Module 11 topic 2 notes
•Download as PPT, PDF•
0 likes•1,545 views
The document provides examples and instructions for simplifying radical expressions: 1) It gives examples of breaking down radicals containing numbers and variables into simpler radical terms by factoring perfect squares. 2) Tips are provided, such as factoring variables in radicals into groups of 2 and simplifying any perfect square radicals or radicals that occur twice. 3) Examples demonstrate finding the area of shapes using simplified radical expressions for length and width.
Report
Share
Report
Share
Recommended
Adding Fraction
To add fractions, there are three steps: 1) Make the denominators the same by finding the least common denominator, 2) Add the numerators and keep the denominator the same, 3) Simplify the fraction if possible. The document then explains how to find the least common denominator by multiplying the individual denominators together. It also discusses how to add mixed fractions by first converting them to improper fractions, then adding the numerators and keeping the denominator the same, and finally converting back to a mixed fraction.
4.8 complex numbers part 2
This document discusses operations with complex numbers such as addition, subtraction, multiplication, division, powers of i, and factoring sums of squares. It provides examples of simplifying expressions with complex numbers using properties like distribution, FOIL, and multiplying conjugates. Students are assigned homework problems factoring and simplifying complex number expressions.
How to add and multiply fractions
This tutorial provides step-by-step instructions for adding and multiplying fractions. It begins with an overview and then covers finding common denominators when adding fractions, adding fractions with unlike denominators by finding the least common denominator, and multiplying fractions. Learners work through examples of adding and multiplying fractions with guidance and then independently practice solving fractional equations.
Fractions
Fractions can represent parts of a whole that is divided into equal sections. A fraction has a numerator above the line and a denominator below. Equivalent fractions have the same value even if they look different. Mixed numbers contain a whole number and fraction, while improper fractions are larger than 1. To add or subtract fractions, their denominators must be the same, so they may need to be converted to an equivalent form by multiplying the numerator and denominator by the same number.
Edi Ns 1 2 Decimal Equivalents of Common Fractions
This document discusses finding decimal equivalents for common fractions. It defines key terms like fraction, decimal, and equivalent. It provides examples of common fractions and their decimal equivalents, such as 1/2 = 0.5. It explains how to convert a fraction to a decimal by dividing the numerator by the denominator and placing the decimal point in the correct location. Students are encouraged to understand decimal equivalents as it will be important for future exams.
Addition of fractions
1) A fraction represents a part of a whole. Adding fractions is different than adding whole numbers. There are two types of fraction addition problems: those where the fractions have the same denominator, and those where the fractions have different denominators.
2) For problems where the fractions have the same denominator, you simply add the numerators and keep the same denominator.
3) For problems where the fractions have different denominators, you find the least common multiple of the denominators and convert the fractions to equivalent fractions with that denominator before adding the numerators and keeping the common denominator.
Adding And Subtracting Like Fractions
1) When adding or subtracting fractions, they must have a common denominator so the bottom numbers are the same. 2) If the denominators are already the same, simply add or subtract the top numbers and simplify. 3) To add or subtract a whole number and fraction, write the whole number as a fraction over 1 before making the denominators the same and then adding or subtracting the fractions.
1 ESO - UNIT 05 - DECIMAL NUMBERS
1. This document discusses decimal numbers and operations involving decimals. It covers place value of decimals, ordering and comparing decimals, rounding decimals, and how to perform the basic math operations of addition, subtraction, multiplication, and division on decimals. It also discusses approximating square roots of decimals.
Recommended
Adding Fraction
To add fractions, there are three steps: 1) Make the denominators the same by finding the least common denominator, 2) Add the numerators and keep the denominator the same, 3) Simplify the fraction if possible. The document then explains how to find the least common denominator by multiplying the individual denominators together. It also discusses how to add mixed fractions by first converting them to improper fractions, then adding the numerators and keeping the denominator the same, and finally converting back to a mixed fraction.
4.8 complex numbers part 2
This document discusses operations with complex numbers such as addition, subtraction, multiplication, division, powers of i, and factoring sums of squares. It provides examples of simplifying expressions with complex numbers using properties like distribution, FOIL, and multiplying conjugates. Students are assigned homework problems factoring and simplifying complex number expressions.
How to add and multiply fractions
This tutorial provides step-by-step instructions for adding and multiplying fractions. It begins with an overview and then covers finding common denominators when adding fractions, adding fractions with unlike denominators by finding the least common denominator, and multiplying fractions. Learners work through examples of adding and multiplying fractions with guidance and then independently practice solving fractional equations.
