides an overview and objectives of a modular workbook on decimal numbers. It introduces decimals and their place value, explaining how to read, write, name, compare, order, and round decimal numbers. Exercises are included to help learners evaluate their understanding of decimals.
This document contains information about geometry and measurement from a math textbook. It includes 7 lessons: on congruent figures, symmetry, perimeter, solving simpler problems, area, choosing a problem-solving strategy, and finding the area of complex figures. The lessons provide definitions, standards, examples and exercises related to these geometry and measurement topics.
This document provides an overview of Chapter 14 from a mathematics textbook. The chapter covers decimals, including tenths, hundredths, relating mixed numbers and decimals, problem-solving strategies involving making models, comparing and ordering decimals, and problem-solving investigations involving choosing the best strategy. It includes learning objectives, standards, examples and explanations for each of the 7 lessons covered in the chapter.
The document discusses simple interest calculations. It defines key terms like principal, rate, and time used to calculate simple interest using the formula I=PRT. It provides examples of simple interest problems, such as calculating interest earned on a $500 savings account with an annual interest rate of 2.5% over 18 months. The document also discusses using simple interest to calculate the total cost of a $7,000 car loan with 9% annual interest over 4 years.
Lesson guide gr. 3 chapter i -comprehension of whole numbers v1.0EDITHA HONRADEZ
Here are the answers to the matching activity:
A B
a 1) 10 bundles of 1000 straws a. 10 000
b 2) 7 bundles of 1000 straws and 1 bundle of 100 straws b. 7 500
This document provides an overview of a modular workbook on mastering fundamental math operations and integers. It contains two units: [1] Mastering basic fundamental operations with whole numbers, covering addition, subtraction, multiplication and division, and [2] Working with integers. The goal is for students to understand the concepts and master skills in performing the four operations on whole numbers and integers through lessons, exercises and word problems. It was created by education students and their advisers to serve as a supplementary reference for teachers and students.
The document is a curriculum guide for 4th grade mathematics that outlines the key concepts and standards for Unit 1 on factors, multiples, and arrays involving multiplication and division. The unit focuses on helping students understand relationships between multiplication and division and strategies for solving word problems using the four operations. It provides examples of how students can find factor pairs, determine if numbers are multiples, and identify prime and composite numbers between 1-100. The unit aims to build students' abstract reasoning skills and ability to model mathematical concepts.
The document provides an overview of the fourth grade mathematics curriculum for Unit 3 on multiplication and division. It includes the big ideas, essential questions, unit vocabulary, and Arizona state standards addressed. It also provides explanations and examples for key concepts around multiplicative comparisons, solving multi-step word problems using the four operations, and interpreting remainders. Students will learn to represent word problems algebraically and assess the reasonableness of their answers.
Lesson plan for x and dividing by 10, 100, 1000Angela Phillips
1) The lesson objective was to teach students to multiply whole numbers by 10, 100, and 1000 at levels 3 and 4. A card sorting activity was used as an entry task to review basic math skills.
2) Students used whiteboards to practice multiplying numbers by 10, 100, and 1000 with teacher demonstration. They showed their understanding using RAG cards.
3) An activity with correct and incorrect examples was completed, followed by demonstration on the interactive board. Students came up to show their work.
4) Students demonstrated understanding of multiples using whiteboards and did a poster activity in pairs to identify multiples of 10, 100, and 1000.
The document provides an overview of Unit 5 of the 4th grade mathematics curriculum for the Isaac School District. The unit focuses on addition, subtraction, and place value with large numbers up to 1,000,000. It includes 27 instructional sessions covering key concepts like using place value to represent numbers in expanded form and standard algorithms for addition and subtraction. Students are expected to fluently perform multi-digit calculations and explain their work by referring to place value. The unit vocabulary and Arizona state math standards addressed are also outlined.
1) The document provides a lesson plan for teaching trainees about shift registers. It includes information on the trainees, classroom, college, curriculum, content, methodology, and objectives of the lesson.
2) The lesson plan uses various teaching methods like lecture, classroom discussion, individual work, partner work and group work. Videos and handouts will also be used.
3) The lesson objectives are for trainees to understand what a shift register is, its types, how it works in serial in/serial out and serial in/parallel out modes, and design simple shift register circuits.
Slide Show Exploring The Numbers By Number Senses And NumerationHoneylay P. Royo
This document provides an overview of a teacher's guide workbook for exploring numbers through numeration for 4th grade students. It includes sections on place value, expanded form, comparing and ordering numbers, rounding numbers, and Roman numerals. The objectives are to help students develop skills and understanding of mathematical concepts related to everyday activities. The workbook is meant to engage students through clear lessons and activities while meeting curriculum requirements. The author acknowledges those who provided support and guidance in creating the workbook.
Higher modern studies extended responses inductionmrmarr
This document provides information about the Higher Modern Studies course in Scotland. It outlines the course content, which is divided into three subject areas: political issues in Scotland and the UK, social issues in the UK, and international issues focusing on poverty. It describes the skills developed in the course, such as writing extended responses and conclusions. Students must pass internal assessments, an added value assignment, and an external exam to complete the course successfully. The document provides examples of PEEL and PEEREEL paragraphs for analyzing issues, and explains how to structure extended response answers for the exam.
1. The document outlines a mathematics curriculum covering the real number system over 20 days. It focuses on helping students understand key concepts like rational and irrational numbers through hands-on activities and solving real-life problems.
2. The curriculum is divided into three stages: exploring real numbers through number lines and games, having students firmly grasp operations and order axioms through investigations, and applying the concepts to daily life problems.
3. Student understanding and performance will be assessed through problems they formulate involving real numbers and multiple solution strategies.
This document outlines a mathematics curriculum guide for 4th grade students in the Isaac School District. Specifically, it details a 22-session unit on size, shape, and symmetry that focuses on 2-D geometry and measurement. The unit aims to teach students about appropriate units of measurement, classifying geometric figures by their attributes, and relationships between geometric attributes such as perimeter and area. It provides learning objectives, essential questions, and examples for helping students learn concepts related to addition, subtraction, measurement, geometry, angles, and classifying shapes.
This document provides an overview of the fourth grade mathematics curriculum for Unit 6 on fractions and decimals. The unit focuses on problem solving strategies, representing fractions and decimals, and understanding that fractions represent parts of a whole. Key concepts covered include equivalent fractions, comparing fractions, and adding/subtracting fractions. Students will represent fractions using visual models and explore strategies like finding common denominators. The unit aims to develop students' conceptual understanding of fractions and decimals through exploration of essential questions.
This document discusses quadratic equations and complex numbers. It begins with an introduction to quadratic equations, their standard form, and examples of writing equations in standard form. It then covers complex numbers, defining them as numbers with real and imaginary parts, and explores the imaginary unit i and complex arithmetic operations. Finally, it discusses various methods for solving quadratic equations, such as factoring, completing the square, using the quadratic formula, and graphing.
Modeling and Simulation - An Interdisciplinary, Project-Based First Year CourseMark Somerville
This is a description of an interdisciplinary first year course at Olin College. The course uses a series of projects to introduce students to major concepts in modeling and simulation.
The document outlines strategies to improve mathematics results for Class X students. It analyzes factors responsible for poor mathematics performance, such as phobia of the subject, lack of practice, and faulty teaching methods. Steps for improvement include focusing on mental math skills, introducing short courses, encouraging more practice, and improving teacher accountability by analyzing results by teacher. Sample questions are provided covering topics like algebra, arithmetic progressions, and quadratic equations at varying difficulty levels. Common student mistakes and ways to emphasize key points for each topic are also discussed.
1. The document discusses multiplying decimal numbers, including multiplying decimals by whole numbers, decimals by decimals, and decimals by 10, 100, and 1,000.
2. Key rules covered are counting decimal places to determine the product's decimal placement and moving the decimal over when multiplying by powers of 10.
3. Examples provide step-by-step workings of multiplying decimals using partial products and placing the decimal point correctly in the final product.
The document is about algebra and graphing. It contains 7 lessons: negative numbers, finding points on a grid, graphing ordered pairs, problem-solving strategies using logical reasoning, functions, graphing functions, and a problem-solving investigation. Each lesson contains examples and practice problems to teach the concepts and standards covered in that lesson.
This document contains an overview of Chapter 10 from a geometry textbook. It covers the following topics across 10 lessons: solid figures, plane figures, problem-solving strategies like looking for patterns, lines/segments/rays, angles, and problem-solving investigations. The chapter introduces key concepts, provides examples, and aligns topics to state math standards. It aims to teach students to identify, describe, classify and solve problems involving various geometric shapes and their properties.
This document provides an overview and objectives of a modular workbook on decimal numbers. It introduces decimals and their place value, explaining how to read, write, name, compare, order, and round decimal numbers. Exercises are included to help learners evaluate their understanding of decimals.
