Lesson 10 - Amazon S3...I can write each decimal as an improper fraction and multiply. The...
Transcript of Lesson 10 - Amazon S3...I can write each decimal as an improper fraction and multiply. The...
40
©C
urricu
lum
Associates, L
LC
C
opying is n
ot permitted.
Practice Lesson 10 Multiply and D
ivide Decim
alsU
nit 2
Practice and Prob
lem Solvin
gU
nit 2 The N
umb
er System
Key
B Basic M Medium C Challenge
©Curriculum Associates, LLC Copying is not permitted. 99Lesson 10 Multiply and Divide Decimals
Name: Multiply and Divide Decimals
Lesson 10
Prerequisite: Multiply Decimals to Hundredths
Study the example showing how to multiply a decimal by a decimal. Then solve problems 1–7.
1 Explain why the factor 1 5 is broken into two numbers in the model
2 What does each small square in the model represent?
3 How would the area model change if the factor 0 4 were changed to 1 4?
Example
Find 1 5 3 0 4
You can use an area model to multiply tenths by tenths
0.4
1.5 3 0.4 5 0.4 1 0.2 5 0.6
1 1 3 0.4 5 0.4
0.5 3 0.4 5 0.20 5 0.20.5
9999
Possible explanation: 1.5 has both ones and tenths.
Possible answer: There would be 10 more columns of 15 small squares each.
one hundredth
B
B
M
©Curriculum Associates, LLC Copying is not permitted.100 Lesson 10 Multiply and Divide Decimals
Solve.
Use the situation below to solve problems 4–5.
Lisa walks at a speed of 3 25 miles per hour for 1 5 hours How many miles does she walk in all?
4 Complete the area model that represents 1 5 3 3 25
5 Explain how you can use the area model to fi nd the number of miles that Lisa walks
6 Moira multiplies 1 8 by 2 4 and writes the product as 0 432 Tom says that her product is incorrect How could Tom know this without multiplying the two numbers?
7 Andrew lives 1 7 kilometers from the soccer fi eld He rode his bike 0 9 of the distance to the fi eld How much farther does Andrew need to ride to reach the soccer fi eld? Include an area model in your answer
Show your work.
Solution:
3 0 25
1 1 3 5 3 1 3 5
0 5 3 3 5 1 5 3 5
100
1 0.7
0.9 0.9 0.63
1.7 3 0.9 5 0.9 1 0.63 5 1.531.7 2 1.53 5 0.17
Andrew needs to ride 0.17 kilometer farther.
M
M
M
I can add the partial products. 3 1 1.5 1 0.25 1 0.125 5 4.875 miles
Possible answer: Tom estimated the answer as 2 times 2, or 4.
C
3
0.5
0.250.25
0.1250.250.5
41©
Cu
rriculu
m A
ssociates, LL
C
Copyin
g is not perm
itted.Practice an
d Problem
Solving
Unit 2 Th
e Num
ber System U
nit 2Practice Lesson 10 M
ultiply and Divide D
ecimals
©Curriculum Associates, LLC Copying is not permitted. 101Lesson 10 Multiply and Divide Decimals
Name: Lesson 10
Multiply Decimals to Thousandths
Study the example problem showing how to multiply decimals to thousandths. Then solve problems 1–7.
1 How does your estimate help you place the decimal point in the product?
2 How can you use fractions to place the decimal point in the product?
3 How does the number of decimal places in the factors relate to the number of decimal places in the product of the example?
Example
A scientist used 4 317 liters of a chemical for one experiment She uses 1 75 times that amount for another experiment How much of the chemical does the scientist use for the second experiment?
First, estimate Because 4 317 is about 4 and 1 75 is about 2, the product will be about 4(2) 5 8
The scientist uses 7 55475 liters of the chemical for the second experiment
4 3173 1 75
21585
302190
1 431700
7 55475
Multiply decimals as you would multiply whole numbers Remember to place the decimal point in the product
101
The answer is around 8, so I can place the decimal point so that the product is around 8.
I can write each decimal as an improper fraction and multiply. The denominator of the
fraction product will tell me how many decimal places the product will have.
There are 3 decimal places in the first factor, 2 decimal places in the second factor, and
5 decimal places in the product. The number of decimal places in the product equals
the sum of the number of decimal places in the factors.
B
B
B
©Curriculum Associates, LLC Copying is not permitted.102 Lesson 10 Multiply and Divide Decimals
Solve.
4 Without multiplying, tell whether the product 0 644 3 0 25 will be greater than 1 or less than 1? Explain how you know Then fi nd the product
5 Selena drove at an average speed of 50 55 miles per hour for 1 75 hours She stopped at a rest stop and then drove at an average speed of 45 2 miles per hour for 2 25 hours Did Selena drive more miles before or after the rest stop? How many more miles?