Fractions
Fractions can represent parts of a whole that is divided into equal sections. A fraction has a numerator above the line and a denominator below. Equivalent fractions have the same value even if they look different. Mixed numbers contain a whole number and fraction, while improper fractions are larger than 1. To add or subtract fractions, their denominators must be the same, so they may need to be converted to an equivalent form by multiplying the numerator and denominator by the same number.
Edi Ns 1 2 Decimal Equivalents of Common Fractions
This document discusses finding decimal equivalents for common fractions. It defines key terms like fraction, decimal, and equivalent. It provides examples of common fractions and their decimal equivalents, such as 1/2 = 0.5. It explains how to convert a fraction to a decimal by dividing the numerator by the denominator and placing the decimal point in the correct location. Students are encouraged to understand decimal equivalents as it will be important for future exams.
Addition of fractions
1) A fraction represents a part of a whole. Adding fractions is different than adding whole numbers. There are two types of fraction addition problems: those where the fractions have the same denominator, and those where the fractions have different denominators.
2) For problems where the fractions have the same denominator, you simply add the numerators and keep the same denominator.
3) For problems where the fractions have different denominators, you find the least common multiple of the denominators and convert the fractions to equivalent fractions with that denominator before adding the numerators and keeping the common denominator.
Adding And Subtracting Like Fractions
1) When adding or subtracting fractions, they must have a common denominator so the bottom numbers are the same. 2) If the denominators are already the same, simply add or subtract the top numbers and simplify. 3) To add or subtract a whole number and fraction, write the whole number as a fraction over 1 before making the denominators the same and then adding or subtracting the fractions.
1 ESO - UNIT 05 - DECIMAL NUMBERS
1. This document discusses decimal numbers and operations involving decimals. It covers place value of decimals, ordering and comparing decimals, rounding decimals, and how to perform the basic math operations of addition, subtraction, multiplication, and division on decimals. It also discusses approximating square roots of decimals.
Fraction decimal equivalence
1) The document discusses the equivalence and relationships between fractions and decimals. It provides examples of how to convert fractions to decimals by dividing the numerator by the denominator.
2) Key questions are defined for fractions and decimals, with fractions describing parts of a whole using numbers and decimals using numbers and a decimal point.
3) Examples are given of converting common fractions such as 1/2, 1/4, and 1/10 to their decimal equivalents through division.
Working with fractions at l1
This document discusses fractions at an adult numeracy level 1. It explains that fractions show a number as a mixture of whole numbers and parts of a whole. It defines proper and improper fractions, and how to convert an improper fraction into a mixed number by dividing the numerator by the denominator. The document also notes that the line separating the numerator and denominator in a fraction represents division.
Fractions (addition, subtraction, multiplication and (1)
This document discusses operations involving fractions such as addition, subtraction, multiplication, and division of fractions. It defines key fraction terms like numerator, denominator, mixed numbers, proper and improper fractions. It provides steps and examples for performing each operation on fractions. The steps for addition and subtraction involve finding a common denominator and then adding or subtracting the numerators. Multiplication involves multiplying the numerators and denominators. Division is performed by changing the second fraction to its reciprocal and then multiplying.
Grade 4 Fractions
The document discusses teaching 4th grade math lessons on fractions, including adding, subtracting, and multiplying fractions. It provides 3 steps for adding and subtracting fractions which involve making the denominators the same before adding or subtracting the numerators. For multiplying fractions, it emphasizes that students should multiply the numerators and denominators across, rather than cross-multiplying. Some sample questions are provided to work on.
Ski trip practice
This document provides instructions for formatting a spreadsheet, including formatting text and cells, using formulas to calculate totals for different cells, using the SUM function to calculate a grand total, and sorting data by different column headings. The instructions include steps for bolding and sizing text, changing cell colors and text wrapping, merging cells, entering formulas using cell references and operators, selecting cell ranges for the SUM function, and sorting data while highlighting only the data range.
4 Rules of Fractions
This presentation teaches how to perform basic fraction operations:
- Adding fractions requires having a common denominator
- Subtracting and multiplying fractions also require a common denominator and use similar processes as addition and multiplication of whole numbers
- Dividing fractions involves flipping the second fraction and turning division into multiplication
- To get a common denominator when adding or subtracting, multiply the denominators and adjust the numerators proportionately
Exploring Fractions Grade 3-4
This document provides an overview for a professional development workshop on teaching fractions. It includes an agenda with topics such as the meaning of fractions, fraction principles like the relationship between the numerator and denominator, exploring part-whole relationships, and experiencing fraction problems. Resources for teaching fractions are also listed, such as fraction games and a number line generator. The workshop utilizes a three-part lesson model of accessing prior knowledge, exploring activities, and reflecting.
