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8VHSDUHQWKHVHVEUDFNHWVRUEUDFHVLQQXPHULFDOH[SUHVVLRQV
AF 1.3*2$
Know and
use the distributive property in equations and
DQGHYDOXDWHH[SUHVVLRQVZLWKWKHVHV\PEROV
UNDERLYING SKILLS AND CONCEPTS:
expressions with variables.
use basic multiplication facts;
multiply with 1- and 2-digit multipliers;
understand expanded notation
Understand the Distributive Property
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.
215 ! 3 " (200 ! 3) # (10 ! 3) # (5 ! 3)
I do?
Sounds complicated!
3 is the multiplier. You have distributed 3 over 215.
E x am p l E
1
Find the product.
185
! 9
I remember!
74
185
! 9
1,665
Write the problem in distributed form.
(80 ! 9)
720
E x am p l E
#
#
(5 ! 9)
45
" 1,665
2
Use the distributive property.
Write a simpler multiplication problem.
Then solve.
I get it!
P stands for product.
(5 ! 6) # (70 ! 6) # (800 ! 6) " P
Step 1. Find the multiplier common to each part.
Each part is multiplied by 6.
Step 2. Rewrite the equation using 6 only once.
6 ! (5 # 70 # 800) " P
Step 3. Find the sum in parentheses.
6 ! 875 " P
Step 4. Complete the computation.
5,250 " P
page 100
Looks like a
number in expanded
notation.
Chapter 9 – Lesson 2
E – © CSL Associates, Inc. All rights reserved.
(100 ! 9) #
900
#
Name
P RAC T I C E
Rewrite each problem in distributed form. Then solve.
1. 379
2.
300 8 2,400
8
70 8 98
560
72
3,032
12.69
15
10 15
2 15
0.6 15
0.09 15
150
30
9
1.35
190.00
Rewrite each expression in simpler form.
3. (200 7) (90 7) (5 7) 295 7 or 7 295
4. (1 5) (0.3 5) (0.05 5) 1.35 5 or 5 1.35
5. (7,000 9) (600 9) (50 9) (3 9)
7,653 9 or 9 7,653
6. (10 125) (3 125) (0.7 125) (0.5 125)
13.75 125 or 125 13.75
7. (7 8) (7 0.3) (7 0.07) (7 0.005)
7 8.375 or 8.375 7
8. (12 1,000) (12 200) (12 50) (12 0)
12 1,250 or 1,250 12
Circle the correct answer. Explain how you decided.
E – © CSL Associates, Inc. All rights reserved.
9. A warehouse sold 4 boxes with 200 pens 10. Sandra has 6 sheets of stamps with 200
in each box, 4 boxes with 60 pens in
each, and 4 boxes with 5 pens each.
Which expression cannot be used to
solve the problem?
A (4 200) (60 5)
B 4 (200 60 5)
C (200 4) (60 4) (5 4)
D 265 4
Math
Reasoning
on each sheet. She has 6 sheets with 70
on each sheet. She has 6 strips with 5 on
each strip. How many stamps does
Sandra have?
A
B
C
D
(6 200) (70 200) (5 200)
(6 200) (6 70) (6 5)
(206 76 11)
6 (200 70 5)
Algebra Challenge
MR 3.2
Look for a pattern. Identify the repeating element.
Write a simpler expression for each expression given.
11. (a b) (a c) (a d) 2
2
2
2
12. (n ) (p ) (q ) (s )
3
3
3
3
Chapter 9 – Lesson 2
a (b c d)
2
(n p q s)
3
page 101
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:02
Page 68
Name
…at home!
P RAC T I C E
Rewrite each problem in distributed form. Then solve.
2.
1. 228
200 9 1,800
9
20 9 89
180
72
2,052
10 12
3 12
0.4 12
0.06 12
13.46
12
120
36
4.8
0.72
161.52
Rewrite each expression in simpler form.
3. (300 7) (80 7) (4 7) 384 7 or 7 384
4. (2 5) (0.6 5) (0.07 5) 2.67 5 or 5 2.67
5. (4,000 9) (500 9) (60 9) (7 9)
4,567 9 or 9 4,567
6. (20 125) (6 125) (0.4 125) (0.2 125)
26.6 125 or 125 26.6
7. (7 6) (7 0.2) (7 0.04) (7 0.008)
7 6.248 or 6.428 7
8. (14 3,000) (14 600) (14 40) (14 0)
14 3,640 or 3,640 14
Circle the correct answer. Explain how you decided.
10. Marjorie has 8 sheets of stamps with 200
200 pencils in each box, 6 boxes with
60 pencils in each, and 6 boxes with
5 pencils each. Which expression
cannot be used to solve the problem?