This document contains information about geometry and measurement from a math textbook. It includes 7 lessons: on congruent figures, symmetry, perimeter, solving simpler problems, area, choosing a problem-solving strategy, and finding the area of complex figures. The lessons provide definitions, standards, examples and exercises related to these geometry and measurement topics.
This document provides an overview of Chapter 14 from a mathematics textbook. The chapter covers decimals, including tenths, hundredths, relating mixed numbers and decimals, problem-solving strategies involving making models, comparing and ordering decimals, and problem-solving investigations involving choosing the best strategy. It includes learning objectives, standards, examples and explanations for each of the 7 lessons covered in the chapter.
The document discusses simple interest calculations. It defines key terms like principal, rate, and time used to calculate simple interest using the formula I=PRT. It provides examples of simple interest problems, such as calculating interest earned on a $500 savings account with an annual interest rate of 2.5% over 18 months. The document also discusses using simple interest to calculate the total cost of a $7,000 car loan with 9% annual interest over 4 years.
The document discusses how to convert fractions to decimals and provides examples. It explains that to change a fraction to a decimal, we divide the numerator by the denominator, carrying the division to the desired number of decimal places. Some key points:
- Fractions can be expressed as decimals by dividing the numerator by the denominator
- To change a fraction to a decimal, divide the numerator by the denominator up to the desired number of decimal places
- Examples are provided such as 2/5 = 0.4
The document discusses the Dewey Decimal System, which was invented by Melvil Dewey to categorize books into 10 main subject groups represented by 3-digit numbers. It explains the general categories including 000s for general works, 100s for philosophy, 200s for religion, and so on up to 900s for history and geography. Nonfiction books are organized on shelves first by their Dewey Decimal number, which helps readers find books on the same subject near each other.
This document outlines lessons on dividing by one-digit numbers. Lesson 9-1 covers division with and without remainders. Lesson 9-2 discusses dividing multiples of 10, 100, and 1,000. Lesson 9-3 introduces the problem-solving strategy of guess and check. Lesson 9-4 is about estimating quotients. Each lesson provides examples and relates the content to California math standards.
The document is about algebra and graphing. It contains 12 lessons: negative numbers, finding points on a grid, graphing ordered pairs, problem-solving strategies using logical reasoning, functions, and graphing functions. The lessons include examples and practice problems related to these algebra and graphing topics.
Let's analyze the pattern to write a rule.
The cost increases by $2 each time.
Rule: Cost = $5 + 2x
To find the cost for 7 people:
Cost = $5 + 2(7) = $5 + 14 = $19
The cost for 8 people is $5 + 2(8) = $5 + 16 = $21
So the amount earned for 7 and 8 people is $19 and $21.
The answer is A.
Here are the steps to make a double bar graph from the given data:
1. Draw two sets of bars side by side on the graph. Label one set "Weekday" and the other "Weekend".
2. For each activity (sleeping, eating, etc.), draw the appropriate length bar for the weekday amounts underneath the "Weekday" label.
3. Do the same for the weekend amounts, drawing the bars underneath the "Weekend" label.
4. Be sure to label the axes and provide a title for the double bar graph.
Let me know if any part needs more explanation! Making graphs from data takes some practice but gets easier with experience.
1. The document introduces a module on solving quadratic equations for high school students.
2. It discusses different methods for solving quadratic equations, including factoring, completing the square, using the quadratic formula, and graphing.
3. It also covers complex numbers and how to solve equations containing radicals or that can be reduced to quadratic equations.
Broad explanation of quadratic equations for grade 10&11. Equations are explained step by step and examples are included and exercises are available for testing your understanding. Please provide feedback on our program so we can for your learning.
Here are the steps to solve the equations and graph them:
1. x2 + 4 = 0
x2 = -4
x = ±2i
Graph: The graph is the imaginary axis.
2. 2x2 + 18 = 0
2x2 = -18
x2 = -9
x = ±3i
Graph: The graph is the imaginary axis.
3. 2x2 + 14 = 0
2x2 = -14
x2 = -7
x = ±√7i
Graph: The graph is the imaginary axis.
4. 3x2 + 27 = 0
3x2 = -27
x2 = -
The document discusses the history and development of mathematics. It describes how mathematics has evolved from early counting and measurement tools to become more rigorous and abstract. It is now used widely in many fields like science, engineering, and medicine. The document also mentions some key people and developments in the history of mathematics like Euclid's Elements and innovations during the Renaissance.
This document provides an overview of the abacus and how it is used to perform mathematical calculations. It describes the basic components and functions of the abacus, including how beads are moved to represent numbers and perform addition. Different methods for addition using the abacus are explained through examples, such as simple addition, combined adding and taking off beads, and more complex scenarios involving multiple bead movements. The purpose is to familiarize readers with the traditional abacus tool and how it has been used for mathematics.
This document provides an overview of the traditional tool known as the abacus and how it is used to perform mathematical calculations. It describes the basic components and functions of an abacus, including how beads are arranged to represent numbers and how simple addition is performed by moving beads up and down. Various techniques for addition using an abacus are explained through diagrams and examples. The document aims to familiarize readers with the abacus and its contributions to the development of mathematics.
The document discusses the history and development of mathematics. It describes how mathematics has evolved from early counting and measurement tools to become more rigorous and abstract. It is now used widely in many fields like science, engineering and medicine. The document also mentions some key people and developments in the history of mathematics like Euclid's Elements and innovations during the Renaissance that accelerated mathematical research.
This document provides information and requirements for students completing a micro-lesson and school experience assignment for a 2011 education course. It outlines administrative details, the grievance procedure, course breakdown, assignment details, lesson designing guidelines, assessment criteria, and scheduling for micro-lessons. Students must complete a 10-minute micro-lesson and 1-week school experience to be assessed on their lesson planning, questioning strategies, use of media, and analysis of lesson introductions and conclusions.
This document summarizes a session for guiding school leaders on the NSW syllabus for the Australian curriculum: Mathematics K-10. It explores the structure of the new syllabus, focusing on elements like the aim, objectives, stage statements, and content organization. It discusses comparing the current and new syllabuses for Early Stage 1, Stage 1, and Stage 2. It also includes activities for teachers to analyze content from these stages. The document emphasizes understanding the implications of changes between syllabuses for teaching practice and professional learning.
This document provides guidance for teachers on identifying and teaching mathematically able pupils in primary schools. It addresses how to organize teaching within the school through setting, grouping with older pupils, or whole-class teaching. It also offers suggestions for adapting termly planning to include more challenging objectives and enrichment activities. Examples are provided for Years 2 and 6 plans. The document also provides potential resources for teachers, such as puzzles and problems in the second part of the document that can develop higher-order thinking skills. National Numeracy Strategy materials that support able pupils are also highlighted.
The document outlines the vision, mission, goals and objectives of a university. It aims to be a premier university offering academic programs and services that respond to the requirements of the Philippines and global economy. Its mission is to provide advanced education, professional, technological and vocational instruction in various fields. It also undertakes research, extension services and provides leadership in its areas of specialization. One of its colleges is committed to developing students' full potential and equipping them with knowledge, skills and attitudes in teacher education and related fields to effectively respond to changing times and global competitiveness.
This document discusses traditional versus modern approaches to mathematics curriculum, instruction, and assessment in Asian countries.
It outlines the traditional approaches, which focus on individual subjects taught from textbooks, teacher-centered instruction, and paper-based assessments. In comparison, modern approaches emphasize integrated subjects, student-centered active learning, and performance-based assessments.
The document also examines factors that influence student excellence in math, including curriculum, teacher preparation, parental support, and using multiple instructional methods to engage different learning styles. It provides examples of teaching addition of integers and direct variation to illustrate modern instructional approaches.
This document discusses four trends in differentiating instruction: technology, group work, learning centers, and hands-on learning through laboratories. For each trend, benefits are outlined such as increased engagement through technology and opportunities for social skill development with group work. Challenges are also noted, like the cost of keeping technology updated and the potential for distraction. The document concludes with an example kindergarten STEM lesson plan incorporating learning centers to teach double digit addition.