Show your work.
Solution:
6 Estimate the product of 23 725 3 6 25 Then fi nd the product Why is it a good idea to estimate fi rst?
7 Ellen walks dogs on weekends She gets paid $8 50 per hour Each day she works 5 hours and 45 minutes Does she earn more or less than $85 in one weekend? How much more or less? Explain
102
Possible explanation: the product will be less than 1 because 0.644 and 0.25 are both
less than 1; The product of 0.644 3 0.25 is 0.16100, which is equal to 0.161.
Selena drove 13.2375 more miles after the rest stop.
Possible estimate: 144; product: 148.28125; Because it helps me place the decimal
point.
Ellen works more than 10 hours in one weekend, so she earns more than $85, or $8.50 3
10. She works 1.5 hours more, so she earns $8.50 3 1.5, or $12.75, more than $85.
Possible student work:
101.7 2 88.4625 5 13.2375
50.553 1.75
25275
35385
1 5055
88.4625
45.23 2.25
2260
904
1 904
101.700
M
C
M
C
42©
Cu
rriculu
m A
ssociates, LL
C
Copyin
g is not perm
itted.Practice an
d Problem
Solving
Unit 2 Th
e Num
ber System
Unit 2
Practice Lesson 10 Multiply and D
ivide Decim
als
©Curriculum Associates, LLC Copying is not permitted.104 Lesson 10 Multiply and Divide Decimals
Solve.
5 Emma made a mistake when she divided 6 4 by 0 02 Describe her mistake and show the correct division
6 Aaron paid $9 75 for markers that cost $0 75 each He bought 4 times as many pencils for $0 35 each How much did Aaron pay for the pencils?
Show your work.
Solution:
7 Mei spent $66 buying fabric that costs $7 50 per yard How many yards of fabric did Mei buy? How do you know that your answer is reasonable?
0 02 q ······ 6 4 32
2 q ······ 64 2 6
42 4
0
104
Possible explanation: She multiplied the
dividend by 10. She should have multiplied the
dividend by 100, as she did with the divisor.
Possible student work:
First, I need to divide 9.75 by 0.75, which is 975 4 75.
Aaron paid $18.20 for the pencils.
8.8 yards; Using estimation, $66 4 $7.50 is about $64 4 $8 5 8. So 8.8 yards
is reasonable.
M
M
C
He bought 13 markers, which means that he bought 52 pencils. So I can multiply $0.35 by 52.
1375 q ······ 975 2 75
2252 225
0
0.353 52
070
1 175
18.20
3202 q ······ 640 2 6
402 40
0
©Curriculum Associates, LLC Copying is not permitted. 103Lesson 10 Multiply and Divide Decimals
Name: Lesson 10
Divide by Decimals
Study the example problem showing how to divide by decimals. Then solve problems 1–7.
1 Why was the divisor changed to a whole number?
2 How do you change 0 35 to a whole number?
3 Why must you multiply the dividend by the same power of 10 that you multiplied the divisor by to write it as a whole number?
4 Complete the equation to show that 4 2 4 0 35 is equivalent to 420 4 35
4 2 4 0 35 5 ———––– 3 ———––– 5 ———––– 5 420 4 35
Example
Jamie has 4 2 pounds of dried fruit to put into bags She puts 0 35 pound of fruit in each bag How many bags of dried fruit does she have?
First, estimate Because 4 2 is about 4 and 0 35 is about 0 4, the quotient is about 4 divided by 4 tenths, or 10
Next, write the divisor as a whole number by multiplying it by a power of 10 Multiply the dividend by that same power Then divide as you would with whole numbers
Jamie has 12 bags of dried fruit
0 35 q ······ 4 20 12
35 q ······ 420 2 35
702 70
0
103
Possible answer: It is easier to divide by a whole number than by a decimal.
multiply by 100; to keep the relationship between the numbers equivalent to the one
in the problem
multiply by 100
B
B
B
B
4.2 100 420
0.35 100 35
43©
Cu
rriculu
m A
ssociates, LL
C
Copyin
g is not perm
itted.Practice an
d Problem
Solving
Unit 2 Th
e Num
ber System U
nit 2Practice Lesson 10 M
ultiply and Divide D
ecimals
©Curriculum Associates, LLC Copying is not permitted. 105Lesson 10 Multiply and Divide Decimals
Name:
Divide Decimals
Study the example problem showing how to divide decimals by using an algorithm. Then solve problems 1–6.