A (6 200) (60 5)
B 6 (200 60 5)
C (200 6) (60 6) (5 6)
D 265 6
Math
Reasoning
on each sheet. She has 8 sheets with
70 on each sheet. She has 8 strips with
5 on each strip. How many stamps does
Marjorie have?
A
B
C
D
(8 200) (70 200) (5 200)
(8 200) (8 70) (8 5)
(208 786 11)
8 (200 70 5)
Algebra Challenge
MR 3.2
Look for a pattern. Identify the repeating element.
Write a simpler expression for each expression given.
11. (e f) (e g) (e h) e (f g h)
2 (a b c d)
2 ) (b 2 ) (c 2 ) (d 2 ) 12. (a 5
5
5
5
5
page 68
Home Resource and Homework
Chapter 9 Lesson 2
E – © CSL Associates, Inc. All rights reserved.
9. A warehouse sold 6 boxes with
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:44 Page 187
Name
P RAC T I C E
Rewrite each problem in distributed form. Then solve.
1. 379
2.
300 8 2,400
8
70 8 98
560
72
3,032
12.69
15
10 15
2 15
0.6 15
0.09 15
150
30
9
1.35
190.00
Rewrite each expression in simpler form.
3. (200 7) (90 7) (5 7) 295 7 or 7 295
4. (1 5) (0.3 5) (0.05 5) 1.35 5 or 5 1.35
5. (7,000 9) (600 9) (50 9) (3 9)
7,653 9 or 9 7,653
6. (10 125) (3 125) (0.7 125) (0.5 125)
13.75 125 or 125 13.75
7. (7 8) (7 0.3) (7 0.07) (7 0.005)
7 8.375 or 8.375 7
8. (12 1,000) (12 200) (12 50) (12 0)
12 1,250 or 1,250 12
Circle the correct answer. Explain how you decided.
E – © CSL Associates, Inc. All rights reserved.
9. A warehouse sold 4 boxes with 200 pens 10. Sandra has 6 sheets of stamps with 200
in each box, 4 boxes with 60 pens in
each, and 4 boxes with 5 pens each.
Which expression cannot be used to
solve the problem?
A (4 200) (60 5)
B 4 (200 60 5)
C (200 4) (60 4) (5 4)
D 265 4
Math
Reasoning
on each sheet. She has 6 sheets with 70
on each sheet. She has 6 strips with 5 on
each strip. How many stamps does
Sandra have?
A
B
C
D
(6 200) (70 200) (5 200)
(6 200) (6 70) (6 5)
(206 76 11)
6 (200 70 5)
Algebra Challenge
MR 3.2
Look for a pattern. Identify the repeating element.
Write a simpler expression for each expression given.
11. (a b) (a c) (a d) 2
2
2
2
12. (n ) (p ) (q ) (s )
3
3
3
3
Chapter 9 – Lesson 2
a (b c d)
2
(n p q s)
3
Student Book Page
page 101
Name
…at home!
P RAC T I C E
Rewrite each problem in distributed form. Then solve.
2.
1. 228
200 9 1,800
9
20 9 89
180
72
2,052
10 12
3 12
0.4 12
0.06 12
13.46
12
120
36
4.8
0.72
161.52
Rewrite each expression in simpler form.
3. (300 7) (80 7) (4 7) 384 7 or 7 384
4. (2 5) (0.6 5) (0.07 5) 2.67 5 or 5 2.67
5. (4,000 9) (500 9) (60 9) (7 9)
4,567 9 or 9 4,567
6. (20 125) (6 125) (0.4 125) (0.2 125)
26.6 125 or 125 26.6
7. (7 6) (7 0.2) (7 0.04) (7 0.008)
7 6.248 or 6.428 7
8. (14 3,000) (14 600) (14 40) (14 0)
14 3,640 or 3,640 14
Circle the correct answer. Explain how you decided.
10. Marjorie has 8 sheets of stamps with 200
200 pencils in each box, 6 boxes with
60 pencils in each, and 6 boxes with
5 pencils each. Which expression
cannot be used to solve the problem?
A (6 200) (60 5)
B 6 (200 60 5)
C (200 6) (60 6) (5 6)
D 265 6
Math
Reasoning
on each sheet. She has 8 sheets with
70 on each sheet. She has 8 strips with
5 on each strip. How many stamps does
Marjorie have?
A
B
C
D
(8 200) (70 200) (5 200)
(8 200) (8 70) (8 5)
(208 786 11)
8 (200 70 5)
Algebra Challenge
MR 3.2
Look for a pattern. Identify the repeating element.
Write a simpler expression for each expression given.
11. (e f) (e g) (e h) e (f g h)
2
2
2
2
2
12. (a ) (b ) (c ) (d ) (a b c d)
5
5
5
5
5
page 68
Home Resource and Homework
Chapter 9 Lesson 2
E – © CSL Associates, Inc. All rights reserved.
9. A warehouse sold 6 boxes with