Download Study Guide and Intervention The Distributive Property

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Study Guide and Intervention
The Distributive Property
Evaluate Expressions The Distributive Property can be used to help evaluate
expressrons.
.
p
For any numbers a, b, and c, a(b + c) = ab + ac and (b
Dlstri utrve roperty I a (b - c) = a b - ac an d (b - c) a = b a - ca.
'~'b
+ c)a = ba + ca and
Rewrite 6(8 + 10) using the Distributive Property. Then evaluate.
6(8 + 10)
=
6 . 8 + 6 . 10
=
48
=
108
Distributive Property
+ 60
Multiply.
Add.
.~
........
.~ +
1) using the Distributive Property.
. ""'Itive Property
.~.
(
13.2(3x
+ 2y -
<:J
1(
16. "4
16x - 12y + 4z).
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Glencoe/McGraw-Hili
17. (2 - 3x +
x~) ....
25
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_ _ _ _ _ PERIOD
Study Guide and Intervention
(continued)
The Distributive Property
Simplify Expressions A term is a number, a variable, or a product or quotient of
numbers and variables. Like terms are terms that contain the same variables, with
corresponding variables having the same powers. The Distributive Property and properties
of equalities can be used to simplify expressions. An expression is in simplest form if it is
replaced by an equivalent expression with no like terms or parentheses.
Simplify 4(a 2 + 3ab) - abo
4(a 2
--
3ab) - ab = 4(a 2 + 3ab) - lab
= 4a 2 + 12ab - lab
= 4a 2 + (12 - l)ab
= 4a 2 + 11ab
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Multiplicative Identity
Distributive Property
Distributive Property
Substitution
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Glencoe Algebra 1
NAME
DATE
_ _ _ _ _ PERIOD
Practice
The Distributive Property
Rewrite each expression using the Distributive Property. Then simplify.
1. 9(7 + 8)
2. 7(6 - 4)
3. 6(b + 4)
4. (9 - p)3
5. (5y - 3)7
6. 15 (f +
7. 16(3b - 0.25)
8. men + 4)
9. (c - 4)d
1\
3J
Use the Distributive Property to find each product.
10.9 . 499
11.7' 110
13.12 . 2.5
14.
12. 21 . 1004
15. 16(4 ~)
27(2~)
Simplify each expression. If not possible, write simplified.
16. w + 14w - 6w
17.3(5 + 6h)
20. 25t 3
22. 3a 2 + 6a + 2b 2
-
l.
18. 14(2r - 3)
17t 3
23.4(6p + 2q - 2p)
24. x +
2
x
3x + 3
DINING OUT For Exercises 25 and 26, use the following information.
The Ross family recently dined at an Italian restaurant. Each of the four family members
ordered a pasta dish that cost $11.50, a drink that cost $1.50, and dessert that cost $2.75.
25. Write an expression that could be used to calculate the cost of the Ross' dinner before
adding tax and a tip.
26. What was the cost of dining out for the Ross family?
ORIENTATION For Exercises 27 and 28, use the following information.
Madison College conducted a three-day orientation for incoming freshmen. Each day, an
average of 110 students attended the morning session and an average of 160 students
attended the afternoon session.
27. Write an expression that could be used to determine the total number of incoming
freshmen who attended the orientation.
28. What was the attendance for all three days of orientation?
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Glencoe Algebra 1