Workbook In Solving Algebraic Expressionsguestbf1e87
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Visual Presentaion in Solving Algebraic ExpressionsEdlyn Ortiz
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1. Learning to Solve DECIMAL NUMBERS (Modular Workbook for Grade VI) Student Researchers/ Authors: PAMN FAYE HAZEL M. VALIN RON ANGELO A. DRONA ASST. PROF. BEATRIZ P. RAYMUNDO Module Consultant MR. FOR – IAN V. SANDOVAL Module Adviser 7 8 1 04 3 6 90 5
3. A premier university in CALABARZON, offering academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly, Asian countries. Vision
4. The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technology and other related fields. It shall also undertake research and extension services, and provide a progressive leadership in its areas of specialization. Mission
5. In pursuit of college mission/vision the college of education is committed to develop the full potential of the individuals and equip them with knowledge, skills and attitudes in teacher education allied fields effectively responds to the increasing demands, challenge and opportunities of changing time for global competitiveness. Goals of College of Education
6. Objectives of Bachelor of Elementary Education 1. Produce graduates who can demonstrate and practice the professional and ethical requirements for the Bachelor of Elementary Education such as: 2. Acquire basic and major trainings in Bachelor of Elementary Education focusing on General Education and Pre - School Education. 3. Produce mentors who are knowledgeable and skilled in teaching pre - school learners and elementary grades and with desirable values and attitudes or efficiency and effectiveness. 4. Conduct research and development in teacher education and other related fields. 5. Extend services and other related activities for the advancement of community life.
8. This Teacher’s Guide Module entitled “Learning to Solve Decimal Numbers (Modular Workbook for Grade VI)” is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Secondary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies.
9. The students are provided with guidance and assistance of selected faculty members of the university through the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kind of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation of instructional materials.
10. The output of the group’s effort may serve as an educational research of the institution in providing effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students.
11. FOR-IAN V. SANDOVAL Computer Instructor / Adviser Educational Technology 2 BEATRIZ P. RAYMUNDO Assistant Professor II / Consultant LYDIA R. CHAVEZ Dean College of Education
13. This instructional modular workbook entitled “Learning to Solve Decimal Numbers (Modular Workbook for Grade VI)”, which geared toward the objective of making quality education available to all and offers you a very interesting and helpful friend in your journey to the world of decimal numbers. Dear Learners,
14. This modular workbook offers you many experiences in learning decimal numbers. This time, you will study how to read, write, and name decimal numbers and how to compare order and round off decimal numbers. Of course you will also express the equivalent fractions and decimals.
15. You will also experience the four (4) fundamental operations (Addition, Subtraction, Multiplication and Division) dealing with decimal numbers. Lastly, you will also solve more difficult problems involving the four (4) fundamental operations using decimal numbers. Learning decimal content is much more skillful in drilling with the application of FUN WITH MATH which designed to achieve with outmost skill and convenience.
16. The authors feel that you can benefit much from this modular workbook if you follow the direction carefully. Be mindful as you lead yourselves to challenge the situation and circumstances and as you faces in every living as well as for the near future. If you do these, you will realize that indeed this modular workbook can be a very interesting and helpful companion. The Authors
18. We would like to express our sincerest gratitude for the following whom in are ways or another help us making this modular workbook become possible: To Prof. Corazon N. San Agustin , for her kindness and understanding to this modular workbook.
19. To Mr. For – Ian V. Sandoval , our instructor and adviser in Educational Technology 2, for giving sufficient technical trainings, suggestions, constructive criticism and unending support in our every needs. To Assistant Professor Beatriz P. Raymundo , our Module Consultant, for making her available most of the time for comments, suggestions and revision of the modular workbook.
20. To Professor Lydia R. Chavez , our Dean, College of Education, for inspiring advises and encouragement. To our classmates and friends for their never ending support.
21. To our beloved families , for unconditional love, emotional, spiritual and financial support all the way to used and for the filling up our duties in our home. And most importantly to Almighty God , for rendering abilities, wisdom, good health, strength, courage, source of enlightenment and inspiration to pursue doing this piece of material. The Authors
24. UNIT I Decimal Numbers Lesson 1 What is Decimal? Lesson 2 Reading and Writing Decimal Numbers Lesson 3 Reading and Writing Mixed Decimal Numbers Lesson 4 Reading and Writing Decimal Numbers Used in Technical and Science Work Lesson 5 Place Value Lesson 6 Comparing Decimal Numbers Lesson 7 Ordering Decimal Numbers Lesson 8 How to Round Decimal Numbers? Lesson 9 The Self-Replicating Gene
25. UNIT II Equivalent Fractions and Decimals Lesson 10 Expressing Fractions to Decimals Lesson 11 Expressing Mixed Fractional Numbers to Mixed Decimals Lesson 12 Expressing Decimals to Fractions Lesson 13 Expressing Mixed Decimals Numbers to Mixed Numbers (Fractions)
26. UNIT III Addition and Subtraction of Decimal Numbers Lesson 14 Meaning of Addition and Subtraction of Decimal Numbers Lesson 15 Addition and Subtraction of Decimal Numbers without Regrouping Lesson 16 Addition and Subtraction of Decimal Numbers with Regrouping Lesson 17 Adding and Subtracting Mixed Decimals Lesson 18 Estimating Sum and Difference of Whole Numbers and Decimals Lesson 19 Minuend with Two Zeros Lesson 20 Problem Solving Involving Addition and Subtraction of Decimal Numbers
27. UNIT IV Multiplication of Decimals Lesson 21 Meaning of Multiplication of Decimals Lesson 22 Multiplying Decimals Lesson 23 Multiplying Mixed Decimals by Whole Numbers Lesson 24 Multiplication of Mixed Decimals by Whole Numbers Lesson 25 Multiplying Decimals by 10, 100 and 1000 Lesson 26 Estimating Products of Decimal Numbers Lesson 27 Problem Solving Involving Multiplication of Decimal Numbers
28. UNIT V Division of Decimal Numbers Lesson 28 Meaning of Division of Decimals Lesson 29 Dividing Decimals by Whole Numbers Lesson 30 Dividing Mixed Decimals by Whole Numbers Lesson 31 Dividing Whole Numbers by Decimals Lesson 32 Dividing Whole Numbers by Mixed Decimals Lesson 33 Dividing Decimals by Decimals Lesson 34 Dividing Mixed Decimals by Mixed Decimals
31. OVERVIEW OF THE MODULAR WORKBOOK In this modular workbook, you will understand the concept of the language of decimal numbers. This modular workbook, will help you to read, write, and name decimal numbers for a given models, standard, mixed and technical and science work form. It provides the knowledge about place value, with the aid of a place - value chart. It also provides information on how to compare and order decimal numbers and also how to round off decimal numbers. This module will provide you a more difficult work in mathematics. Exercises will help the learners evaluate themselves to understand decimal numbers.
32. OBJECTIVES OF THE MODULAR WORKBOOK After completing this modular workbook, you expected to: 1. Know the language of decimal numbers. 2. Read, write, and name decimal numbers in different forms. 3. Read and write decimal numbers with the aids of place - value chart. 4. Compare and order decimal numbers. 5. Rounding off decimal numbers by following its rule.
33.
34. One important feature of our number system is the decimal. It involved many computational operations. It is very useful in the measurement of very thin sheets and in the computation involving in exact amount. But what is decimal? Look at the following examples:
35.
36. From the example given above, a “ decimal ” may be defined as a fraction whose denominator is in the power of 10.
37. Numbers in the power of 10 are 10, 100, 1000, 1000, etc. The dot before a digit in a decimal is called “ decimal point ” which is an indicator that the number is a decimal. The place on the position occupied by a digit at the right of the decimal point is called a “ decimal place ”.
38. I. Give the meaning and explain the use of the following. 1. What are decimals? 2. What is decimal point? 3. What is decimal place? 4. Give some examples of decimal numbers. 1 Worksheet
43. How to read and write decimals or decimal numbers? A decimal is read and write according to the number of decimal place it has. Here are the rules in reading and writing decimal numbers.
44. RULE I. A decimal of one decimal place is to be read and to be written as tenth. .4 is read as “4 tenths” and is to be written as “four tenths”; 4/10 .2 is read as “2 tenths” and is to be written as “two tenths”. 2/10
45. RULE II. A decimal of two decimal places is to be read and to be written as hundredth. .35 is read as “35 hundredths” and is to be written as “thirty – five hundredths”; 35/100 .43 is read as “43 hundredths” and is to be written as “forty – three hundredths”.43/100
46. RULE III. A decimal of three decimal places is to be read and written as thousandth. .261 is read as “261 thousandths” and is to be written as “two hundred sixty – one thousandths”; 261/1000 .578 is read as “578 thousandths” and is to be written as “five hundred seventy – eight thousandths”.578/1000
47. RULE IV. A decimal of four decimal places is to be read and to be written as ten thousandth. .4917 is read as “4917 ten thousandths” and is to be written as “four thousand, nine hundred seventeen ten thousandths”; 4917/10,000 .5087 is read as “5087 ten thousandths” and is to be written as “five thousand eighty - seven ten thousandths”.5078/10,000
48. A decimal is read and written like an integer with the name of the order of the right most digits added. tenths hundredths thousandths ten thousandths hundred thousandths Millionths ten millionths hundred millionths billionths ten billionths hundred billionths trillionths 0 . 4 3 5 7 8 9 6 1 2 5 3 4
49. Note: the names of the order of the different decimal places. Quadrillionths Pentillionths Hexillionths Heptillionths Octillionths Nonillionths Decillionths Undecillionths Dodecillionths Tridecillionths… SEQUENCES
50.
