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This document discusses order of operations in math and the four main operations - parentheses and brackets, exponents, multiplication and division, and addition and subtraction. It provides examples of how the order of operations affects the outcome of calculations. Rules for solving problems with missing operations are also presented. Finally, the document introduces different number systems and properties like closure, commutative, associative, identity, and distributive properties.
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Order of operations
Order of operations provides a standard method for simplifying mathematical expressions to avoid confusion. It establishes a set of rules for performing operations in a specific sequence: 1) Simplify within grouping symbols, 2) Perform exponents, 3) Complete multiplication and division from left to right, and 4) Complete addition and subtraction from left to right. Following these rules ensures consistent evaluation and simplification of expressions.
Order of Operations
The document explains the order of operations (PEMDAS) for solving mathematical expressions:
1) Parentheses and division bars are solved first from left to right.
2) Exponents are solved next from left to right.
3) Multiplication and division are solved next from left to right.
4) Addition and subtraction are solved last from left to right.
It provides examples of solving expressions using PEMDAS and emphasizes the importance of checking your work.
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To multiply a binomial and a trinomial:
1) Set up a grid with the terms of each factor and multiply corresponding terms, keeping track of exponents by adding them.
2) Order the terms of the product from highest to lowest exponent.
3) The final product is the sum of these terms, unless like terms can be combined.
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The document discusses exponents and multiplying monomials. It provides examples of exponents like 32 meaning 3 x 3 and explains that 32 does not mean 3 x 2. It also shows how to evaluate exponents, like 63 = (6 x 6) x 6 = 216. The document then explains that when multiplying terms with the same base, you add the exponents, like 32 x 33 = 35. Finally, it defines monomials as expressions involving constants and variables and shows how to multiply them by separating coefficients and variables, like (5t)(20t3) = 100t4.
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This document summarizes key concepts about number patterns, sequences, and related topics:
1) It defines terms like sequences, patterns, Fibonacci sequence, odd and even numbers, prime numbers, factors, prime factors, multiples, lowest common multiple (LCM), common factors, and highest common factor (HCF).
2) It provides examples of how to identify these concepts, like determining if a number is prime, finding all factors of a number, listing multiples, and calculating LCM and HCF.
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Order of operations
Order of operations provides a standard method for simplifying mathematical expressions to avoid confusion. It establishes a set of rules for performing operations in a specific sequence: 1) Simplify within grouping symbols, 2) Perform exponents, 3) Complete multiplication and division from left to right, and 4) Complete addition and subtraction from left to right. Following these rules ensures consistent evaluation and simplification of expressions.
Order of Operations
The document explains the order of operations (PEMDAS) for solving mathematical expressions:
1) Parentheses and division bars are solved first from left to right.
2) Exponents are solved next from left to right.
3) Multiplication and division are solved next from left to right.
4) Addition and subtraction are solved last from left to right.
It provides examples of solving expressions using PEMDAS and emphasizes the importance of checking your work.
Multiplying a binomial and trinomial
To multiply a binomial and a trinomial:
1) Set up a grid with the terms of each factor and multiply corresponding terms, keeping track of exponents by adding them.
2) Order the terms of the product from highest to lowest exponent.
3) The final product is the sum of these terms, unless like terms can be combined.
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The document discusses exponents and multiplying monomials. It provides examples of exponents like 32 meaning 3 x 3 and explains that 32 does not mean 3 x 2. It also shows how to evaluate exponents, like 63 = (6 x 6) x 6 = 216. The document then explains that when multiplying terms with the same base, you add the exponents, like 32 x 33 = 35. Finally, it defines monomials as expressions involving constants and variables and shows how to multiply them by separating coefficients and variables, like (5t)(20t3) = 100t4.
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The document provides a quick review for a quiz on writing equations of lines. It includes 4 problems: writing the equation of a line with a given slope and point, through two given points, a horizontal line through a given point, and a vertical line through a given point. It then transitions to discussing solving systems of equations using the elimination method, providing 3 examples of solving systems by eliminating a variable through adding or subtracting the equations.
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This document summarizes key concepts about number patterns, sequences, and related topics:
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2) It provides examples of how to identify these concepts, like determining if a number is prime, finding all factors of a number, listing multiples, and calculating LCM and HCF.
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The document provides instructions and examples for various math concepts:
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1. The document provides examples for evaluating expressions with scientific notation, square roots, and cube roots. It includes step-by-step workings for finding square roots of perfect squares and cube roots of perfect cubes.
2. Key concepts explained are square roots, perfect squares, radical signs, cube roots, and perfect cubes. Examples are provided to find square roots of numbers less than 100 and cube roots of small numbers.
3. Knowing how to find the exact square roots of perfect squares helps estimate the square roots of nearby non-perfect squares. Being able to write the perfect square root without the radical provides understanding and allows for computations.
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The document discusses the order of operations in mathematics. It explains that the order of operations (PEMDAS) - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction - provides rules for which operations to perform first in a mathematical expression without changing the result. It provides examples of evaluating expressions using the proper order of operations and also provides links to online games for practicing order of operations skills.
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations:
1) Perform operations inside parentheses first from left to right.
2) Perform exponents next from left to right.
3) Perform multiplication and division from left to right.
4) Perform addition and subtraction from left to right.
Some example problems are worked out step-by-step to demonstrate how to follow PEMDAS.
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The document provides instructions and examples for various math concepts:
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The document discusses different ways of representing integers using red and blue chips, with red representing positive integers and blue representing negative integers. It introduces the concept of the "distinguished representation" and has examples of representing various integers in their distinguished representation and other representations. It then discusses how to perform addition and subtraction of integers by taking the union or difference of the chip representations and finding the distinguished representation of the result.
