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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

1-5 The Distributive Property

Objective: Simplify algebraic expressions using the distributive property.


5 minute check

5-Minute Check

Name the property shown by each statement.

  • (4b)c = 4(bc)


5 minute check1

5-Minute Check

Name the property shown by each statement.

  • (4b)c = 4(bc)associative, X


5 minute check2

5-Minute Check

Name the property shown by each statement.

  • (4b)c = 4(bc)

  • (7 + 4)0 = 0


5 minute check3

5-Minute Check

Name the property shown by each statement.

  • (4b)c = 4(bc)

  • (7 + 4)0 = 0mult. prop. of 0


5 minute check4

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 check5

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 check6

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 check7

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 check8

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 check9

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

The Distributive Property


The distributive property1

The Distributive Property

Example 1

Find 11(13) mentally using the distributive property.


The distributive property2

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 property3

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 property4

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 property5

The Distributive Property

  • Example 2

  • Simplify each expression.

  • 56x + 73x


The distributive property6

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 property7

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 property8

The Distributive Property

Example 2

Simplify each expression.

b. 5a + a


The distributive property9

The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

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


The distributive property10

The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

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

= (5 + 1)aDistributive property


The distributive property11

The Distributive Property

Example 2

Simplify each expression.

b. 5a + a

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

= (5 + 1)aDistributive property

= 6a


The distributive property12

The Distributive Property

  • Example 2

  • Simplify each expression.

  • (8 + x)5 + 2x


The distributive property13

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 property14

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 property15

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 property16

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


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