51. 0.43578 Read as forty-three thousand, five hundred seventy-eight hundred thousandths. 0.435789 Read as four hundred thirty-five thousand, seven hundred eighty nine millionths. 0.4357896 Read as four million, three hundred fifty-seven thousand, eight hundred ninety-six ten millionths.
52. 0.43578961 Read as forty three million, five hundred seventy-eight thousand, nine hundred sixty-one hundred millionths. 0.435789612Read as four hundred thirty-five million, seven hundred eighty nine thousand, six hundred twelve billionths. 0.4357896125 Read as four billion, three hundred fifty seven million, eight hundred ninety six thousand, one hundred twenty five ten billionths.
53. 0.43578961253 Read as forty-three billion, five hundred seventy eight million, nine hundred sixty-one thousand, two hundred fifty three hundred billionths. 0.435789612534 Read as four hundred thirty-five billion, seven hundred eighty-nine million, six hundred twelve thousand, five hundred thirty-four trillionths.
54. I. Write each decimal numbers in words on the space provided. 1. 0.167213143____________________________ ______________________________________ 2. 0.52541876_____________________________ ______________________________________ 3. 0.263411859____________________________ ______________________________________ 4. 0.984562910____________________________ ______________________________________ 5. 0.439621512____________________________ _______________________________________ 2 Worksheet
55. II. Write the decimal number in standard form. 1. Nine tenths ______________________________________________ 2. Four hundredths ______________________________________________ 3. Two thousand, two hundred and two hundred thousandths ____________________________________________ 4. Four hundred seventy – six millionths ________________________________________________ 5. Forty thousand, one hundred forty – one millionths ________________________________________________
56.
57. Look at the following examples: a. 5.8 is read as “5 and 8 tenths” and is to be written as “five and eight tenths” b. 26.38 is read as “26 and 38 hundredths” and is to be written as “twenty – six and thirty – eight hundredths” c. 49.246 is read as “49 and 246 thousandths” and is to be written as “forty – nine and two hundred forty – six thousandths” d. 348.578 is read as “348 and 578 thousandths” and is to be written as “three hundred forty – eight and five hundred seventy – eight thousandths”
58. It is seen that the following rule has been followed in the above examples. RULE: In reading a mixed decimal numbers, read the integral part as usual “and” in place of the decimal point, the decimal point is read as usual also.
59.
60. II. Write decimal numbers for each of the following sentences: 1. Sixteen and sixteen hundredths _____________________________________________ 2.Two and one ten – thousandths _____________________________________________ 3.Ten thousand four and fourteen ten – thousandths _____________________________________________ 4. Ninety – nine billion and eight tenths _____________________________________________ 5. Twelve hundred two and seven millionths _____________________________________________
61. 6. Ninety – nine and nine hundred nine thousand, nine millionths_________________________________ 7. Five billion and sixty – five hundredths ______________________________________________ 8. Three billion, six thousand and three thousand six millionths _____________________________________ 9. Seventy – one million, one hundred and fifty – five hundred thousandths ______________________________________________ 10. Two hundred two million, two thousand, two and two hundred two thousand two millionths ______________________________________________
62.
63. This method of reading decimals and mixed decimals is often used by people engaged in technical and science work. But this can be used by lay people especially if the part of the number has many digits. Observe the following examples:
64.
65. The rule followed in the above examples is as follows: To read decimals or mixed decimal numbers used in technical and science work or when the numbers of digits in the decimal is too many, just mention the values of the digits and separate the integral part by saying “point” instead of “and”. RULE:
71. 6. three point seven six nine ______________________________________________ 7. two one seven point one five ____________________________________________ 8. point zero eight zero zero zero ___________________________________________ 9. nine point zero four zero ______________________________________________ 10. two point six seven two five ____________________________________________ 11. zero point nine eight nine ______________________________________________
72. 12. zero point five two six eight two nine ____________________________________________ 13. five six zero point four zero one eight ____________________________________________ 14. one point one nine one eight ____________________________________________ 15. eight point five four three ____________________________________________
73.
74. PLACE VALUE CHART Place Value Names M I L L I O N S H T U H N O D U R S E A D N D S T T E H N O U S A N D S T H O U S A N D S H U N D R E D S T E N S O N E S T E N T H S H U N D R E D T H S T H O U S A N T H S T T E H N O U S A N T H S H T U H N O D U R S E A D N T H S M I L L I O N T H S Numerals 1 9 4 6 3 4 1 . 1 3 4 5 8 7 × × × × × × × . × × × × × × 10 6 10 5 10 4 10 3 10 2 10 1 1/10 0 1/10 1 1/10 2 1/10 3 1/10 4 1/10 5 1/10 6
75. What relationship exists in the diagram? What does the 1 in the tenths place mean? What does the 3 in the hundreds place represent? How about the 3 in the hundredths place?
78. II. Answer the following. 1. In 246.819, what number is in each of the following place value? Example: __ 6 __ a. ones _ 246 _ c. hundreds _ 46 __ b. tens _ _.8 __ d. tenths _ .81 __ e. hundredths __ .819 _ f. thousandths 2. In 65.42387, tell what number is in each of the following places. _____a. tenths _____d. ten–thousandths _____b. hundredths _____e. hundred – thousandths _____c. thousandths _____f. ones _____g. tens
79. 3. In 9023.45867, tell what number is in each of the following places. _____a. ones _____e. hundredths _____b. tens _____f. thousandths _____c. tenths _____g. thousands _____d. hundreds _____h. ten – thousandths _____i. hundred–thousandths _____j. millionths
80.
81. If there are two decimal numbers we can compare them. One number is either greater than (>), less than (<) or equal to (=) the other number.
82. A decimal number is just a fractional number. Comparing 0.7 and 0.07 is clearer if we compared 7/10 to 7/100. The fraction 7/10 is equivalent to 70/100 which is clearly larger than 7/1000.
83. Therefore, when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal, compare the hundredths, then the thousandths, etc. Until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.
84. Worksheet I. Fill the frame with the correct sign (>) “less than”, (=) “equal to”, or (>) “greater than” between two given numbers. Example: 0.9 = 9/10 0.90 = 10/100 = 6
85. b. 9.004 0.040 f. 51.6 51.59 c. 20.80533 20.06 g. 50.470 50.469 d. 0.070 0.07 h. 0.90 0.9 e. 0.540 0.054 i. 0.003 0.03 j. 0.8000 0.080
86.
87. Numbers have an order or arrangement. The number two is between one and three. Three or more numbers can be placed in order. A number may come before the other numbers or it may come between them or after them.
88.
89. REMEMBER: The order may be ascending (getting larger in value) or descending (becoming smaller in value).
90. I. Write in order from ascending order and descending order by completing the table. 7 Worksheet Ascending Order Descending Order 1. 2.0342; 2.3042; 2.3104 Example: 2.0342 2.3042 2.3104 2.3104 2.3042 2.0342 2. 5; 5.012; 5.1; .502 3. 0.6; 0.6065; 0.6059;0.6061
92. FUN WITH MATH!!! Arrange the given decimal numbers from the least to greatest and you will find a famous quotation by Shakespeare.
93. Shakespeare (least) 7.301 All 8.043 climb 7.8 except 7.310 ambitious 8.88 or 7.84 those 9.100 of 7.911 which 10.5 mankind 7.33 are 8.43 up 8.513 upward 7.352 lawful 8.901 the 9.003 miseries
94. All ___ _______ ________ ________ ________ ________ 7.301 _______ ________ ________ ________ ________ _______ ________ ________ ________ ________ ________ _______ ________ ________ ________ ________ ________ _______ ________ ________ _______ ________ ________ . - Shakespeare II. Answer the following. a. The list below is the memory recall time of 5 personal computers. Which model has the fastest memory recall?
96. b. Arrange the memory recall time of computers in number 1 in ascending order. Answer: __________________________________________________________________________________ c. A carpenter uses different sizes of drill bits in boring holes. The sizes are in fractional form and their equivalent decimals. Arrange the decimal equivalent in descending order. 1/16 = 0.0625 ¼ = 0.25 1/8 = 0.125 5/6 = 0.3125
98. e. Which has the greatest decimal equivalent the drill bits in item C? Answer: ________________________________________ ________________________________________
99.
100. To round decimal numbers means to drop off the digits to the right of the place-value indicated and replace them by zeros. The accuracy of the place-value needed must be stated and it depends on the purpose for which rounding is done. We give rounded decimal numbers when we do not need the exact value or number. Instead, we are after an estimated value or measure that will serve our purpose. These are many instances in daily life when rounded numbers are what we need to use.
