# Addition and Subtraction of Fractions/Decimals

## Objective

Add and subtract more than two fractions.

## Common Core Standards

### Core Standards

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• 5.NF.A.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

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• 4.NF.A.1

• 4.NF.A.2

• 4.NF.B.3

## Criteria for Success

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• Find a common unit for more than two fractions, ideally (but not necessarily) by finding the least common denominator since it means the computation is more manageable with larger units (i.e., smaller denominators).
• Add more than two fractions with unlike denominators.
• Subtract more than two fractions with unlike denominators.
• Use the properties of addition and subtraction to make a multi-term computation easier (e.g., to add ${{{{1\over3}}}+{3\over5}+{{{2\over3}}}}$, first add ${{1\over3}}$ and ${{2\over3}}$ to make $1$, making the computation easier) (MP.7).

## Tips for Teachers

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• This lesson provides an opportunity to refer back to the order of operations, particularly that addition and subtraction should be performed in tandem from left to right.
• If you are worried about pacing, you can cut Anchor Task #1 since it doesn’t provide necessary skills or concepts needed to master the objective that aren’t addressed in the more straightforward computational problems below it. However, it is an engaging way to introduce the idea of adding more than two fractions, which is why it is included.
• Note that on the Problem Set, Problem 6 is a partner game that requires two dice. Because of the difficulty of previous problems on the problem set, it’s not especially likely that students will get to this task, but make sure to have the materials ready in case any students do.

### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 4 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Ancient Egyptians used unit fractions, such as ${{1\over2}}$ and ${{1\over3}}$, to represent all fractions. For example, they might write the number ${{{{2\over3}}}}$ as ${{{1\over2}}}+{1\over6}$

We often think of ${{{{2\over3}}}}$ as ${{{1\over3}}}+{{{1\over3}}}$, but the ancient Egyptians would not write it this way because they didn’t use the same unit fraction twice.

1. Write each of the following Egyptian fractions as a single fraction:

i.     ${{{1\over2}}}+{{{1\over3}}}$

ii.   ${{{1\over2}}}+{{{1\over3}}}+{1\over5}$

iii.  ${{1\over4}+{1\over5}+{1\over12}}$

1. How might the ancient Egyptians have written the fraction we write as ${{3\over4}}$?

#### References

Illustrative Mathematics Egyptian Fractions

Egyptian Fractions, accessed on Feb. 8, 2018, 12:52 p.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.

### Problem 2

Solve. Show or explain your work.

a.     ${{2\over3}+{1\over4}+{1\over2}}$

b.     ${{2\over3}+{1\over5}+{1\over3}+1{4\over5}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 9Concept Development

Grade 5 Mathematics > Module 3 > Topic C > Lesson 9 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 Fishtank Learning, Inc.
EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 Fishtank Learning, Inc.

### Problem 3

Solve. Show or explain your work.

a.     ${8{11\over12}-{14\over3}-{9\over4}}$

b.     ${5{7\over8}-{1\over2}-{7\over8}-1{1\over2}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 Fishtank Learning, Inc.

### Problem 4

Solve. Show or explain your work.

a.     ${6{3\over4}+{3\over5}-5{1\over2}}$

b.     ${2{5\over6}-{1\over3}+{1\over6}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 Fishtank Learning, Inc.

## Problem Set & Homework

### Discussion of Problem Set

• Look at #3. How did you solve?
• Look at #5. Was Lucy’s method correct? Can she use it to measure out ${{1\over12}}$of a cup? What other amounts of water can she measure?
• Look at #6. What equation did you come up with? Is there more than one correct answer?

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### Problem 1

Solve.

${{3\over4}+{4\over5}-{7\over10}}$

#### References

PARCC Mathematics Practice Tests Grade 5 Mathematics Paper-Based Practice TestQuestion Stem #26

### Problem 2

Solve.

${8{4\over5}-{2\over3}+3{7\over10}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Exit Ticket, Question #2

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 Fishtank Learning, Inc.