Fractions-Adding/Subtracting and Multiplying/Dividing
This powerpoint explains and demonstrates the distinct procedures for adding and subtracting fractions, or for multiplying and dividing them.
Fractions - Add, Subtract, Multiply and Divide
The document discusses different arithmetic operations that can be performed on fractions, including addition, subtraction, multiplication, and division. It provides examples of how to convert fractions to equivalent fractions with a common denominator to allow for addition and subtraction. For multiplication and division, it notes that fractions can be directly multiplied or divided without requiring a common denominator. Steps are demonstrated through examples for how to perform each operation on fractions.
Fractions for year 3
1. Fractions represent parts of a whole that is divided into equal parts. A fraction has a numerator above a denominator, where the numerator tells how many parts are being considered and the denominator tells how many parts make the whole.
2. Fractions can be represented on a number line, where each increment represents another equal part of the whole. Common fractions include halves, thirds, and quarters.
3. Fractions are used in everyday situations like baking, where recipes call for measurements like 1/4 cup of an ingredient. They help describe portions or percentages of a whole object or quantity.
Operations with rational numbers
This document discusses rational numbers and different types of fractions including mixed numbers, improper fractions, adding, subtracting, multiplying, and dividing fractions. It explains that rational numbers are numbers that can be made by dividing one integer by another. Fractions have a numerator and denominator and can be added or subtracted by finding a common denominator. To multiply fractions, you multiply the numerators and denominators. To divide fractions, you keep the first fraction the same, change the operation to divide, and flip the second fraction to its inverse.
Adding And Subtracting Fractions With Different Denominators
This document discusses how to add and subtract fractions with different denominators. It explains that to add or subtract fractions, you first need to find the common denominator by listing all factors of each denominator. Then the fractions are converted to equivalent fractions with the common denominator before adding or subtracting the numerators. Finally, any improper fractions are converted to mixed numbers.
Adding and subtracting fractions with like denominators
To add fractions with the same denominator:
1) Add the numerators and keep the denominators the same
2) Simplify or reduce the fraction by finding the greatest common factor of the numerator and denominator and dividing both by it
3) An improper fraction resulting from the addition can be converted to a mixed number by dividing the numerator by the denominator and writing any remainder over the original denominator
Adding and Subtracting Fractions
The document discusses adding and subtracting simple fractions and harder fractions. It explains that when adding or subtracting fractions, they must have the same denominator. It provides examples such as 3/5 + 1/5 = 4/5 and 7/8 - 3/8 = 4/8. For harder fractions with different denominators, the document explains that we can find equivalent fractions with a common denominator to add them.
Fractions Class 7 Maths
The document outlines an agenda for a lesson on fractions that includes defining fractions and their types, methods for conversion between improper, mixed and proper fractions, finding simplest and irreducible forms, and a quiz. Key topics are fractions as parts of a whole, proper, improper, mixed and equivalent fractions, algorithms for conversion between fraction types, and identifying simplest and irreducible fractions. A brain booster, examples, and opportunities for student questions are also included.
Fractions Power Point
This power point may be used as a review for adding, subtracting, dividing, and multiplying fractions. There are video links to reviews on you tube and practice problems.
Ece141u29 32online
This document provides an overview of units 29-32 from an early childhood education math and science course. It discusses teaching fractions to young children using parts and wholes rather than symbols. It also covers place value, explaining that the same numeral represents different quantities depending on its position. The document asks the reader to define key terms from each unit and respond to specific review questions. It describes adding complexity to topics like graphing, operations, shapes, and geometry.
Adding And Subtracting Fractions
The document discusses adding and subtracting fractions with like denominators. It provides steps for adding and subtracting numerators while keeping the denominators the same. Examples are shown of adding and subtracting fractions with like denominators. Additional practice problems are presented for the reader to work through.
Fractions
The document discusses key topics about fractions including:
1. The agenda covers fractions, their types, conversions between mixed and improper fractions, quizzes, and homework.
2. Fractions are parts of a whole, such as one-fifth or half. There are proper, improper, mixed, like, and unlike fractions.
3. Converting mixed to improper fractions involves writing the whole number as the numerator, multiplying it by the denominator, and adding the remaining fractional part.
Roots and Radical Expressions Notes
This document provides information on radicals and root expressions. It defines the key parts of a radical expression, including the index and radicand. It explains that roots and radicals are inverse operations of exponents, and how to "undo" a power or radical. Examples are given of various nth roots and their relationships to exponents. The document outlines the rules for principal roots, noting even roots have two solutions while odd roots only have one. It cautions the reader to check the index when evaluating roots. Finally, it discusses how to simplify nth roots involving variables by dividing the exponent by the index.