101. How well do you remember in rounding whole numbers? Study the example below. Round to the nearest 4935 ten 4940 hundred 4900 thousand 5000
102.
103.
104. Example: Round off 78.4651 to the nearest hundredths. 7 8 . 4 6 5 1 = 78.47 Dropping digit Decimal number to be rounded off Examples: Round the following. a. 5.767 to the nearest tenths = 5.8 Since the digit to the right of 7 is 6.
105. b. 65.499 to the nearest hundredths = 65.50 Since the digit to the right of 9 is 9. c. 896.4321 to the nearest thousandths = 896.432 Since the digit to the right of 2 is 1. d. 32.28 to the nearest tenths = 32.3 Since the digit to the right of 2 is 8 e. 1000.756 to the nearest hundredths = 1000.80 Since the digit to the right of 5 is 6 f. 56.58691 to the nearest thousandths = 56.5870 Since the digit to the right of 6 is 9
106.
107. 2. 3.097591 to the nearest: a. ones _______________________ b. tenths _______________________ c. hundredths _______________________ d. thousandths _______________________ e. ten-thousandths _______________________ 3. 6.152292 to the nearest: a. ones ______________________ b. tenths ______________________ c. hundredths ______________________ d. thousandths ______________________ e. ten-thousandths ______________________
108. 4. 10.01856 to the nearest: a. ones ____________________ b. tenths ____________________ c. hundredths ____________________ d. thousandths ____________________ e. ten-thousandths ____________________ 5. 123.831408 to the nearest: a. ones ____________________ b. tenths ____________________ c. hundredths ____________________ d. thousandths ____________________ e. ten-thousandths ____________________
109.
110.
111. IV. Answer the following with TRUE or FALSE. ________________ 1. 0.32 rounded to the nearest tenths is 0.3. ________________ 2. 0.084 rounded to the nearest hundredths is 0.09. ________________3. 0.483 rounded to the nearest thousandths is 0.048. ________________4. 0.075 rounded to the nearest hundredths is 0.06. ________________5. 0.375 rounded to the nearest tenths is 0.4.
112. V. Round each of the following by completing the tables. Number 1 serves as an example. Decimals Round to the nearest Tenths Hundredths Thousandths Ten Thousandths Example: 1. 0.89432 0.9 0.89 0.894 0.8943 2. 5.09998 3. 2.96425 4. 5.2358 5. 5.39485 6. 0.86302 7. 28154 8. 42356
114. FUN WITH MATH!!! I. Find the answer by rounding off to the nearest place value indicated. Draw a line to the correct rounded number. Each line will pass through a letter. Write the letter next to the rounded number. ONES 1.6 ● ● 1.63 __________ 5.38 ● ● 3.4 __________ 52.52 ● ● 2 __________ TENTHS 0.45 ● ● 3.433 __________ 3.421 ● ● 53 __________ 12.76 ● ● 0.35 __________ 88.55 ● ● 5 __________ HUNDREDTHS 0.345 ● ● 12.8 __________ 1.634 ● ● 0.044 __________ 13.479 ● ● 0.5 __________ 201.045 ● ● 11.68 __________ 11.677 ● ● 16.778 __________ THOUSANDTHS 0.0437 ● ● 88.6 __________ 3.4325 ● ● 105.312 __________ 16.7777 ● ● 13.48 __________ 23.40092 ● ● 23.401 __________ 105.31238 ● ● 201.05 __________ T V E H W G E N T O O L H M S E T What happened to the man who stole the calendar?
115. Lesson 9 FACTS AND FIGURES (The self-replicating Gene) or centuries, generations of scientists in Numerica had been working relentlessly on what had been dubbed as The Genetic Enterprise. It was founded for the purpose of controlling a runaway gene that had beleaguered the Decimal citizens of Numerica for millennia: the repeating decimal gene. F 4 ___ 44
116. Their history revealed that it all began when a woman named Four (4) united with a man named Forty-Four (44) positioned as 4/44. Their first offspring, a fraction, came out all right, and they named her Three-Thirty-thirds (3/33). Such a beautiful fraction she was. But their second child came out with the first problematic replicating gene--- the boy looked different and came with a long tail: 0.0909090909… Arbitrarily multiplying both sides of the equation by any power of ten does not change the value of the decimal nor does it destroy the balance of the equation. This is because of the Multiplication Property of Equality of the Real Numbers.
117. That wasn’t the end of it. Every week, the boy’s tail added a new segment of 09, and it just never ended! It wasn’t so much the unusual appearance of the boy that worried every one, as the difficulty of naming him. Point-Zero-Nine-Zero-Nine-Zero-Nine- Zero -Nine-Zero-Nine, going on forever, was just too long a name! There were many others in the community whose tails also continuously and regularly increased. Despite their peculiar form, though, those trouble with the repeating gene were never shunned, were treated equally with love, respect, and total acceptance. Still, the continually growing tail proved cumbersome for the Decimals, and they prayed to be changed to regular forms.
118. Arbitrarily multiplying both sides of the equation by any power of ten does not change the value of the decimal nor does it destroy the balance of the equation. This is because of the Multiplication Property of Equality of the Real Numbers. Remember
119. One fateful day, the newspaper headlines screamed: “The Genetic Enterprise: Finally Success!” All of Numerica was thrilled! At the state conference the next day, every citizen was present, especially those with continuously growing tails. “ And now, I must ask for a volunteer,” said Doctor One Half (½), head scientist of the project, over the microphone. Immediately, 0.33333…, friend of Point-Zero-Nine-Zero-Nine…, was up the stage. “ O-Point-Three-Three-Three…” One Half began, “do not be afraid. Go into that glass capsule to your left, for we must first clone you.”
120. The crowd was aghast. One Half reassured every one immediately. “Do not worry, it is only temporary.” When 0.33333… came out, his clone came out from the other capsule. The doctor spoke again. “I will run you all through the process as we proceed. First, we shall designate the clone as Ex = 0.33333… “ Now, 0.33333…, go back into the capsule---we will introduce a new gene into you. This gene is called Tenn (10), and this will change your appearance, so that we will temporarily call you Tennexx (10x). Do not be alarmed!” One Half added quickly at every one’s reaction.
121. When 0.33333… stepped out of the capsule, he had become 3.33333… 10x = 10 x 0.3333… = 3.3333… 10x = 3.3333… The crowd was mesmerized. “ Tennexx, go back into the capsule. Exx, go into the other capsule. This time, we shall remove the repeating gene from Tennexx---by taking out Exx!” 10x – x = 3.3333… - 0.333… 9x = 3 Now, Tennex come out! Let us all see what you have become…” One Half said dramatically.
122. The purpose of assigning a variable and multiplying both sides of the equation by 10 is to come up with whole numbers on both sides of the equation (on one side, with the variable, and on the other side of the equation, with just an integer). From this form we obtain a fraction equal to the original decimal. Note when finally making a subtraction, the digits in the decimal parts MUST be the same in order for the difference to be an integer. FACT BYTES
123. When Tennex came out, he had become 1/3. 9x = 3 x = 3/9 or 1/3 The applause was thunderous! 1/3 spoke on the microphone, tears of joy poring down his cheeks. “Once! Was Zero-point-Three- -Three-Three-Three-Three… now I am One-Third. Thank you, Doctor One Half!” he said.
124. LESSON LEARNED In the article, we see that there is still hope for repeating Decimal genes like Point O Nine O Nine O Nine and O Point Three-Three-Three. It is all about representing them using any variable, say, x, and taking away their never-ending tail. Any repeating decimal represents a geometric series 0.3333… is 0.3 + 0.03+ 0.03 +… The common ratio is 0.1, that is, the next term is obtained by multiplying the previous term by 0.1. The formula S= a1/1-r may be used if (r) < 1. S = a1/1-r S = 0.3/1-0.1 = 0.3/0.9 or 1/3 FACT BYTES 1 __ 3
125. PROBLEM BUSTER A DIFFERENT GENE May I have another Volunteer? Ah, yes. 0.83333 Do you think we can change 0.833333...in exactly the same way as what we did to 0.33333…? Notice that in this case, the numeral 8 does not repeat. If we introduced 10 like we did to0.33333…, by multip- lying 0.833333…by 10, 0.833333…will become 8.33333… Following the process, we have, 10x –x = 8.33333… - 0.833333… which is the same as 9x =7.5 where the right side of the equation is not an integer! What are we to do? 1 / 2 1 / 2
126.
127.
