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### 1-5 The Distributive Property

Objective: Simplify algebraic expressions using the distributive property.

5-Minute Check

Name the property shown by each statement.

- (4b)c = 4(bc)
- (7 + 4)0 = 0

Find each sum or product mentally.

3. 18 + 13 + 2 + 7

5-Minute Check

Name the property shown by each statement.

- (4b)c = 4(bc)
- (7 + 4)0 = 0

Find each sum or product mentally.

3. 18 + 13 + 2 + 7 40

5-Minute Check

Name the property shown by each statement.

- (4b)c = 4(bc)
- (7 + 4)0 = 0

Find each sum or product mentally.

3. 18 + 13 + 2 + 7

4. 6 . 7 . 5

5-Minute Check

Name the property shown by each statement.

- (4b)c = 4(bc)
- (7 + 4)0 = 0

Find each sum or product mentally.

3. 18 + 13 + 2 + 7

4. 6 . 7 . 5 210

5-Minute Check

Find each sum or product mentally.

5. A recent study showed that 63 million Americans choose swimming as their favorite sport, 55 million chose hiking, and 47 million chose camping. How many people chose one of these three sports as their favorite?

5-Minute Check

Find each sum or product mentally.

5. A recent study showed that 63 million Americans choose swimming as their favorite sport, 55 million chose hiking, and 47 million chose camping. How many people chose one of these three sports as their favorite? 165 million

The Distributive Property

Example 1

Find 11(13) mentally using the distributive property.

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

The Distributive Property

Example 1

Find 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.

The Distributive Property

Example 1

Find 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

The Distributive Property

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

The Distributive Property

- Example 2
- Simplify each expression.
- 56x + 73x
- 56x + 73x = (56 + 73)x x is a factor in both 56x and 73x.

The Distributive Property

- Example 2
- Simplify each expression.
- 56x + 73x
- 56x + 73x = (56 + 73)x x is a factor in both 56x and 73x.
- = 129x Use the distributive property.

The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

5a + a = 5a + 1a a = 1.a by multiplicative property.

The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

5a + a = 5a + 1a a = 1.a by multiplicative property.

= (5 + 1)a Distributive property

The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

5a + a = 5a + 1a a = 1.a by multiplicative property.

= (5 + 1)a Distributive property

= 6a

The Distributive Property

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

The Distributive Property

- Example 2
- Simplify each expression.
- (8 + x)5 + 2x
- (8 + x)5 + 2x = 8.5 + x.5 + 2x Distributive Property

The Distributive Property

- Example 2
- Simplify each expression.
- (8 + x)5 + 2x
- (8 + x)5 + 2x = 8.5 + x.5 + 2x Distributive Property
- = 40 +5x + 2x Substitution Property

The Distributive Property

- Example 2
- Simplify each expression.
- (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

The Distributive Property

- Example 2
- Simplify each expression.
- (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

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