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1-1 Study Guide and Intervention

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Lesson 1-3. Chapter 1. 19. Glencoe Algebra 1. Study Guide and Intervention (continued). Properties of Numbers. 1-3. Commutative and Associative Properties

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PERIOD. Lesson 1-2. Chapter 1. 11. Glencoe Algebra 1. Evaluate Numerical Expressions Numerical expressions often contain more than one operation.

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NAME DATE PERIOD

Chapter 1 18 Glencoe Algebra 1

Evaluate 24 ? 1 - 8 + 5(9 ÷ 3 - 3). Name the property used in each step. 24
24
8 24
8

0 Multiplicative Property of Zero; 5(0) = 0

0 Substitution; 24 - 8 = 16

16 Additive Identity; 16 + 0 = 16

Exercises

Evaluate each expression. Name the property used in each step. 1. 2 1 4 1 2 2 1 4

1-3Study Guide and Intervention

Properties of Numbers

Identity and Equality Properties The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical e xpressions.Additive IdentityFor any number a, a + 0 = a.

Additive Inverse

For any number

a , a + (-a) = 0.

Multiplicative Identity

For any number

a , a . 1 = a.

Multiplicative Property of 0

For any number

a , a . 0 = 0.

Multiplicative Inverse

PropertyFor every number a

b , where a, b ≠ 0, there is exactly one number b a such that a b b a = 1.

Reflexive Property

For any number

a , a = a.

Symmetric Property

For any numbers

a and b , if a = b, then b = a.

Transitive Property

For any numbers

a , b, and c , if a = b and b = c, then a = c.

Substitution Property

If a = b, then a may be replaced by b in any expression.Example = 2(15 ? 1 - 14) - 4 ? 1 4

Subst. = 18 ? 1 - 3 ? 2 +

2(2

2) Subst.

2(15 14) 4 ? 1 4 Mult. Identity = 18 ? 1 - 3 ? 2 + 2(0) Substitution 2(1) 4 1 4 Substitution = 18 - 3 ? 2 + 2(0) Mult. Identity 2 4 1 4

Mult. Identity = 18 - 6 + 2(0) Substitution

1 Mult. Inverse = 18 - 6 + 0 Mult. Prop. Zero

= 1 Substitution = 12 + 0 Substitution = 12 Add. Identity = 2 ( 1 4 1 4 Substitution = 15 ? 1 - 9 +2(5 - 5) Substitution 2 1 2

Substitution = 15

? 1 - 9 +2(0) Substitution

1 Mult. Inverse = 15

NAME DATE PERIOD

Lesson 1-3

Chapter 1 19 Glencoe Algebra 1

Study Guide and Intervention

(continued)

Properties of Numbers

1-3 Commutative and Associative Properties The Commutative and Associative Properties can be used to simplify expressions. The Commutative Properties state that the order in which you add or multiply numbers does not change their sum or product. The Associative Properties state that the way you group three or more numbers when adding or multiplying does not change their sum or product.

Evaluate 6 ? 2 ? 3 ? 5

using properties of numbers. Name the property used in each step. 6

Commutative Property

= 180 Multiply.

The product is 180. Evaluate

8.2 + 2.5 + 2.5 + 1.8 using properties of

numbers. Name the property used in each step.

8.2 + 2.5 + 2.5 + 1.8

8.2 1.8 2.5 2.5

Commutative Prop.

(8.2 1.8) (2.5

2.5) Associative Prop.

5 Add.

15 Add.

The sum is 15.

Exercises

Evaluate each expression using properties of numbers. Name the property used in each step. 7. 3 1 2 + 4 + 2 1 2 + 3 8. 3 4 10. 4 1 2 + 5 + 1 2 13. 4 5 2 9 1 5 1 2 1 4 1 7 1 2 1 9 18. 3 4 1 2

Example 1Example 2

3558175

4804760

137213.7

13 5.611 80324

16860Properties will vary. See students' work.

Commutative PropertiesFor any numbers a and b, a + b = b + a and a ? b = b ? a.

Associative Properties

For any numbers

a , b, and c, (a + b) + c = a + (b + c ) and (ab)c = a(bc).quotesdbs_dbs22.pdfusesText_28

[PDF] 1-3 Study Guide and Intervention

NAME DATE PERIOD

Chapter 1 18 Glencoe Algebra 1

0 Multiplicative Property of Zero; 5(0) = 0

0 Substitution; 24 - 8 = 16

16 Additive Identity; 16 + 0 = 16

Exercises

1-3Study Guide and Intervention

Properties of Numbers

Additive Inverse

For any number

Multiplicative Identity

For any number

Multiplicative Property of 0

For any number

Multiplicative Inverse

PropertyFor every number a

Reflexive Property

For any number

Symmetric Property

For any numbers

Transitive Property

For any numbers

Substitution Property

Subst. = 18 ? 1 - 3 ? 2 +

2) Subst.

Mult. Identity = 18 - 6 + 2(0) Substitution

1 Mult. Inverse = 18 - 6 + 0 Mult. Prop. Zero

Substitution = 15

1 Mult. Inverse = 15

NAME DATE PERIOD

Lesson 1-3

Chapter 1 19 Glencoe Algebra 1

Study Guide and Intervention

Properties of Numbers

Evaluate 6 ? 2 ? 3 ? 5

Commutative Property

The product is 180. Evaluate

8.2 + 2.5 + 2.5 + 1.8 using properties of

8.2 + 2.5 + 2.5 + 1.8

Commutative Prop.

2.5) Associative Prop.

5 Add.

15 Add.

The sum is 15.

Exercises

Example 1Example 2

3558175

4804760

137213.7

16860Properties will vary. See students' work.

Associative Properties

For any numbers