128. II. Change the following to fraction in simplest form. 3. 0.77777… 4. 0.9166666… 5. 0.9545454… 6. 0.891891891… 7. 0.153846153846153846… 8. 0.9692307692307692307…
131. After completing this Unit, you are expected to: 1. Transform fraction/mixed fractional numbers to decimals/mixed decimal. 2. Change decimal/mixed decimal to fraction /mixed numbers (fractions). 3. Follow the rules in expressing equivalent fractions and decimals. OBJECTIVES OF THE MODULAR WORKBOOK
132.
133. Decimals are a type of fractional number. Let us now study how to write fractions to decimal form.
134. We will apply the principle of equality of fractions that is, if a/b =c/d then ad = bc .
135. Example 1: Write the fraction 2/5 as a tenth decimal. In this case we are interested to find the value of x such that 2/5=x/10. Since the two fractions name the same rational number, we can proceed: 5x = 2(10) – applying equality principle 5x = 20 x = 20/5 or 4 Hence, 2/5 = 4/10 = 0.4
136. Example 2: Write the fraction 3 as a hundredth decimal. We are 4 interested to find the value of x such 3 that = x . 4 100 Applying the principle of equality we have 4x = 3(100) 4x = 300 x = 75 Hence, ¾ = 75/100 = 0.75
137. On the other hand, fractions can also be expressed as a decimal without using the equality principle. Instead we have to think of a fraction as a quotient of two integers that is a/b=a = a b. Example 3: Express 2/5 as a decimal. Expressing 2/5 as quotient of 2 and 5 we have 2/5 = 0.4
138. RULE To change a fraction to decimal, divide the numerator by the denominator up to the desired number of decimal places.
139. I. Give the meaning and explain the use of the following 1. How to change fractions to decimal? 2. What are the rules in changing fractions to decimals? 3. What is decimal? 4. Give some examples of fractions to decimals. 10 Worksheet
140.
141.
142.
143. FUN WITH MATH!!! It was very fortunate that Sophie Germain , a woman mathematician was born at a time when people looked down on women. In 1776, women then were not allowed to study formal, higher level mathematics. Thus, this persistent woman reads books of famous mathematicians and studied on her own. Aware of her situation, she shared her theorems and mathematical formulae to other mathematicians and teachers through correspondence using a pseudonym.
144. Can you guess the pseudonym that she used? Yes, you can. Simply follow the instruction.
145. Select the right answer to the equation below. Write the letter of the correct answer on the respective number decode pseudonym that she used. You may use the letter twice. ______ ______ ______ ______ (1) (2) (3) (4) ______ ______ ______ ______ (5) (6) (7) (8) ______ ______ ______ (9) (10) (11) ______ ______ ______ ______ (12) (13) (14) (15)
146. Answers: A = 0.25 F = 0.65 K = 0.512 P = 0.27 B = 0.15 G = 0.28 L = 0.125 Q = 0.006 C = 0.6 H = 0.77 M = 0.333… R = 0.72 D = 0.54 I = 0.24 N = 0.40 S = 0.6 E = 0.76 J = 0.532 O = 0.75 T = 0.4113 U = 0.325
147.
148. How can we change mixed fractional numbers to mixed decimals? See the following examples. 4 1/2 = 4.5 c. 21 1/8 = 21.125 14 3/8 = 14.375 d. 32 3/7 = 32.4285
149. From the examples given above, it can be seen that the rule in changing a mixed fractional number to mixed decimal is:
150. RULE To change a mixed fractional number to a mixed decimal, change the fraction to decimal up to the number of decimal places desired and then annex it to the integral part.
156. As what we have learned earlier, decimals are common fractions written in different way.
157. There are certain instances when it becomes necessary to change decimal into fraction. Hence, it is necessary to acquire skill in changing a decimal to faction. Now we will study how to write decimals in fractions.
158. Example 1: Write 0.5 in a faction form. 5 or 1 10 2 0.5 = 5(1/10) Example 2: Write 0.72 in a fraction form. 0.72 = 7(1/10) + 2(1/100) 18 25 = 72/100 or 18 25
159. On the other hand, a simple way of expressing decimal to factions is possible without writing the numeral in expanded form. What we need is only to determine the place value of the last digit as we read if from left to right.
160. Example 1: Write 0.5 in a faction form. Notice that the digit 5 is in the tenth place, we can write immediately: 0.5 = or 1 2 __ 5 __ 1000
161. The digit 2 is in the thousandths place so we write: 0.072 = 72/1000 = 9/125
162.
163. Identifying Equivalent Decimals and Fractions Decimals are a type of fractional number. The decimal 0.5 represents the fraction 5/10. The decimal 0.25 represents the fraction 25/100. Decimal fractions always have a denominator based on a power of 10. We know that 5/10 is equivalent to 1/2 since 1/2 times 5/5 is 5/10. Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, etc.
164. It can be seen from the examples above the rule in changing a decimal to fraction is as follows:
165. RULE To change a decimal number to a fraction, discard the decimal point and the zeros at the left of the left-most non-zero digit and write the remaining digits over the indicated denominator and reduce the resulting fraction to its lowest terms. (The number of zeros in the denominator is equal to the number of decimal places in the decimal number.
168. FUN WITH MATH!!! How can you make a tall man short? To find the answer, change the following decimal number to lowest factional form. Each time an answer is given in the code, write the letter for that exercise.
169. 1. 0.6 = A 6. 0.24 = _______ O 2. 0.5 = __ _____ B 7. 0.125 = _______ H 3. 0.7 = _______ N 8. 0.55 = _______ L 4. 0.4 = _______ I 9. 0.3 = _______ W 5. 0.75 = _______ O 10. 0.048 = _______ R 11. 0.25 = ______ O 12. 0.75 = _____ L 13. 0.2 = _____ E 14. 0.225 =______ O 15. 0.24 = _____ Y 16. 0.8 = _____ S 17. 0.5688=______ R
177. OVERVIEW OF THE MODULAR WORKBOOK This modular workbook provides you greater understanding in all aspects of addition and subtraction of decimal numbers. It enables you to perform the operation correctly and critically. It includes all the needed information about the addition and subtraction of decimal numbers, its terminologists to remember, how to add and how to subtract decimals with or without regrouping, how to estimate sum and differences, and subtracting decimal numbers involving zeros in minuends. This modular work will help you to enhance your minds and ability in answering problems deeper understanding and analysis regarding all aspects of adding and subtracting decimal numbers.
178. OBJECTIVES OF THE MODULAR WORKBOOK After completing this Unit, you are expected to: 1. Familiarize the language in addition and subtraction. 2. Learn how to add and subtract decimal numbers with or without regrouping. 3. Know how to check the answers. 4. Estimate the sum and differences and how it is done. 5. Know how to subtract decimal numbers with zeros in the minuend. 6. Develop speed in adding and subtracting decimal numbers. 7. Analyze problems critically.
179.
180. Addition is the process of combining together two or more decimal numbers. It is putting together two groups or sets of thing or people.
181. Example: 0.5 + 0.3 = 0.8 Addends Sum or Total Addends are the decimal numbers that are added. Sum is the answer in addition. The symbol used for addition is the plus sign (+).
182. The process of taking one number or quantity from another is called Subtraction . It is undoing process or inverse operation of addition. It is an operation of taking away a part of a set or group of things or people. Note: Decimal points is arrange in one column like in addition of decimals.
183.
184. Worksheet I. Give the meaning and explain the use of the following. 1. What is addition? 2. What is subtraction? 3. What are the parts of addition? 4. What are the parts of subtraction? 14
185. 1. Addition ______________________________________________ 2 Subtraction ______________________________________________ 3. Parts of addition ______________________________________________ 4. Parts of subtraction ______________________________________________
186. II. Identify the following decimal numbers whether it is addends, sum, minuend, subtrahend or difference. Put an if addends, if sum, if minuend, if subtrahend and if difference. 1. 0.9 _______ + 0.8 _______ 1.7 _______ 2. 2.24 _______ + 2.38 _______ 4.62 _______ 3. 12.85 _______ - 0. 87 _______ 11.98 _______ 4. 7.602 _______ - 2.664 _______ 4.938 _______
188. III. Answer the following by completing the letter in each box which indicate the parts of addition and subtraction of decimals. 1. It is the numbers that are added. 2. The answer in addition. 3. It is the process of combining together two or more numbers.
189. 4. Sign used for addition. 5. It is undoing process or inverse operation of addition. 6. Sign used for subtraction. 7. It is the answer in subtraction.
190. 8. It is in the top place and the bigger number in subtraction. 9. It is the smaller number in subtraction. 10. Subtraction is an operation of _________ a part of a set or group of things or people.
191.
192. Add the following decimals: 28. 143 and 11.721. If you added them this way, you are right. 28. 143 + 11. 721 39. 864 Let us add the decimals by following these steps.