Blogging & e Portfolios PD by Jocelyn Sutherland
This is a PD I developed for IB PYP teachers at our International School. The slides contained a lot of multi-media elements that don't fit on SlideShare. You can see the presentation on my youtube channel. Feb 2015
More Related Content
What's hot
Fraction decimal equivalence
1) The document discusses the equivalence and relationships between fractions and decimals. It provides examples of how to convert fractions to decimals by dividing the numerator by the denominator.
2) Key questions are defined for fractions and decimals, with fractions describing parts of a whole using numbers and decimals using numbers and a decimal point.
3) Examples are given of converting common fractions such as 1/2, 1/4, and 1/10 to their decimal equivalents through division.
Working with fractions at l1
This document discusses fractions at an adult numeracy level 1. It explains that fractions show a number as a mixture of whole numbers and parts of a whole. It defines proper and improper fractions, and how to convert an improper fraction into a mixed number by dividing the numerator by the denominator. The document also notes that the line separating the numerator and denominator in a fraction represents division.
Fractions (addition, subtraction, multiplication and (1)
This document discusses operations involving fractions such as addition, subtraction, multiplication, and division of fractions. It defines key fraction terms like numerator, denominator, mixed numbers, proper and improper fractions. It provides steps and examples for performing each operation on fractions. The steps for addition and subtraction involve finding a common denominator and then adding or subtracting the numerators. Multiplication involves multiplying the numerators and denominators. Division is performed by changing the second fraction to its reciprocal and then multiplying.
Grade 4 Fractions
The document discusses teaching 4th grade math lessons on fractions, including adding, subtracting, and multiplying fractions. It provides 3 steps for adding and subtracting fractions which involve making the denominators the same before adding or subtracting the numerators. For multiplying fractions, it emphasizes that students should multiply the numerators and denominators across, rather than cross-multiplying. Some sample questions are provided to work on.
Ski trip practice
This document provides instructions for formatting a spreadsheet, including formatting text and cells, using formulas to calculate totals for different cells, using the SUM function to calculate a grand total, and sorting data by different column headings. The instructions include steps for bolding and sizing text, changing cell colors and text wrapping, merging cells, entering formulas using cell references and operators, selecting cell ranges for the SUM function, and sorting data while highlighting only the data range.
4 Rules of Fractions
This presentation teaches how to perform basic fraction operations:
- Adding fractions requires having a common denominator
- Subtracting and multiplying fractions also require a common denominator and use similar processes as addition and multiplication of whole numbers
- Dividing fractions involves flipping the second fraction and turning division into multiplication
- To get a common denominator when adding or subtracting, multiply the denominators and adjust the numerators proportionately
Exploring Fractions Grade 3-4
This document provides an overview for a professional development workshop on teaching fractions. It includes an agenda with topics such as the meaning of fractions, fraction principles like the relationship between the numerator and denominator, exploring part-whole relationships, and experiencing fraction problems. Resources for teaching fractions are also listed, such as fraction games and a number line generator. The workshop utilizes a three-part lesson model of accessing prior knowledge, exploring activities, and reflecting.
Fractions-Adding/Subtracting and Multiplying/Dividing
This powerpoint explains and demonstrates the distinct procedures for adding and subtracting fractions, or for multiplying and dividing them.
Fractions - Add, Subtract, Multiply and Divide
The document discusses different arithmetic operations that can be performed on fractions, including addition, subtraction, multiplication, and division. It provides examples of how to convert fractions to equivalent fractions with a common denominator to allow for addition and subtraction. For multiplication and division, it notes that fractions can be directly multiplied or divided without requiring a common denominator. Steps are demonstrated through examples for how to perform each operation on fractions.
Fractions for year 3
1. Fractions represent parts of a whole that is divided into equal parts. A fraction has a numerator above a denominator, where the numerator tells how many parts are being considered and the denominator tells how many parts make the whole.
2. Fractions can be represented on a number line, where each increment represents another equal part of the whole. Common fractions include halves, thirds, and quarters.
3. Fractions are used in everyday situations like baking, where recipes call for measurements like 1/4 cup of an ingredient. They help describe portions or percentages of a whole object or quantity.
Operations with rational numbers
This document discusses rational numbers and different types of fractions including mixed numbers, improper fractions, adding, subtracting, multiplying, and dividing fractions. It explains that rational numbers are numbers that can be made by dividing one integer by another. Fractions have a numerator and denominator and can be added or subtracted by finding a common denominator. To multiply fractions, you multiply the numerators and denominators. To divide fractions, you keep the first fraction the same, change the operation to divide, and flip the second fraction to its inverse.
