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1-5 The Distributive Property

Objective: Simplify algebraic

expressions using the distributive property.

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc)

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc) associative, X

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc)2. (7 + 4)0 = 0

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc)2. (7 + 4)0 = 0 mult. prop. of 0

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc)2. (7 + 4)0 = 0Find each sum or product mentally.

3. 18 + 13 + 2 + 7

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc)2. (7 + 4)0 = 0Find each sum or product mentally.

3. 18 + 13 + 2 + 7 40

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc)2. (7 + 4)0 = 0Find each sum or product mentally.

3. 18 + 13 + 2 + 74. 6 . 7 . 5

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5-Minute Check

Name the property shown by each statement.1. (4b)c = 4(bc)2. (7 + 4)0 = 0Find each sum or product mentally.

3. 18 + 13 + 2 + 74. 6 . 7 . 5 210

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5-Minute Check

Find each sum or product mentally.5. A recent study showed that 63 million

Americans choose swimming as theirfavorite sport, 55 million chose hiking,and 47 million chose camping. How many

people chose one of these three sports astheir favorite?

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5-Minute Check

Find each sum or product mentally.5. A recent study showed that 63 million

Americans choose swimming as theirfavorite sport, 55 million chose hiking,and 47 million chose camping. How many

people chose one of these three sports astheir favorite? 165 million

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 1Find 11(13) mentally using the distributive property.

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 1Find 11(13) mentally using the distributive property.

11(13) = 11(10 + 3) Replace 13 with 10 + 3.

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 1Find 11(13) mentally using the distributive property.

11(13) = 11(10 + 3) Replace 13 with 10 + 3.

=11.

10 + 11.

3 Think of 110 + 33.

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 1Find 11(13) mentally using the distributive property.

11(13) = 11(10 + 3) Replace 13 with 10 + 3.

=11.

10 + 11.

3 Think of 110 + 33.= 110 + 33 or 143

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.a. 56x + 73x

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.a. 56x + 73x

56x + 73x = (56 + 73)x x is a factor in both 56x and 73x.= 129x Use the distributive property.

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.

b. 5a + a

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.

b. 5a + a

5a + a = 5a + 1a a = 1.

a by multiplicative property.

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.

b. 5a + a

5a + a = 5a + 1a a = 1.

a by multiplicative property.= (5 + 1)a Distributive property

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.

b. 5a + a

5a + a = 5a + 1a a = 1.

a by multiplicative property.= (5 + 1)a Distributive property= 6a

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.c. (8 + x)5 + 2x

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.c. (8 + x)5 + 2x

(8 + x)5 + 2x = 8.

5 + x.

5 + 2x Distributive Property

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.c. (8 + x)5 + 2x

(8 + x)5 + 2x = 8.

5 + x.

5 + 2x Distributive Property= 40 +5x + 2x Substitution Property= 40 +(5 + 2)x Distributive Property

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The Distributive Property

The Distributive Property1. a(b + c) = ab + ac2. (b + c)a = ba + ca

Example 2Simplify each expression.c. (8 + x)5 + 2x

(8 + x)5 + 2x = 8.

5 + x.

5 + 2x Distributive Property= 40 +5x + 2x Substitution Property= 40 +(5 + 2)x Distributive Property= 40 + 7x Substitution Property