NAME ______________________________________________ DATE
3-1 The Distributive Property
____________ PERIOD _____
(Pages 98–102)
The Distributive Property allows you to combine addition and
multiplication. For example, 5(3 1) can be evaluated in two ways.
First, we will evaluate 5(3 1) by using the order of operations.
5(3 1) 5 (3 1) 5 (4) 20. In this method we added first
because the order of operations requires arithmetic within grouping
symbols be completed first. Now let’s do the same problem by
multiplying first.
5(3 1) 5 (3 1) 5 3 5 1 15 5 20. The second method
demonstrates the Distributive Property.
Distributive Property
To multiply a number by a sum, multiply each number in the sum by the number next to
the parenthesis.
a(b c) ab ac or (b c)a ba ca
Examples
a. 10(4 7)
10 4 10 7
40 70
Use the Distributive Property to write each expression
as an equivalent expression.
b. (5 2)6
[5 (2)]6
5 6 (2) 6
30 (12)
Distributive Property
Multiplication
Rewrite 5 2 as 5 (2).
Distributive Property
Try These Together
Restate each expression as an equivalent expression using the Distributive Property.
1. 6(7 2)
2. 4(9 4)
3. 3(5 1)
4. 2(8 3)
Practice
Use the Distributive Property to write each expression as an
equivalent expression. Then evaluate the expression.
5. 2(6 1)
9. (7 2)4
6. 13(10 7)
10. 2(7 6)
7. 11(3 9)
11. 9(7 9)
8. [21 (14)]5
12. (6 3)5
Use the Distributive Property to write each expression as an
equivalent algebraic expression.
13. 7(x 2)
14. 5(b 8)
15. (q 9)4
16. 3(c 6)
17. (m 2)10
18. 12(d 14)
19. 18(n 10)
20. 5(h 48)
21. Standardized Test Practice Use the Distributive Property to write an
equivalent algebraic expression for 22(x y z 13).
A 22x 22y 22z 286
B 22x y z 13
C 22x 22y 22z 286
D 22x 22y 22z 286
Answers: 1. 42 12 2. 36 (16) 3. 15 (3) 4. 16 6 5. 14 6. 39 7. 132 8. 175 9. 36 10. 2 11. 144
12. 15 13. 7x 14 14. 5b (40) 15. 4q 36 16. 3c (18) 17. 10m (20) 18. 12d (168) 19. 18n 180
20. 5h (240) 21. D
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Glencoe/McGraw-Hill
16
Glencoe Pre-Algebra