Adding And Subtracting Fractions With Different Denominators
This document discusses how to add and subtract fractions with different denominators. It explains that to add or subtract fractions, you first need to find the common denominator by listing all factors of each denominator. Then the fractions are converted to equivalent fractions with the common denominator before adding or subtracting the numerators. Finally, any improper fractions are converted to mixed numbers.
Adding and subtracting fractions with like denominators
To add fractions with the same denominator:
1) Add the numerators and keep the denominators the same
2) Simplify or reduce the fraction by finding the greatest common factor of the numerator and denominator and dividing both by it
3) An improper fraction resulting from the addition can be converted to a mixed number by dividing the numerator by the denominator and writing any remainder over the original denominator
Adding and Subtracting Fractions
The document discusses adding and subtracting simple fractions and harder fractions. It explains that when adding or subtracting fractions, they must have the same denominator. It provides examples such as 3/5 + 1/5 = 4/5 and 7/8 - 3/8 = 4/8. For harder fractions with different denominators, the document explains that we can find equivalent fractions with a common denominator to add them.
Fractions Class 7 Maths
The document outlines an agenda for a lesson on fractions that includes defining fractions and their types, methods for conversion between improper, mixed and proper fractions, finding simplest and irreducible forms, and a quiz. Key topics are fractions as parts of a whole, proper, improper, mixed and equivalent fractions, algorithms for conversion between fraction types, and identifying simplest and irreducible fractions. A brain booster, examples, and opportunities for student questions are also included.
Fractions Power Point
This power point may be used as a review for adding, subtracting, dividing, and multiplying fractions. There are video links to reviews on you tube and practice problems.
Ece141u29 32online
This document provides an overview of units 29-32 from an early childhood education math and science course. It discusses teaching fractions to young children using parts and wholes rather than symbols. It also covers place value, explaining that the same numeral represents different quantities depending on its position. The document asks the reader to define key terms from each unit and respond to specific review questions. It describes adding complexity to topics like graphing, operations, shapes, and geometry.
Adding And Subtracting Fractions
The document discusses adding and subtracting fractions with like denominators. It provides steps for adding and subtracting numerators while keeping the denominators the same. Examples are shown of adding and subtracting fractions with like denominators. Additional practice problems are presented for the reader to work through.
Fractions
The document discusses key topics about fractions including:
1. The agenda covers fractions, their types, conversions between mixed and improper fractions, quizzes, and homework.
2. Fractions are parts of a whole, such as one-fifth or half. There are proper, improper, mixed, like, and unlike fractions.
3. Converting mixed to improper fractions involves writing the whole number as the numerator, multiplying it by the denominator, and adding the remaining fractional part.
What's hot (19)
Fractions (addition, subtraction, multiplication and (1)
Fractions (addition, subtraction, multiplication and (1)
Fractions-Adding/Subtracting and Multiplying/Dividing
Fractions-Adding/Subtracting and Multiplying/Dividing
Adding And Subtracting Fractions With Different Denominators
Adding And Subtracting Fractions With Different Denominators
Adding and subtracting fractions with like denominators
Adding and subtracting fractions with like denominators
Viewers also liked
Roots and Radical Expressions Notes
This document provides information on radicals and root expressions. It defines the key parts of a radical expression, including the index and radicand. It explains that roots and radicals are inverse operations of exponents, and how to "undo" a power or radical. Examples are given of various nth roots and their relationships to exponents. The document outlines the rules for principal roots, noting even roots have two solutions while odd roots only have one. It cautions the reader to check the index when evaluating roots. Finally, it discusses how to simplify nth roots involving variables by dividing the exponent by the index.
Blogging & e Portfolios PD by Jocelyn Sutherland
This is a PD I developed for IB PYP teachers at our International School. The slides contained a lot of multi-media elements that don't fit on SlideShare. You can see the presentation on my youtube channel. Feb 2015
Birtud
1. The document discusses virtues and values associated with work such as diligence, perseverance, and discipline that are important for success in any endeavor.
2. It provides examples of household and school tasks and asks the reader to explain which values should be applied to each.
3. Values like working even without being told, continuing to work even when difficult, finishing tasks on time, doing quality work, and helping those in need are listed and the reader is asked to identify the value each represents.
