# 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

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 = _______

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 = _______

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?

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

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?

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

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.

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

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 = __________

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 