Relate Decimal and Fraction Multiplication

Examples, solutions, videos and lessons to help Grade 5 students learn how to relate decimal and fraction multiplication.

Common Core Standards: 5.NBT.7, 5.NF.4a, 5.NF.6, 5.MD.1, 5.NF.4b

New York State Common Core Math Module 4, Grade 5, Lesson 17, Lesson 18
Worksheets for Grade 5

Lesson 17 Problem Set

1. Multiply and model. Rewrite each expression as a multiplication sentence with decimal factors.
   b. 4/10 × 3/10
   d. 6/10 × 1.7
2. Multiply.
   d. 6 × 0.3 = _______
   e. 0.6 × 0.3 = _______
   f. 0.06 × 0.3 = _______
   g. 1.2 × 4 = _______
   h. 1.2 × 0.4 = _______
   i. 0.12 × 0.4 = _______

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Lesson 17 Homework

1. Multiply and model. Rewrite each expression as a number sentence with decimal factors.
   b. 6/10 × 2/10
   d. 6/10 × 1.9
2. Multiply.
   g. 1.3 × 5 = _______
   h. 1.3 × 0.5 = _______
   i. 0.13 × 0.5 = _______

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Lesson 17 Homework
This video shows how to convert fractions to decimals and decimals to fractions within a the operation of multiplication. Area models and place value charts are used to concretely demonstrate the meaning within the process.

1. Multiply and model. Rewrite each expression as a number sentence with decimal factors.
   a) 1/10 × 1/10
   c) 1/10 × 1.6
2. Multiply.
   a) 4 × 0.6
   b) 7 × 0.3
3. Jennifer makes 1.7 liters of lemonade. If she pours 3 tenths of the lemonade in the glass, how many liters of lemonade are in the glass?

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Lesson 17 Homework

1. Multiply and model. Rewrite each expression as a number sentence with decimal factors.
   a) 1/10 × 1/10
   c) 1/10 × 1.6
   d) 6/10 × 1.9

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Lesson 17 Homework
2. Multiply.
a. 4 × 0.6
b. 0.4 × 0.6
c. 0.04 × 0.6
d. 7 × 0.3
e. 0.7 × 0.3
f. 0.07 × 0.3
g. 1.3 × 5
h. 1.3 × 0.5
i. 1.3 × 0.05

3. Jennifer makes 1.7 liters of lemonade. If she pours 3 tenths of the lemonade in the glass, how many liters of lemonade are in the glass?
4. Cassius walked 6 tenths of a 3.6 mile trail.
a. How many miles did Cassius have left to hike?
b. Cameron was 1.3 miles ahead of Cassius. How many miles did Cameron hike already?

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Lesson 18 Application Problem
An adult female gorilla is 1.4 meters tall when standing upright. Her daughter is 3 tenths as tall. How much more will the young female gorilla need to grow before she is as tall as her mother?

Lesson 18 Concept Development
Problem 1:
a. 3.2 × 2.1
b. 3.2 × 0.44
c. 3.2 × 4.21

Problem 2:
2.6 × 0.4

Problem 3:
a. 3.1 × 1.4
b. 0.31 × 1.4

Problem 4:
4.2 × 0.12

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Lesson 18 Problem Set

1. Multiply
   c. 6.6 × 2.8 =
   d. 3.3 × 1.4 =
   
2. Solve using the standard algorithm. Use the thought bubble to show your thinking about the units of your product.
   c. 8.31 × 2.4 = _______
   
3. A kitchen measures 3.75 m by 4.2 m.
   a. Find the area of the kitchen.
   b. The area of the living room is one and a half times that of the kitchen. Find the total area of the living room and the kitchen.

Lesson 18 Homework
5. A swimming pool at a park measures 9.75 m by 7.2 m.
a. Find the area of the swimming pool.
b. The area of the playground is one and a half times that of the swimming pool. Find the total area of the swimming pool and the playground.

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Lesson 17 Homework

1. Multiply and model. Rewrite each expression as a number sentence with decimal factors.
   1/10 × 1.6

Lesson 18 Homework

1. Multiply.
   3.3 × 0.8

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Lesson 18 Problem Set
Lesson 18 Homework
This video shows how to relate decimal and fraction multiplication using mainly algorithms.

1. Multiply.
   a) 3.3 × 1.6
   b) 3.3 × 0.8
2. Multiply.
   b) 3.35 × 0.7
3. Solve using the standard algorithm. Use the thought bubble to show your thinking about the units of your product.
   a. 3.2 × 0.6 = __________
   b. 3.2 × 1.2 = __________

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