K TO 12 GRADE 7 LEARNING MODULE IN EDUKASYON SA PAGPAPAKATAO (Q3-Q4)
Learning materials / modules in ESP Grade 7 Quarter 3 and 4
Viewers also liked (7)
ESP 7 Modyul 9: KAUGNAYAN NG PAGPAPAHALAGA AT BIRTUD
ESP 7 Modyul 9: KAUGNAYAN NG PAGPAPAHALAGA AT BIRTUD
K TO 12 GRADE 7 LEARNING MODULE IN EDUKASYON SA PAGPAPAKATAO (Q3-Q4)
K TO 12 GRADE 7 LEARNING MODULE IN EDUKASYON SA PAGPAPAKATAO (Q3-Q4)
Similar to Module 11 topic 2 notes
Ficha proy científico nee matematica
This document provides information about a science project for 1st year high school students studying sciences and technical subjects at the Colegio de Bachillerato "Ciudad de Portovelo" in Portovelo, Ecuador. The project objectives are to produce, communicate, and generalize information through writing, speaking, symbols, graphics, and technology using mathematical knowledge and responsible use of data sources to understand other disciplines and make socially responsible decisions. The document outlines activities for weeks 1 through 4 on topics like properties of integer exponents, square roots, and operations involving roots like multiplication, division, and exponents of roots.
Lesson plan exponents and powers class VIII
The document provides details about the author's experience creating educational content and lesson plans. It then shares a sample lesson plan about exponents and powers for 8th grade students. The lesson plan includes recaps of previous topics, learning outcomes, methodology, worksheets and self-assessments. It aims to help students understand exponents, roots, rules and applications through engaging activities and practice questions.
Section 2.3 2.4 mult div rational (algebra)
Rational numbers include fractions, integers, whole numbers, and numbers that can be written as fractions. To multiply fractions, multiply the numerators and denominators. To divide fractions, change the division to multiplication and take the reciprocal of the second fraction. Examples are provided for multiplying and dividing fractions and mixed numbers.
Simplifying+radicals
The document provides instructions for students on how to simplify radicals. It defines what it means to simplify a radical as having no perfect square factors in the radicand. The objective is for students to be able to simplify at least 9 out of 10 radicals correctly. Students are taught to rewrite the radicand using prime factorization, replace any perfect square factors with their numeric equivalent, and check if the radicand is simplified by having no remaining perfect square factors. Examples are worked through and students complete guided practice problems to demonstrate their understanding.
7-20-11
The document outlines the agenda and objectives for a math class focusing on fractions. The class will complete real-world math problems involving fractions, take notes on working with fractions, and practice subtracting fractions using borrowing. They will also work on word problems requiring adding and subtracting fractions. The document provides examples and steps for adding, subtracting, converting between improper and mixed numbers, finding common denominators, reducing fractions, and borrowing in fraction subtraction.
Power Laws
This document discusses various methods for estimating and calculating square roots. It begins by defining irrational numbers as non-repeating decimals that can result from taking the square root of a non-perfect square. It then discusses estimating square roots by knowing perfect square numbers and using guess and check methods. Later sections cover using calculators, applying square roots in formulas, exponent rules including multiplication, division, powers, and scientific notation for writing extremely large numbers.
Math Q1 - Week 2.pdf
The document provides a lesson on factoring the sum and difference of two cubes. It begins with definitions of perfect cubes and examples of factoring expressions like x3 - 27 and x3 + 27 using the rule that (x - a)(x2 + ax + a2) = x3 - a3 and (x + a)(x2 - ax + a2) = x3 + a3. Students are then asked to determine if additional expressions are the sum or difference of two cubes and factor them accordingly. The next section covers factoring perfect square trinomials, defining them as expressions of the form a2 + 2ab + b2 and providing the factoring pattern (a + b)2. Examples
grade 6 Budget Of Works in Math
The document outlines the mathematics curriculum for the first quarter of grade 6. It covers several topics: whole numbers, decimals, fractions, ratios, proportions, percentages, probability, integers, geometry, measurement, and graphs. For each topic, it lists the key concepts and skills to be taught, such as order of operations, addition and subtraction of decimals, multiplication of fractions, solving word problems involving percentages, and interpreting circle graphs.
1 mathematics
1. The document provides information about basic mathematical concepts such as numbers, calculations, fractions, powers, roots, measurements, geometry, and circle terminology. It includes examples and definitions of these terms.
2. Geometry concepts discussed include different types of angles, triangles classified by sides and angles, and two-dimensional and three-dimensional shapes. Pythagorean theorem is defined as a2 + b2 = c2.
3. Parts of a circle are defined, including circumference, diameter, semicircle, tangent, secant, sector, segment, chord, and arc. Formulae for calculating circumference and diameter using pi are provided.
Section 4.7 And 4.8 Plus Warm Ups
This document discusses rules for multiplying and dividing expressions with exponents. It states that to multiply terms with the same base, add the exponents. To divide terms with the same nonzero base, subtract the exponents. If subtracting exponents results in zero, the expression equals one. Negative exponents can be written as reciprocals with positive exponents. Examples are provided to illustrate simplifying expressions using these rules.
