# Fraction Operations

## Objective

Convert fractions greater than 1 to mixed numbers.

## Common Core Standards

### Core Standards

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• 4.NF.B.3.B — Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

• 4.NF.B.3.C — Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

• 4.NF.B.4.A — Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

## Criteria for Success

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1. Determine which two whole numbers a fraction greater than 1 lies between.
2. Convert from fractions greater than 1 to mixed numbers using a number line or other model.
3. Convert from fractions greater than 1 to mixed numbers using the general method involving the Grade 4.NBT skill of finding quotients and remainders. For example, $\frac{47}{6}=\frac{(7\times6)+5}{6}=\frac{7\times6}{6}+\frac{5}{6}=7+\frac{5}{6}=7\frac{5}{6}$(NF Progression, p. 13).

## Tips for Teachers

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Before the Problem Set, you could have students play a game to practice converting fractions greater than one to mixed numbers, such as the "Converting Mixed Numbers Game: Pin the Fraction on the Number Line (whole-group version)” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Ms. Giordano, a high school soccer coach, tells her players to run between $3$ and $4$ miles every week over the summer in preparation for the fall season. Kayla runs ${{1\over2}}$ mile every day. Will Kayla run enough each week for Ms. Giordano? How do you know?

### Problem 2

Convert the following fractions to mixed numbers. Show or explain your work.

a.   ${{8\over3}}$

b.   ${{15\over4}}$

c.   ${{32\over6}}$

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic E > Lesson 24Concept Development

Grade 4 Mathematics > Module 5 > Topic E > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 3

Alice wrote the fraction ${{36\over5}}$ as a mixed number. Here is her work:

 $\frac{36}{5} = \frac{35}{5} + \frac{1}{5}$ (Step 1) $=\left(7\times\frac{5}{5}\right)+\frac{1}{5}$ (Step 2) ${=7+{1\over5}}$ (Step 3) ${=7{1\over5}}$ (Step 4)

Explain what Alice did in each step.

#### References

Illustrative Mathematics Writing a Mixed Number as an Equivalent Fraction

Writing a Mixed Number as an Equivalent Fraction, accessed on July 18, 2018, 9:50 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

## Discussion of Problem Set

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• What is ${{13\over5}}$ written as a mixed number? How did the tape diagram in #1 help you figure that out?
• How can drawing a number line help you when converting a fraction to a mixed number?
• How was #3 related to today’s work? How is it related to the work we did with quotients and remainders?
• In #4, which fractions were the easiest for you to convert? Which were the most challenging? Why?
• What mistake did Rex make in #5? What is the correct equivalent fraction? How do you know?

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Convert each fraction to a mixed number. Show or explain your work.

1.   ${{17\over5}}$

2.   ${{19\over3}}$

3.   ${{11\over4}}$

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic E > Lesson 24Exit Ticket

Grade 4 Mathematics > Module 5 > Topic E > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

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