# 1-5 The Distributive Property - PowerPoint PPT Presentation

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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). 5-Minute Check. Name the property shown by each statement. (4b)c = 4(bc) associative, X. 5-Minute Check.

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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.

### 5-Minute Check

Name the property shown by each statement.

• (4b)c = 4(bc)

### 5-Minute Check

Name the property shown by each statement.

• (4b)c = 4(bc)associative, X

### 5-Minute Check

Name the property shown by each statement.

• (4b)c = 4(bc)

• (7 + 4)0 = 0

### 5-Minute Check

Name the property shown by each statement.

• (4b)c = 4(bc)

• (7 + 4)0 = 0mult. prop. of 0

### 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 + 740

### 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 . 5210

### 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.

### 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 + 11.3Think 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 + 11.3Think 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)xx is a factor in both 56x and 73x.

### The Distributive Property

• Example 2

• Simplify each expression.

• 56x + 73x

• 56x + 73x = (56 + 73)xx is a factor in both 56x and 73x.

• = 129xUse the distributive property.

### The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

### 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.

### The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

5a + a = 5a + 1a a = 1.a by multiplicative 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)xDistributive 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)xDistributive Property

• = 40 + 7xSubstitution Property