Grade 9 Maths - Fractions 1
This document provides a review of fractions for grade 9 math students. It covers the basics of fractions including what fractions are, the parts of a fraction, different types of fractions, simplifying fractions, converting between improper and mixed numbers, comparing fractions, and example worksheet questions. Students are instructed to complete exercises in their math books covering these fraction topics.
Mult div frac_nt2
Rational numbers include fractions, integers, and decimals. To multiply rational numbers, multiply the numerators and denominators. Dividing rational numbers is done by changing the division to multiplication and taking the reciprocal of the second number. Rational numbers can be simplified before or after multiplication and division.
Mult Div Frac Nt2
Rational numbers include fractions, integers, and decimals. To multiply rational numbers, multiply the numerators and denominators. Dividing rational numbers is done by changing the division to multiplication and taking the reciprocal of the second number. Both multiplication and division of rational numbers do not require a common denominator.
Basic Algebra Ppt 1.1
The document introduces key concepts in algebra including variables, constants, types of numbers (counting, integers, rational, irrational, real), graphs, averages, and positive and negative numbers. It provides examples and guidelines for understanding these concepts. Variables represent quantities that can vary, while constants represent fixed values. Different number sets are explained and visualized on a number line. Averages are calculated by adding values and dividing by the total count. Positive numbers are greater than zero, while negative numbers are less than zero.
Ch. 5 2 Rectangles
The document provides an agenda and homework assignments for a math class, including converting fractions to decimals and vice versa. Students are asked to create a Thanksgiving project folder and share it. They also have homework on fractions, decimals, and terminology around terminating and repeating decimals.
Teknik Menjawab Matematik
This document provides an overview of the topics that will be covered in the UPSR Mathematics exam, along with strategies for solving different types of questions. The topics include numbers and operations, fractions, decimals, percentages, mixed operations, average, money, shape and space, measurement, graphs, and data handling. It discusses the skills needed for each topic and provides examples of question types and strategies for showing work, understanding word problems, and managing information from questions and diagrams. The document emphasizes solving problems systematically and clearly showing all work.
MATH 6 Q1 WK 9 D3-4-C.pptx
This document discusses dividing decimals. It explains that division is the inverse of multiplication and that decimals are fractions written in a special form. It defines terminating and non-terminating decimals and provides examples of each. It describes how to convert terminating decimals to fractions by removing the decimal point and non-terminating decimals using a repeating pattern. The document provides steps for dividing whole numbers by decimals, decimals by whole numbers, and decimals by decimals. It includes examples and problems for readers to practice these skills.
Succeeding in Business with Microsoft Excel 2010 A Problem Solving Approach 1...
Full download : https://alibabadownload.com/product/succeeding-in-business-with-microsoft-excel-2010-a-problem-solving-approach-1st-edition-gross-solutions-manual/ Succeeding in Business with Microsoft Excel 2010 A Problem Solving Approach 1st Edition Gross Solutions Manual , Succeeding in Business with Microsoft Excel 2010 A Problem Solving Approach,Gross,1st Edition,Solutions Manual
March 17, 2014
1. The document discusses various algebra topics for the day including make-up tests, expanding and factoring polynomials, and polynomial long division.
2. It emphasizes that factoring polynomials is important as it is often the first step in solving problems, and describes different methods for factoring including finding all terms that were multiplied together.
3. The document also covers the processes of expanding polynomials through distribution, and dividing polynomials using both long division and dividing out common monomial factors. Examples are provided for each topic.
Module 9.4.9.5,9.6
This document discusses solving radical equations through multiple steps:
1) Isolate the radical on one side of the equation and square both sides to eliminate the radical.
2) Radicals can also be cubed roots, requiring the same process of isolating the radical and squaring both sides.
3) Radical equations can also be solved by graphing each side as functions and finding the intersection point of the graphs.
4) Transformations of radical equations, such as changing coefficients, affect the graph by shifting it up or down (changing k) or left or right (changing h).
Similar to Module 11 topic 2 notes (20)
Succeeding in Business with Microsoft Excel 2010 A Problem Solving Approach 1...
Succeeding in Business with Microsoft Excel 2010 A Problem Solving Approach 1...
More from cauleyc
Module 6 topic 1 notes
This document discusses the properties for solving one-step inequalities, which are the same as the properties for equations. It explains the addition, subtraction, multiplication, and division properties for inequalities and notes that when multiplying or dividing by a negative number, the inequality sign changes. The objective is to use these properties to solve one-step inequalities.
