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1-5 The Distributive Property

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1-5 The Distributive Property

Objective: Simplify algebraic expressions using the distributive property.

Name the property shown by each statement.

- (4b)c = 4(bc)

Name the property shown by each statement.

- (4b)c = 4(bc)associative, X

Name the property shown by each statement.

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

Name the property shown by each statement.

- (4b)c = 4(bc)
- (7 + 4)0 = 0mult. prop. of 0

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

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 + 740

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

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 . 5210

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?

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

Example 1

Find 11(13) mentally using the distributive property.

Example 1

Find 11(13) mentally using the distributive property.

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

Example 1

Find 11(13) mentally using the distributive property.

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

=11.10 + 11.3Think of 110 + 33.

Example 1

Find 11(13) mentally using the distributive property.

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

=11.10 + 11.3Think of 110 + 33.

= 110 + 33 or 143

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

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

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

Example 2

Simplify each expression.

b. 5a + a

Example 2

Simplify each expression.

b. 5a + a

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

Example 2

Simplify each expression.

b. 5a + a

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

= (5 + 1)aDistributive property

Example 2

Simplify each expression.

b. 5a + a

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

= (5 + 1)aDistributive property

= 6a

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

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

- 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)xDistributive 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)xDistributive Property
- = 40 + 7xSubstitution Property