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use the distributive property in equations and
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expressions with variables.
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UNDERLYING SKILLS AND CONCEPTS:
understand the distributive property;
use letters for the unknown;
solve for the unknown
Use the Distributive Property
You can use the distributive property to solve equations
with unknowns.
Remember, the distributive property states that multiplying
a sum by a number is the same as multiplying each addend
by the number and then adding the products.
First simplify the expression with the variable.
Then use mental math to solve.
E x am p l E
1
Find the value of y in
Find the value of a in
(20 ! y) " (5 ! y) # 100
Find the common element. Each part is
multiplied by y.
(200 ! a) " (4 ! a) # 408
Find the common element.
Each part is multiplied by a.
(20 " 5) ! y # 25y
(200 " 4) ! a # 408
So, (20 ! y) " (5 ! y) # 25y.
Then use mental math to solve for y.
25y # 100
408
204a # $
204
y# 4
a# 2
E x am p l E
2
Find the value of y in
(100 ! y) " (20 ! y) " (2 ! y) # 366.
You know that 100, 20, and 2 are the parts of one number.
These parts are multiplied by the other number, y.
So, (100 ! y) " (20 ! y) " (2 ! y) is the same as
(100 " 20 " 2) ! y
The equation can be written
Divide each side by 122.
122 ! y # 366
This is like
122
! y
366
122
366
122 ! y # $
122
y# 3
page 112
Chapter 10 – Lesson 2
E – © CSL Associates, Inc. All rights reserved.
204a # 408
Name
P RAC T I C E
Use the distributive property to find the value of each unknown. Show your work.
1. (10 y) (2 y) 36
2. (100 b) (20 b) (2 b) 244
(10 2) y 36
12 y 36
y3
3. (10 y) (2 y) 60
(100 20 2) b 244
122 b 244
b 2
4. (100 b) (30 b) (4 b) 670
(10 2) y 60
12 y 60
y5
5. (20 y) (5 y) 75
(100 30 4) b 670
134 b 670
b 5
6. (1,000 y) (2 y) 2,004
(20 5) y 75
25 y 75
y3
E – © CSL Associates, Inc. All rights reserved.
7. (20 a) (4 a) 48
(1,000 2) y 2,004
1,002 y 2,004
y 2
8. (10,000 x) (8 x) 20,016
(20 4) a 48
24 a 48
a2
Solve.
9. Mai-lin has 8 boxes of computer disks.
Tyrone has 30 boxes of disks. Together
they have 380 computer disks. How
many disks are in each box?
(10,000 8) x 20,016
10,008 x 20,016
x 2
(8 d) (30 d) 380
38 d 380
d 380 38
d 10
Math
Reasoning
Algebra Challenge
MR 3.3
10. The value of the unknown depends on the particular equation. Can you find two
different equations for which the unknown x has the same value?
Many possible answers. For example 20 x 100 and
3 x 15, x 5 in both equations.
Chapter 10 – Lesson 2
page 113
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:02
Page 76
Name
…at home!
P RAC T I C E
Use the distributive property to find the value of each unknown. Show your work.
1. (10 y) (2 y) 48
2. (100 b) (20 b) (2 b) 366
(10 2) y 48
12 y 48
y4
4. (100 b) (30 b) (4 b) 804
(10 5) y 75
15 y 75
y5
5. (20 y) (5 y) 100
(100 30 4) b 804
134 b 804
b 6
6. (1,000 y) (2 y) 4,008
(20 5) y 100
25 y 100
y4
7. (20 a) (4 a) 120
(1,000 2) y 4,008
1,002 y 4,008
y 4
8. (10,000 x) (8 x) 30,024
(20 4) a 120
24 a 120
a5
Solve.
9. Emeline has 6 boxes of computer disks.
(10,000 8) x 30,024
10,008 x 30,024
x 3
(6 d) (20 d) 260
Tei Li has 20 boxes of disks. Together
they have 260 computer disks. How
many disks are in each box?
26 d 260
d 260 26
d 10
Math
Reasoning
Algebra Challenge
MR 3.3
10. The value of the unknown depends on the particular equation. Can you find two
different equations for which the unknown x has the same value?
Many possible answers. For example 20 x 100 and
3 x 15, x 5 in both equations.
page 76
Home Resource and Homework
Chapter 10 Lesson 2
E – © CSL Associates, Inc. All rights reserved.
3. (10 y) (5 y) 75
(100 20 2) b 366
122 b 366
b 3
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:45 Page 209
Name
P RAC T I C E
Use the distributive property to find the value of each unknown. Show your work.
1. (10 y) (2 y) 36
2. (100 b) (20 b) (2 b) 244
(10 2) y 36
12 y 36
y3
(100 20 2) b 244
122 b 244
b 2
3. (10 y) (2 y) 60
4. (100 b) (30 b) (4 b) 670
(10 2) y 60
12 y 60
y5
(100 30 4) b 670
134 b 670
b 5
5. (20 y) (5 y) 75
6. (1,000 y) (2 y) 2,004
(20 5) y 75
25 y 75
y3
(1,000 2) y 2,004
1,002 y 2,004
y 2
E – © CSL Associates, Inc. All rights reserved.
7. (20 a) (4 a) 48
8. (10,000 x) (8 x) 20,016
(20 4) a 48
24 a 48
a2
(10,000 8) x 20,016
10,008 x 20,016
x 2
Solve.
9. Mai-lin has 8 boxes of computer disks.
(8 d) (30 d) 380
Tyrone has 30 boxes of disks. Together
they have 380 computer disks. How
many disks are in each box?
38 d 380
d 380 38
d 10
Math
Reasoning
Algebra Challenge
MR 3.3
10. The value of the unknown depends on the particular equation. Can you find two
different equations for which the unknown x has the same value?
Many possible answers. For example 20 x 100 and
3 x 15, x 5 in both equations.
Chapter 10 – Lesson 2
Student Book Page
page 113
Name
…at home!
P RAC T I C E
Use the distributive property to find the value of each unknown. Show your work.
1. (10 y) (2 y) 48
2. (100 b) (20 b) (2 b) 366
(10 2) y 48
12 y 48
y4
4. (100 b) (30 b) (4 b) 804
(10 5) y 75
15 y 75
y5
5. (20 y) (5 y) 100
(100 30 4) b 804
134 b 804
b 6
6. (1,000 y) (2 y) 4,008
(20 5) y 100
25 y 100
y4
7. (20 a) (4 a) 120
(1,000 2) y 4,008
1,002 y 4,008
y 4
8. (10,000 x) (8 x) 30,024
(20 4) a 120
24 a 120
a5
Solve.
9. Emeline has 6 boxes of computer disks.
Tei Li has 20 boxes of disks. Together
they have 260 computer disks. How
many disks are in each box?
(10,000 8) x 30,024
10,008 x 30,024
x 3
(6 d) (20 d) 260
26 d 260
d 260 26
d 10
Math
Reasoning
Algebra Challenge
MR 3.3
10. The value of the unknown depends on the particular equation. Can you find two
different equations for which the unknown x has the same value?
Many possible answers. For example 20 x 100 and
3 x 15, x 5 in both equations.
page 76
Home Resource and Homework
Chapter 10 Lesson 2
E – © CSL Associates, Inc. All rights reserved.
3. (10 y) (5 y) 75
(100 20 2) b 366
122 b 366
b 3