# Chapter Essay

**Topics:**Integer, Real number, Negative and non-negative numbers

**Pages:**117 (18415 words)

**Published:**August 25, 2013

1A

1-1 1-2 1-3 1-4 1-5 1-6

Expressions and Integers

Evaluating Algebraic Expressions Writing Algebraic Expressions Integers and Absolute Value Adding Integers Subtracting Integers Multiplying and Dividing Integers

1B

1-7 1-8 LAB 1-9

Solving Equations

Solving Equations by Adding or Subtracting Solving Equations by Multiplying or Dividing Model Two-Step Equations Solving Two-Step Equations

KEYWORD: MT8CA Ch1

Firefighters can use algebra to find out how fast a fire is spreading and to create a plan to stop it.

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Chapter 1

Vocabulary

Choose the best term from the list to complete each sentence. 1. __?__is the __?__ of addition. 2. The expressions 3 4 and 4 3 are equal by the __?__. 3. The expressions 1 the __?__. (2 3) and (1 2) 3 are equal by

addition Associative Property Commutative Property division multiplication opposite operation subtraction

4. Multiplication and __?__ are opposite operations. 5. __?__ and __?__ are commutative.

Complete these exercises to review skills you will need for this chapter.

Whole Number Operations

Simplify each expression. 6. 8 116 43 7. 2431 187 8. 204 38 9. 6447 21

Compare and Order Whole Numbers

Order each sequence of numbers from least to greatest. 10. 1050; 11,500; 105; 150 11. 503; 53; 5300; 5030 12. 44,400; 40,040; 40,400; 44,040

Inverse Operations

Rewrite each expression using the inverse operation. 13. 72 18 90 14. 12 9 108 15. 100 34 66 16. 56 8 7

Order of Operations

Simplify each expression. 17. 2 21. 5 3 4 6 2 18. 50 22. 16 2 5 4 2 3 19. 6 3 3 23. (8 3)(8 3 3) 20. (5 24. 12 2)(5 3 2 2) 5

Evaluate Expressions

Determine whether the given expressions are equal. 25. (4 7) 2 and 4 (7 2) 29. 9 (4 2) and (9 4) 2 26. (2 4) 2 and 2 (4 2) 27. 2 (3 3) and (2 3) 31. (16 4) 4 and 16 (4 3 28. 5 (50 44) and 5 50 44 32. 5 (2 3) 4) and (5 2) 3

30. 2 3 2 4 and 2 (3 4)

Principles of Algebra

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The information below “unpacks” the standards. The Academic Vocabulary is highlighted and defined to help you understand the language of the standards. Refer to the lessons listed after each standard for help with the math terms and phrases. The Chapter Concept shows how the standard is applied in this chapter.

California Standard

NS2.5 Understand the meaning of absolute value of a number; interpret the the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. (Lessons 1-3 and 1-5)

Academic Vocabulary

absolute value the distance a number is from zero on a number line interpret to understand and explain the meaning of

Chapter Concept

You find the absolute value of a number by determining how far it is from zero on a number line. Example: Since 3 is 3 units from 0 on a number line, the absolute value of 3 is 3. You rewrite a verbal statement using mathematical symbols. Example: three less than a number n 3

AF1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). (Lesson 1-2)

variable a symbol, usually a letter, used to show an amount that can change Example: x verbal using words

AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x 5)2. (Lesson 1-1)

evaluate find the value Example: x x 2 5 3 for x 3 3 2

You find the value of expressions by performing basic arithmetic operations in a specific order.

AF1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly. (Lessons 1-1 and 1-7)

terminology words used to represent certain items or ideas

You learn the names of different mathematical concepts.

AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from...

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