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations:
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It provides examples of how to use the order of operations to solve problems step-by-step, including solving expressions within parentheses first, then exponents, then multiplication/division from left to right, and finally addition/subtraction from left to right. Some example problems are worked out to demonstrate applying the PEMDAS method.
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations:
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations:
1) Perform operations inside parentheses first, from left to right.
2) Evaluate exponents next, from left to right.
3) Multiply and divide from left to right.
4) Add and subtract from left to right.
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations:
1) Perform operations inside parentheses first, from left to right.
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations:
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Several examples are provided to demonstrate how to use PEMDAS to evaluate expressions step-by-step.
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1. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This determines the order you solve terms in a mathematical expression.
2. First you solve anything inside parentheses. Then exponents, then multiplication and division from left to right. Finally, addition and subtraction are solved from left to right.
3. Some example problems are worked out step-by-step to demonstrate using PEMDAS, with the answers provided to check your work. Key vocabulary terms are also defined.
Order of Operations.powerpoint presentation
This document explains the order of operations, which is a set of rules for evaluating mathematical expressions with multiple operations. It introduces PEMDAS/GEMDAS as a mnemonic to remember the order: 1) Grouping symbols (parentheses), 2) Exponents, 3) Multiplication/Division (left to right), 4) Addition/Subtraction (left to right). Several examples are provided to demonstrate applying the order of operations to evaluate expressions step-by-step according to this sequence.
MATH 5 PRESENTATION classroom observation
This document contains a mathematics lesson on order of operations and applying the PEMDAS/GEMDAS rules to simplify expressions and equations. It includes:
- Examples of applying order of operations to evaluate expressions and equations step-by-step.
- Explanations of performing operations within grouping symbols, exponents, multiplication, division, addition and subtraction in the proper sequence.
- Practice problems for students to simplify expressions and equations involving grouping symbols and exponents.
- An activity for students to write and solve a mathematical equation based on a word problem.
3 Performing Mensuration and Calculation.pptx
Performing Mensuration and Calculation discusses fundamental math operations like addition, subtraction, multiplication, and division. It focuses on performing these operations on whole numbers and fractions. Key steps are provided for each operation, like adding digits place by place without regrouping for addition and subtraction. Conversion between English and metric units of measurement is also covered. The basic metric units are the meter, decimeter, centimeter and millimeter while the basic English units are the yard, feet and inches.
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The document discusses arithmetic means and arithmetic series. It provides examples of calculating the arithmetic mean between two numbers using the formula a2 = (a1 + a3)/2. It also gives examples of inserting arithmetic means between terms in a sequence. The document then discusses arithmetic series and provides formulas for calculating the sum of terms in an arithmetic sequence when given the first term, common difference, or first and last terms. It illustrates these formulas with examples of finding sums of arithmetic sequences.
209620644 introduction-to-factorization
This document introduces factorization and finding the greatest common divisor (GCD). It discusses factors, prime numbers, prime factorization, and common factors. Examples are provided to show how to determine if a number is a factor, find all factors of a number, and use the Sieve of Eratosthenes method to identify prime numbers up to a given value. The document aims to build mastery of these concepts through practice questions provided at the end of each section.
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42-4Inadequacy.pptx
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051#Scaffolding.pptx
Scaffolding is a teaching method where students learn with the help of teachers or more advanced peers to achieve learning goals beyond what they could do independently. The theory behind scaffolding is that students learn more through collaboration with others who have a wider range of skills and knowledge. Scaffolding helps students expand their learning within their Zone of Proximal Development, which is the set of skills they can perform with assistance that are just above their current ability level.
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Syllabus
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Introduction to objective, scope and outcome the subject
Chapter 2
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Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
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Chapter 5
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Chapter 6
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003#pedagogy math test
- 1. 003#Pedagogy Math Test Number & Quantity
- 2. Order Operations Math rules which tells us that which math operations to do first. Like: Addition Multiplication Division Subtraction
- 3. For Example different operation different answer Rule 1: 5+4x6= addition first 9X6=54 Rule 2: 5+4x6= Multiplication first=24+5=29
- 4. Four Operations 1. Parentheses & Brackets 2. Exponents 3. Multiplications & Division 4. Addition and Subtraction
- 5. 1: Parentheses & Brackets Parentheses ( ) numbers in Parentheses are called Group (3+4) Brackets [3+4] Both are used to group things together. For example 5x(7+3) two Operations and three numbers Parentheses helps to know what part of the problem we need to do first.
- 6. 2. Exponents Repeated Multiplication For example Simplify exponent first Like: 4x =4x16
- 7. 3: Multiplication and Division From left to right
- 8. 4: Addition & Subtraction 5+4X3=5+12=17 5-3X6=5-18=-13
- 9. Find the Missing Operations
- 10. 1. 5 − (9 − 3) + 6 A. 5 B. 10 C. 6 D. -5
- 11. 2: 8 ÷ 1 × 6) ÷ 6 − 4 = a. 5 b. 4 c. 1 d. 8
- 12. 3: 2 + 7 × (7 × 9) ÷ 3= a. 149 b. 89 c. 179 d. 49
- 13. Number System N=Natural numbers W= Whole Numbers Z=Integers Q=Rational Numbers I=Irrational Numbers R= Real numbers
- 14. Properties of the Number System Closure Property Commutative Property Associate Property Identity Property Distributive Property