Multiplication and Division of Decimals using Models-Gr 5-Solved Examples

Solved Examples and Worksheet for Multiplication and Division of Decimals using Models

Q1Identify a number sentence that describes the model.

A. 0.5 × 0.6
B. 0.07 × 0.06
C. 0.5 × 0.7
D. 0.5 × 0.5

Solutions

Step: 1

0.5 can be shown as

Step: 2

0.7 can be shown as

Step: 3

0.5 × 0.7 can be shown as

Correct Answer is : 0.5 × 0.7

Q2Identify the fraction model that best represents the model 0.4 × 0.4.

A. Model 4
B. Model 1
C. Model 3
D. Model 2

Solutions

Step: 1

Step: 2

40 out of 100 squares are shaded in the above model represents 40 hundredths = 40100 = 25

Step: 3

Step: 4

40 out of 100 squares are shaded in the above model represents 40 hundredths = 40100 = 25

Step: 5

The fraction 25 can be shown as

Step: 6

The fraction 25 can be shown as

Step: 7

The fraction 25 × 25 can be shown as

Step: 8

So, Model 1 represents 25 × 25.

Correct Answer is : Model 1

Q3The model represents the product 0.3 × 0.8. Choose its equivalent fraction form.

A. 15 × 25
B. 12 × 35
C. 35 × 25
D. 310 × 45

Solutions

Step: 1

Step: 2

30 out of 100 squares are shaded in the model represents 30 hundredths = 30100 = 310

Step: 3

Step: 4

80 out of 100 squares are shaded in the model represents 80 hundredths = 80100 = 45

Step: 5

Step: 6

The above model represents the fraction form 310 × 45

Step: 7

So, the equivalent fraction form of the given model is 310 × 45 .

Correct Answer is : 310 × 45

Q4Identify a number sentence that describes the model.

A. 0.5 × 0.7
B. 0.9 × 0.2
C. 0.3 × 0.8
D. 0.06 × 0.03

Solutions

Step: 1

0.9 can be shown as

Step: 2

0.2 can be shown as

Step: 3

0.9 × 0.2 can be shown as

Step: 4

So, the number sentence is 0.9 × 0.2.

Correct Answer is : 0.9 × 0.2

Q5Identify the model for 0.9 × 0.1.

A. Model 4
B. Model 2
C. Model 1
D. Model 3

Solutions

Step: 1

0.9 can be shown as

Step: 2

0.1 can be shown as

Step: 3

0.9 × 0.1 can be shown as

Step: 4

So, model 2 represents the number sentence 0.9 × 0.1.

Correct Answer is : Model 2

Q6Identify a number sentence that describes the model.

A. 0.8 × 0.8
B. 0.9 × 0.9
C. 0.09 × 0.09
D. 0.9 × 0.8

Solutions

Step: 1

0.9 can be shown as

Step: 2

0.9 can be shown as

Step: 3

0.9 × 0.9 can be shown as

Step: 4

So, the number sentence is 0.9 × 0.9.

Correct Answer is : 0.9 × 0.9

Q7The model represents the product of 35 and 35. Choose its equivalent decimal form.

A. 0.6 × 0.6
B. 0.6 × 0.5
C. 0.4 × 0.5
D. 0.6 × 0.4

Solutions

Step: 1

The fraction 35 can be shown as

Step: 2

The above model represents the fraction 35 = 60100 = 60 hundredths = 0.6

Step: 3

The fraction 35 can be shown as

Step: 4

The above model represents the fraction 35 = 60100 = 60 hundredths = 0.6

Step: 5

Step: 6

So, the equivalent decimal form of the given model is 0.6 × 0.6.

Correct Answer is : 0.6 × 0.6

Q8The model represents the product of 0.8 × 0.8. Choose its equivalent fraction form.

A. 35 × 45
B. 25 × 45
C. 35 × 35
D. 45 × 45

Solutions

Step: 1

Step: 2

80 out of 100 squares are shaded in the above model represents 80 hundredths = 80100 = 45

Step: 3

Step: 4

80 out of 100 squares are shaded in the above model represents 80 hundredths = 80100 = 45

Step: 5

Step: 6

The above model represents the fraction form 45 × 45.

Step: 7

So, the equivalent form of the given model is 45 × 45.

Correct Answer is : 45 × 45

Q9Using models, find the quotient of 0.7 ÷ 0.07

A. 7
B. 0.01
C. 0.1
D. 10

Solutions

Step: 1

Model the decimal 0.7 as below

Step: 2

Circle groups of 0.07 as below.

Step: 3

There are 10 groups.

Step: 4

So, the quotient is 10.

[0.07 × 10 = 0.7]

Correct Answer is : 10

Q10Find the quotient of 2.1 ÷ 0.3.
A. 0.3
B. 5.4
C. 7
D. 6

Solutions

Step: 1

Model the decimal 2.1 as below.

Step: 2

Circle groups of 0.3 as below.

Step: 3

There are 7 groups.

Step: 4

So, the quotient is 7.

Correct Answer is : 7

Q11Using models, find the quotient of 0.4 ÷ 0.04.

A. 0.1
B. 10
C. 0.001
D. 0.01

Solutions

Step: 1

Model the decimal 0.4 as below.

Step: 2

Circle groups of 0.04 as below.

Step: 3

There are 10 groups.

Step: 4

So, the quotient is 10.

[0.04 × 10 = 0.4]

Correct Answer is : 10

Q12Find the quotient of 1.24 ÷ 0.02.

A. 12
B. 52
C. 62
D. 37

Solutions

Step: 1

Model the decimal 1.24 as shown.

Step: 2

Circle groups of 0.02 as shown

Step: 3

There are 62 groups.

Step: 4

So, the quotient is 62.

Correct Answer is : 62

Q13Find the quotient of 2.4 ÷ 0.2.
A. 5
B. 12
C. 14
D. 7

Solutions

Step: 1

Model the decimal 2.4 as shown.

Step: 2

Circle groups of 0.2 as shown.

Step: 3

There are 12 groups.

Step: 4

So, the quotient is 12.

Correct Answer is : 12

Q14Find the quotient of 2.2 ÷ 0.2.
A. 14
B. 11
C. 12
D. 8

Solutions

Step: 1

Model the decimal 2.2 as shown.

Step: 2

Circle groups of 0.2 as shown.

Step: 3

There are 11 groups.

Step: 4

So, the quotient is 11.

Correct Answer is : 11

Q15Find the quotient of 1.15 ÷ 0.05.

A. 1.3
B. 1.5
C. 25
D. 23

Solutions

Step: 1

Model the decimal 1.15 as shown.

Step: 2

Circle groups of 0.05 as shown.

Step: 3

There are 23 groups.

Step: 4

So, the quotient is 23.

Correct Answer is : 23

Solved Examples and Worksheet for Multiplication and Division of Decimals using Models

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HighSchool Math