193. STEP 1 STEP 2 Add the thousandths place 3+ 1 = 4 28. 143 + 11. 721 4 Add the hundredths place 4 + 2 = 6 28. 143 + 11. 721 64
194. STEP 3 STEP 4 Add the tenths place 7 + 1 = 8 28. 143 + 11. 721 864 Add the following up to the ones. 8 + 1 = 9 28. 143 + 11. 721 9. 864
195. STEP 5 Add the following up to the tens. 2 + 1 = 3 28. 143 + 11. 721 39. 864
196. Now subtract 39. 864 to 11. 721. 39. 864 minuend - 11. 721 subtrahend 28. 143 difference
198. If you subtract the difference from minuend and the answer is subtrahend the answer is correct. Also, adding the difference and subtrahend will the result to the minuend: it is also correct.
202. FUN WITH MATH!!! Add and subtract the following to find the mystery words and write the letter of each answer in the code below. This appears twice in the Bible (In Matthew VI and Luke II).
203.
204.
205.
206. In the past lesson, you’ve learned how to add and subtract decimal numbers without regrouping. The only difference in this lesson is that it involves regrouping and borrowing. It is easy to add and subtract decimal numbers without regrouping.
207. Regrouping is a process of putting numbers in their proper place values in our number system to make it easier to add and subtract. Here’s how to add decimal numbers with regrouping.
215. B. Subtract the following and check your answer on the Check Box below. 1. 0.62 2. 0.762 - 0.58 - 0.325 3. 0.850 4. 0.452 - 0.328 - 0.235
216.
217.
218. Ramon traveled from his house to school, a distance of 1.39845 kilometers. After class, he traveled to his friend’s house 1.85672 kilometer away in another direction. From his friends to his own house, he rode another 1.23714 km over. How many kilometers did Ramon traveled? 3 . T H Th T Th H Th 1 1 1 +1 . . . 1 3 8 2 2 9 5 3 1 8 6 7 1 4 7 1 5 2 4 4 . 4 9 2 3 1
219. He traveled a total of 4.49231 km. The following day, he traveled to the school and the seashore for a total of 6.35021 km. How many more kilometers did Ramon traveled than previous day? O T H Th T Th H Th 5 6 -4 . . 12 3 4 14 5 9 9 0 2 12 2 3 1 1 1 . 8 5 7 9 0
220. Ramon traveled 1.85790 kilometers more. In adding and subtracting mixed decimals, remember to align the decimal points and regroup when necessary.
225. Estimation is a way of answering a problem which does not require an exact answer. An estimate is all that is needed when an exact value is not possible. Estimation is easy to use and or to compute. Rounding is one way of making estimation. Each decimal number is rounding to some place value, usually to the greatest value and the necessary operation is performance on the rounded decimal numbers.
226. Two methods are used in making estimation, the rounding off the desired digit one and finding the sum of the first digit only. We have learned how to round decimal numbers in this section, first only the front digits are used. If an improved or refined estimate is desired, the next digits are used.
227.
228.
229. Thus the sum 3.455 + 2.672 + 5.134 can be roughly estimated by 11.000. If a better estimate is required or desired, then add 1.300 to get 11.300.
230. Estimate 5.472147 – 2.976543 Rounded to the nearest ones Actual Subtraction 5.472147 5.000000 5.472147 - 2.976543 - 3.000000 - 2.976543 2.000000 2.495604
231.
232. b. Estimate the difference by rounding method. Example : 14.525 15.000 - 11.018 - 11.000 4.000 By the rounding method, the first example is estimated by 17.000 and the second one by 4.000. The actual value of the sum of example no.1 is 16.668 and the difference of example no. 2 is 3.507 respectively. Both methods give a reasonable estimate.
233. Remember: In estimating the sums, first round each addend to its greatest place value position. Then add. If the estimate is close to the exact sum, it is a good estimate. Estimating helps you expect the exact answer to be about a little less or a little more than the estimate. However, in estimating difference, first round the decimal number to the nearest place value asked for. Then subtract the rounded decimal numbers. Check the result by actual subtraction.
234. Worksheet I. Estimates the sum and difference to the greatest place value. Check how close the estimated sum (E.S.) / estimated difference (E.D.) by getting the actual sum (A.S.) and actual difference (A.D.) . A. Actual Sum/ Estimated Sum 1. 3.417 3.000 2. 36.243 36.000 2.719 3.000 29.641 30.000 + 1.829 + 2.00 + 110.278 + 110.000 A.S. E.S. A.S. E.S. 18
236. B. Actual Difference/ Estimated Difference 7. 14.255 14.000 8. 28.267 28.000 - 11.812 - 12.000 - 16.380 - 16.000 A.D. E.D A.D. E.D. 9. 345.678 346.000 10. 92.365 92.000 - 212.792 - 213.000 - 75.647 - 76.000 A.D. E.D. A.D. E.D. 11. 62.495 62.000 12. 9.2875 9.0000 - 17.928 - 18.000 - 6.8340 - 7.0000 A.D. E.D. A.D. E.D.
237. FUN WITH MATH!!! Match a given decimals with the correct estimated sum / difference to the greatest place – value. The shortest verse in the Bible consists of two words.
238. To find out, connect each decimals with he correct estimated sum / difference to the greatest place – value. Write the letter that corresponds to the correct answer below it. 1. 36.5+18.91+55.41 U. 939.00 2. 639.27-422.30 S. 216.00 3. 48.21+168.2 P. 2.0000 4. 285.15+27.35+627.30 E. 146.000 5. 8.941-8.149 W. 28.10 6. 18.95+9.25 J. 111.00 7. 129.235+16.41 T. 537.00 8. 9.2875-6.834 S. 1.000 9. 989.15-451.85 E. 217.00
241. You always have to regroup in subtracting decimal numbers with zeros. You will have to regroup from one place to the next until all successive zeros are renamed and ready for subtraction.
242.
243. Example: 0.8005 - 0.6372 O T H Th T Th 0. 8 0 0 5 0. 7+1 10 9+1 10 0. 7 9 10 5 0. 6 3 7 2 0. 1 6 3 3
246. FUN WITH MATH!!! Answer the following to find the mystery words. In what type of ball can you carry? To find the answer, draw a line connecting each decimal number with its equal difference. The lines pass through a box with a letter on it. Write what is in the box on the blank next to the answer.
247.
248.
249. Kristina saves her extra money to buy a pair of shoes for Christmas. Last week she saved Php. 82.60; two weeks ago, she saved Php. 100.05. This week she saved Php. 92.60. How much did she save in three weeks? Steps in Solving a Problem 1. Analyze the problem 2. What is asked? Total amount did Kristina save in three weeks. 3. What are the given facts? Php. 82.60, Php. 100.05, and Php. 96.10 Know
250. 3. What is the word clue? Save. What operation will you use? We use addition. 4. What is the number sentence? Php. 82.60 + Php. 100.05 + Php. 96.10 = N 5. What is the solution? Php. 82.60 Php. 100.05 + Php. 96.10 Php. 278.75 Solve Decide Show
251. Check 6. How do you check your answer? We add downward. Php. 82.60 Php. 100.05 + Php. 96.10 Php. 278.75 “ Kristina saves Php. 278.75 in three weeks.” It is easy to solve word problems by simply following the steps in solving word problem.
252. Worksheet I. Read the problem below and analyze it. A. Baranggay Maligaya is 28.5 km from the town proper. In going there Angelo traveled 12.75 km by jeep, 8.5 km by tricycle and the rest by hiking. How many km did Angelo hike? 1. What is asked? __________________________________________________________________________________________ 2. What are the given facts? __________________________________________________________________________________________ 20
253. 3. What is the process to be used? ______________________________________________________________________________________________ 4. What is the mathematical sentence? ______________________________________________________________________________________________ 5. How the solution is done? 6. What is the answer? ______________________________________________________________________________________________
254. 7. How do you check the answer? B. Faye filled the basin with 2.95 liters of water. Her brother used 0.21 liter when he washed his hands and her sister used 0.8 liter when she washed her face. How much water was left in the basin?
255. 1. What is asked? __________________________________________________________________________________________ 2. What are the given facts? __________________________________________________________________________________________ 3. What is the process to be used? __________________________________________________________________________________________ 4. What is the mathematical sentence? __________________________________________________________________________________________ 5. How the solution is done?
256. 6. What is the answer? __________________________________________________________________________________________ 7. How do you check the answer?
257. C. Ron cut four pieces of bamboo. The first piece was 0.75 meter; the second was 2.278 meters; the third was 6.11 meters and the fourth was 6.72 meters. How much longer were the third and fourth pieces put together than the first and second pieces put together? 1. What is asked? __________________________________________________________________________________________ 2. What are the given facts? __________________________________________________________________________________________
258. 3. What is the process to be used? __________________________________________________________________________________________ 4. What is the mathematical sentence? __________________________________________________________________________________________ 5. How the solution is done? 6. What is the answer? _________________________________________________________________________________________
259. 7. How do you check the answer? D. Pamn and Hazel went to a book fair. Pamn found 2 good books which cost Php. 45.00 and Php. 67.50. She only had Php.85.00 in her purse but she wanted to buy the books. Hazel offered to give her money. How much did Hazel share to Pamn?