1 In the example, the dividend and divisor were multiplied by what power of 10? Explain why they were multiplied by this power of 10
2 Complete the equation to show that 19 625 4 2 5 is equivalent to 196 25 4 25
3 Would the quotient be the same if you multiplied the numerator and the denominator by 100? Explain
Example
Tanisha rode her bike 19 625 miles in 2 5 hours What was her average speed?
First, estimate Because 19 625 is about 20, the quotient is about 20 divided by 2 5, or 8 Next divide 19 625 by 2 5
Tanisha’s average speed was 7 85 miles per hour
Lesson 10
2 5 q ······ 19 625 7 85
25 q ······ 196 25 2 175
2122 200
1252 125
0
19 625 4 2 5 5 ————– 3 ————– 5 ————– 5 196 25 4 25
105
They were both multiplied by 10 so that the divisor 2.5 became a whole number.
Yes; Possible explanation: Dividing 1962.5 by 250 is equivalent to dividing
196.25 by 25.
B
M
M
19.625 10 196.25
2.5 10 25
©Curriculum Associates, LLC Copying is not permitted.106 Lesson 10 Multiply and Divide Decimals
Solve.
Use the information below to solve problems 4–5.
Jake bought 14 5 pounds of dried navy beans for $25 52
4 Explain how to estimate the price per pound
5 What is the price per pound of the beans? Explain how you know that your answer is reasonable
Show your work.
Solution:
6 Jeff is training for a walkathon He walked 8 84 miles at an average speed of 3 4 miles per hour Then he walked for an additional 1 6 hours at the same speed How many hours did Jeff walk in all?
Show your work.
Solution:
106
Possible explanation: I know that 14.5 is close to 15 and $25.52 is close to $30.
Because 30 4 15 5 2, a reasonable estimate is $2 per pound.
Possible student work:25.52 4 14.5 5 255.2 4 145
The price per pound is $1.76. Possible explanation: The answer is reasonable
because it is close to $2, the estimated price per pound.
Jeff walked for a total of 2.6 1 1.6 5 4.2 hours.
1.76145 q ······ 255.20
2 145
11022 1015
8702 870
0
Possible student work:For the first part, the number of hours Jeff walked is 8.84 4 3.4 5 88.4 4 34.
2.6 1 1.6 5 4.2 hours
2.634 q ······ 88.4 2 68
2042 204
0
C
M
M
44
©C
urricu
lum
Associates, L
LC
C
opying is n
ot permitted.
Practice and Prob
lem Solvin
gU
nit 2 The N
umb
er System
Unit 2
Practice Lesson 10 Multiply and D
ivide Decim
als
©Curriculum Associates, LLC Copying is not permitted.108 Lesson 10 Multiply and Divide Decimals
5 Hillary earned $17 92 weeding gardens for 3 2 hours She was paid the same hourly rate to mow lawns Hillary mowed lawns for 2 75 hours How much did Hillary earn mowing lawns?
Show your work.
Solution:
Solve.
3 Is each expression equivalent to 23 6 4 4 02? Select Yes or No
a. 2 36 4 40 2 u Yes u No
b. 2360 4 402 u Yes u No
c. 2 36 4 0 402 u Yes u No
d. 236 4 4020 u Yes u No
4 Isabel’s car gets 33 5 miles per gallon Her gas tank holds 15 1 gallons of gas How many miles can Isabel drive on a full tank of gas?
A 2 22 miles C 505 85 miles
B 22 2 miles D 5,058 5 miles
John chose D as the correct answer How did he get that answer?
How can you use estimation to determine whether your answer makes sense?
Do you multiply or divide to find the hourly rate?
How can you tell whether each quotient is equivalent to the original problem?
108
333
3
Possible student work:
17.92 4 3.2 5 179.2 4 32
5.632 q ······ 179.2 2 160
192 2 192
0
2.753 5.6
1650
1 1375
15.400
Hillary earned $15.40 mowing lawns.
He multiplied correctly, but he did not place the
decimal point correctly.
C
M
M
©Curriculum Associates, LLC Copying is not permitted. 107Lesson 10 Multiply and Divide Decimals
Name: Lesson 10
Multiply and Divide Decimals
Solve the problems.
2 Which expressions represent the model? Select all that apply
A 0 84
B 0 6 1 0 4
C 0 6 1 0 24
D 1 4 3 0 6
1 A total of 6 825 inches of snow fell during a storm The snow fell at an average rate of 1 3 inches per hour For how many hours did the snow fall?
Show your work.
Solution:
How many decimal places are in the divisor?
What does each small square in the model represent?0.6
1
0.4
107
6.825 4 1.3 5 68.25 4 13
The snow fell for 5.25 hours.
B
M
5.2513 q ······ 68.25 2 65
322 26
652 65
0