Lesson 2.7, For use with pages 88-92

Evaluate the expression.

1. 14 + 38 + 16 2. 47 – 9 • 3

Lesson 2.7, For use with pages 88-92

ANSWER 20ANSWER 68

Evaluate the expression.

1. 14 + 38 + 16 2. 47 – 9 • 3

Distributive Property2.7

Vocabulary• Coefficient (of a variable): the number in

front of the variable.2x, 5ab, x think (1)x, -y think (-1)y

• Like terms: terms that have the same variable raised to the same power.

3x and -8x are like terms

5xy2 and xy2 are like terms

• Constant terms- plain numbers – no variable attached. 3x +7, x2 – 5x - 9

• 5x – 2y + 8x -7

– Coefficients

• 5, -2, 8

– Like Terms

• 5x and 8x

– Constant terms

• -7

Distributive PropertyWords You can multiply a number and a sum by

multiplying the number by each part of the sum and then adding these products. The same property applies to subtraction.

Algebra a(b+c) = ab + ac a(b-c) = ab - ac

Numbers 6(4+3) = 6(4) + 6(3) 7(8-5) = 7(8) – 7(5)

There is an error in your textbook so make sure you write down the algebra and numbers part in your notes.

5(10 + 8) =

Look at this example. If you followed the order order of operationsof operations, what would you do first?

Now if you had 5(18) could you do that in mentally?

• 5(10 + 8) =

• If you used the distributive property, what would you do first?

• Now 5(10) + 5(8)

50 + 40 = 90

• Use the distributive property to simply each expression:

12(-10 + -2) = 12( ) + 12 ( )

8( -3 - 6) = Think 8 ( -3 + -6)

2( 4 + 5 + 10)

7 ( 43) =

EXAMPLE 2 Using the Distributive Property

a. –5(x + 10) = –5x + (–5)(10) Distributive property

= –5x + (–50) Multiply.

b. 3(x + 8) = 3x + (3)(8) Distributive property

= 3x + 24 Multiply.

EXAMPLE 2 Using the Distributive Property

c. 3[1 – 20 + (–5)] = 3(1) – 3(20) + 3(–5)

= 3 – 60 + (–15)

= 3 + (–60) + (–15)

= –72

Distributive property

Multiply.

Add the opposite of 60.

Add.

Find the difference mentally.

Find the products mentally.

The mental math is easier if you think of $11.95 as $12.00 – $.05.

Write 11.95 as a difference.

You are shopping for CDs.You want to buy six CDs

for $11.95 each.

Use the distributive property

to calculate the total cost mentally.

6(11.95) = 6(12 – 0.05)

Use the distributive property.

= 6(12) – 6(0.05)

= 72 – 0.30

= 71.70

The total cost of 6 CDs at $11.95 each is $71.70.

SOLUTION

• You want to buy 4 tires for $45 each. Use the distributive property to calculate the total cost mentally.

• The Drama Club is selling candy bars for $1.20 each. You buy 15. Use the distributive property to calculate the total mentally.

Homework • Page 90 #1-21