Module 12 topic 1 notes
The document discusses exponential functions of the form y = a(b)x and provides examples of exponential growth and decay. It explains that exponential growth occurs when b is greater than 1 and exponential decay occurs when b is between 0 and 1. The document also contains an example of using an exponential decay function to model and predict the number of farms in Minnesota between 1983 and 2010, assuming a 2% annual decline.
Module 11 topic 1 notes(2)
The document discusses graphing and solving quadratic equations. It defines key terms like parabolas, vertices, and axes of symmetry. It provides examples of using the quadratic formula to find the vertex and shows how to factor and set factors equal to zero to solve quadratic equations and find their roots.
Module 11 topic 1 notes
The document discusses graphing and solving quadratic equations. It defines key terms like parabolas, vertices, and axes of symmetry. It provides examples of using the quadratic formula to find the vertex and shows how to factor and set factors equal to zero to solve quadratic equations and find their roots.
Module 6 topic 2 notes
The document provides examples of solving multi-step inequalities using various algebraic techniques: isolating variables by adding or subtracting like terms, distributing coefficients, and combining variables on one side of the inequality symbol. It demonstrates solving inequalities with variables on both sides of the inequality and discusses keeping track of inequality signs when multiplying or dividing both sides by negative numbers.
Module 6 topic 1 notes
This document discusses the properties for solving one-step inequalities, which are the same as the properties for equations. It explains the addition, subtraction, multiplication, and division properties for inequalities and notes that when multiplying or dividing by a negative number, the inequality sign changes. The objective is to use these properties to solve one-step inequalities.
Module 5 topic 2 notes
The document discusses parallel and perpendicular lines and their slopes. It contains 3 short videos that explain the concepts of parallel lines having the same slopes, perpendicular lines having opposite reciprocal slopes, and how to write equations for parallel and perpendicular lines based on their slopes. The document instructs the user to watch the videos, complete a quiz for practice, and work on assignments to master the concepts.
Module 4 topic 3 notes
This document discusses writing linear equations from different information provided. It explains that the slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. It also explains that the point-slope form, y-y1=m(x-x1), is used when given a point and the slope. Finally, it notes that when given two points, the slope must first be calculated as m=(y2-y1)/(x2-x1) before using the point-slope form.
Module 4 topic 1 part 2 notes
The document discusses the midpoint formula and how to calculate the midpoint between two points on a coordinate plane. It provides the example of finding the midpoint between the points (1,2) and (3,-2). The midpoint is calculated by taking the average of the x-coordinates and the average of the y-coordinates of the two points, which in this case is (2,0). It also includes a link to a video that further explains how to use the midpoint formula.
Module 4 topic 1 part 1 notes
The document introduces concepts related to the coordinate plane, including the x-axis, y-axis, origin, quadrants, ordered pairs, and graphing points. It explains that the x-axis is horizontal, the y-axis is vertical, and the origin is at the center point (0,0). Points can fall into four quadrants depending on whether their x and y values are positive or negative. An example point (-5,3) is shown to lie in Quadrant II. The coordinates of two points A and B are given as (-5,-7) and (7,-2).
Module 3 topic 3 notes
The document provides examples of solving literal equations by rearranging the equations to isolate the variable of interest. It discusses solving equations to express variables like r, y, x, and H in terms of other variables. Additional examples show how to use literal equations to find constants in direct variation equations and to calculate heights using a bricklaying formula.
Module 3 topic 2 notes
This document discusses solving multi-step linear equations in 3 sentences or less:
The document provides examples and steps for solving multi-step linear equations, which may require using the distributive property, combining like terms, or having variables on both sides of the equation. It also discusses setting up and solving equations related to consecutive integers and word problems involving linear equations with more than one step.
Module 3 topic 1 notes
This document discusses solving one-step linear equations. It explains that to solve equations using addition or subtraction, the inverse operations of subtraction or addition are used respectively. Similarly, to solve equations using multiplication or division, the inverse operations of division or multiplication are used. It provides examples of solving equations using these inverse operations. It also explains how to write and solve equations to represent word problems involving linear equations with one variable.
More from cauleyc (13)
Module 11 topic 2 notes
- 1. GOAL 1: THE LEARNER WILL PERFORM OPERATIONS WITH NUMBERS AND EXPRESSIONS TO SOLVE PROBLEMS. OBJECTIVE 1.01: WRITE EQUIVALENT FORMS OF ALGEBRAIC EXPRESSIONS TO SOLVE PROBLEMS. CLICK ON THE MICROPHONE SPEAKER TO HEAR EACH SLIDE OF THIS POWERPOINT! Module 11 Topic 2 Simplifying Radical Expressions
- 2. so so so You should know the squares of the numbers 1 through 20 to make your life easier.