Fraction and Decimal Equivalence

Videos, examples, solutions, and lessons to help Grade 5 students learn how to explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.

Common Core Standards: 5.NF.5, 5.NF.6

New York State Common Core Math Grade 5, Module 4, Lesson 21
Worksheets for Grade 5

Application Problem
Carol had 3/4 yard of ribbon. She wanted to use it to decorate two picture frames. If she uses half the ribbon on each frame, how many feet of ribbon will she use for one frame? Use a tape diagram to show your thinking.

Concept Development
Problem 1:
2/2 of 3/4

Problem 2: Express fractions as an equivalent decimal.

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Lesson 21 Problem Set

1. Fill in the blanks.
   b. 3/4 x 1 = 3/4 x ___ = 21/28
   c. 7/4 x 1 = 7/4 x ___ = 35/20
2. Express each fraction as an equivalent decimal.
   c. 1/5 x ___ = ___
   d. 4/5 x ___ = ___
   e. 1/20 =
   f. 27/20 =
   g. 7/4 =
   h. 8/5 =
   i. 24/25 =
   j. 93/50 =
3. Jack said that if you take a number and multiply it by a fraction, the product will always be smaller than what you started with. Is he correct? Why or why not? Explain your answer and give at least two examples to support your thinking.
4. There is an infinite number of ways to represent 1 on the number line. In the space below, write at least four expressions multiplying by 1. Represent ԯneԠdifferently in each expression.
5. Maria multiplied by one to rename 1/4 as hundredths. She made factor pairs equal to 10. Use her method to change one-eighth to an equivalent decimal.
   Paulo renamed 1/8 as a decimal, too. He knows the decimal equal to 1/4, and he knows that 1/8 is half as much as 1/4. Can you use his ideas to show another way to find the decimal equal to 1/8?

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Lesson 21 Homework

1. Fill in the blanks.
   a. 1/3 x 1 = 1/3 x 3/3 = __ /9
   b. 2/3 x 1 = 2/3 x __ = 14/21
   c. 5/2 x 1 = 5/2 x __ = 25/__
2. Express each fraction as an equivalent decimal.
   a. 3/4 x 25/25 = ___ /100 =
   b. 1/4 x 25/25 =
   c. 2/5 x ___ =
   e. 3/20 =
   
   
3. Elise has 3/4 dollar. She buys a stamp that costs 44 cents. Change both numbers into decimals, and tell how much money Elise has after paying for the stamp.

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Lesson 21 Homework

Express each fraction as an equivalent decimal.

2/5 x ____ =
3/20 x ____ =

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Lesson 21 Homework

This video shows how to create decimal equivalent values from fractions using fractional multiplication.

2. Express each fraction as an equivalent decimal.
a. 3/4
c. 2/5
d. 3/5
e. 3/20
f. 25/20

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