260. 1. What is asked? __________________________________________________________________________________________ 2. What are the given facts? __________________________________________________________________________________________ 3. What is the process to be used? __________________________________________________________________________________________ 4. What is the mathematical sentence? __________________________________________________________________________________________ 5. How the solution is done?
261. 6. What is the answer? __________________________________________________________________________________________ 7. How do you check the answer?
262. E. Marlene wants to buy a bag that cost Php. 375.95. If she has saved Php. 148.50 for it, how much more does she need? 1. What is asked? __________________________________________________________________________________________ 2. What are the given facts? __________________________________________________________________________________________ 3. What is the process to be used? __________________________________________________________________________________________
263. 4. What is the mathematical sentence? ______________________________________________________________________________________________ 5. How the solution is done? 6. What is the answer? ______________________________________________________________________________________________ 7. How do you check the answer?
265. OVERVIEW OF THE MODULAR WORKBOOK This modular workbook provides you with the understanding of the meaning of multiplication of decimals, multiply decimals in different form and how to estimate products. It will develop the ability of the students in multiplying decimal numbers. This modular workbook will help you to solve problems accurately and systematically.
266. OBJECTIVES OF THE MODULAR WORKBOOK After completing this Unit, you are expected to: 1. Define multiplication, multiplicand, multiplier, products and factors. 2. Know the ways of multiplying decimal numbers. 3. Learn the ways of multiplying decimal numbers involving zeros. 4. Learn how to make an estimate and know the ways of making estimates.
267.
268. Multiplication is a short cut for repeated addition. It is a short way of adding the same decimal number. It is the inverse if division. .4 + .4 + .4 + .4 + .4 + .4 = 2.4 In multiplication, it is written as: .4 -> multiplicand x 6 -> multiplier 2.4 -> product (answer in multiplication) factors
269. The decimal numbers we multiply are called multiplicand and multiplier is the decimal number that multiplies. The answer in the multiplication is the product . The decimal numbers multiplied together are factors . Another examples: 9 0.08 1.24 0.007 x 0.5 x 3 x 2 x 4 4.5 0.24 2.48 0.028
270. 1. What is multiplication? 2. What are factors? 3. What are products? 4. Give some examples of multiplication decimals. I. Give the meaning and explain the use of the following. 21 Worksheet
271.
272.
273. ____________ 1. The number we if multiply. ____________ 2. The numbers multiplied together. ____________ 3. The number that multiplies. ____________ 4. It is a short way of adding the same number of number times. ____________ 5. Multiplication is the inverse of _____________
277. Study these examples. Where do you place the decimal point in the product? 0.432 0.614 × 0.15 × 0.37 2160 4298 + 432 + 1842_ 0.06480 0.22718
278. Remember: In multiplying decimals, the placement of the decimal point in the product is determined by the total number of decimal places in the factors. Count the number of decimal places from the right. To check, divide the product by either factors.
279. 6480 four digits 22718 five digits Add a zero to make Additional zeros is five decimal places in the product. not needed. 0.06480 0.2271 Additional Zero Add the decimal places in the factors. Then see how many decimal places the product has. 0.432 × 0.15 Five decimal places 0.614 × 0.37 Five decimal places
280. PRACTICE: Find the product by fill in the boxes for the correct answer. 0.3 0.2 0.4 0.1 0.5 0.6 0.4 0.7 0.3 0.5 0.4 0.3 0.7 0.6 0.8 0.4 0.2 0.1 0.5 0.4 0.3 0.7 0.6 0.8 0.4 0.2 0.1
285. What did the big flower say about the little flower? FUN WITH MATH!!! To find the answer, write each of the following products in multiplying decimals.
288. Christopher can save Php. 18.65 in one month. How much money can he save in four months? 18.6 -> two decimal places x 4 74.60 Decimals are multiplied the same way as whole number.
289. Remember: In multiplying mixed decimals by whole numbers, count the decimal places in the mixed decimal to determine the placement of the decimal point in the product. Start counting the number of decimal places from the right.
290. Study other examples. 23.729 -> three decimal places x 47 166103 + 94916 1115.263 ↑ Partial product
291. 6.3572 -> four decimal places x 158 508576 317860 + 63572 1004.4376 ↑ Partial product
294. II. Find the product. 7. 934.04 8. 282.5601 9. 37.5852 × 251 x 49 × 784 10. 51.207 11. 4672.397 12. 693.3521 × 490 × 268 × 922
295. 13. 75.373 14. 149.1811 15. 10.1496 x 44 x 1012 x 189
296.
297. What is the area of Ariel’s backyard if it is 12.932 m long and 8.45 m wide? NOTE: Area = length x width = 12.93m x 8.45m = 109.27540 sq.m² = m x m = m² 12.932 -> three decimal places × 8.45 -> two decimal places 64660 51728 + 103456 109.27540 -> five decimal places The backyard is 109.27540 square meters.
298. NOTE: Area = length x width = 12.93m x 8.45m = 109.27540 sq.m² = m x m = m² When multiplying mixed decimals by mixed decimals, the decimal point of the product is determined in this manner.
299. Decimal Decimal Decimal Places of first Places of second Places of Factor Factor the product
300. Worksheet I. Rewrite and arrange the partial products properly. Find the product and place the decimal points in the correct position. 1. 4.9526 2. 9.18234 × 3.215 × 75.68 247630 7345872 49526 5509404 99052 451170 + 148578 + 6427638 25
304. Take a decimal, 0.7568. Multiply it by 10, by 100 and by 1,000. What are the products? Look at the following: 0.7568 0.7568 0.7568 × 10 × 100 × 1000 7.5680 75.6800 756.8000
305. You see that the number of zeros contained in the factors 10, 100 and 1,000 tells how many places the decimal point in the other factor must be moved to the right to get the product. Examples: 10 × 0.75 = _______ 100 × 0.75 = _______ 1,000 × 0.75 = _______
306. Observe: Move 1 place to the right. Move 2 place to the right. Move 3 place to the right. 750. 75. 7.5 0. 750 0. 75 0.75 0.750 0.75 0.75 0.75 × 1,000 × 100 × 10 Decimal
318. Example 1: A cone of ice cream costs Php. 16.25, how much in all did the 6 children spend for ice cream?
319. Example 2: What is the area of a rectangle with a length of 9.72 cm and width of 6.34 cm?
320. Worksheet Read, analyze and translate these problems to number sentence then solve. 1. Mrs. Hernandez baked 1,000 pineapple pies for a party of her daughter Kiana. If each pie costs Php. 17.85, how much did the 1,000 pies cost? 27
321. 2. If a car travels 55.6 km an hour, how far will it travel in 8 hours?
322. 3. Mang Freddie sold 46 cotton candies at Php. 2.15 each. How much altogether is the cost of the cotton candies?
323. 4. A rope measures 4.63 m. How long is it in centimeters?
324. 5. If 1 meter of cloth costs Php. 72.95, how would 6.5 meters cost?
325. 6. Mang John, a balot vendor bought 120 new duck eggs at Php. 3.85 each. How much did he pay all the eggs?
326. 7. A can of powdered milk has a mass of 0.345 kilogram. What is the mass of 12 cans of milk?
327. 8. Mr. Gelo Drona bought a residential lot with an area of 180.75 m at Php. 650.00 per square meter. How much did he pay for the lot?
328. 9. Niña works 40 hours a week. If his hourly rate is Php. 640.25, how much is she paid a week?
329. 10. The rental for a Tamaraw FX is Php. 3,500 a day. What will it cost you to rent it in 3.5 days?
333. Division is the process of finding out how many times one number is contained in another number. 0.09 -> quotient 9 0.81 -> dividend - 0 81 - 81 0 Divisor
334. The number that contains another number a number of times is called the dividend . The number that is contained in another number a number of times is called the divisor . The number that indicated how many times a number contained in another number is called the quotient . Division may also be defined as the process of separating a number into as many equal parts as indicated by another number. The symbol for division ( ÷ ), which is read as “divided by”. Thus, 0.81 ÷ 9 = 0.09 is read as “eight-one hundredths divided by nine equals nine thousandths.”
335. Another symbol is a line written over and above the dividend and a slanting line connecting it at the left of the dividend and at the right of the divisor. Another symbol is a line over which the dividend is written and the divisor below. 0.81 9
336. Worksheet I. Give the meaning and explain the use of the following: 5points each. What is division? What is divisor? What is dividend? What is quotient? 28