# Addition and Subtraction of Fractions/Decimals

## Objective

Add fractions with unlike denominators whose sum is less than 2.

## 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.)

• 5.NF.A.2 — Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

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• 4.NF.A.1

• 4.NF.A.2

• 4.NF.B.3

## Criteria for Success

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1. Find common units for fractions with unlike denominators by finding equivalent fractions using a number line, an area model, or using multiplication or division.
2. Understand that there is more than one possibility for the common unit used, and use that to optionally find the least common denominator.
3. Assess the reasonableness of an answer using number sense and estimation (MP.1).
4. Add two fractions with unlike denominators that require regrouping whose sum is between 1 and 2, simplifying and writing the sum as a mixed number, if applicable.
5. Solve one-step word problems involving the addition of two fractions with unlike denominators whose sum is less than 2 (MP.4).

## Tips for Teachers

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For some problems in this lesson, students may use the computation-specific strategy of making a whole (e.g., $\frac{2}{5}+\frac{4}{5}=\frac{10}{15}+\frac{12}{15}=\frac{7}{15}+\frac{3}{15}+\frac{12}{15}=\frac{7}{15}+1=1\frac{7}{15}$). Discussing various strategies and their advantages and disadvantages “provide opportunities for students to compare approaches and justify steps in their computations (MP.3)” (NF Progression, p. 13).

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### Problem 1

1. Estimate the following sums.

a.   ${{1\over3}+{1\over4}}$

b.   ${{1\over2}+{2\over3}}$

1. Solve for the actual sums in #1 above. Are your answers reasonable? Why or why not?

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 4Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 4 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 2

1. Estimate whether the following sum will be more or less than 1. Then compute.

$\frac{4}{5}+\frac{6}{7}$

1. What do you notice about your solution? What do you wonder?

#### Guiding Questions

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### Problem 3

1. Estimate whether the following sums will be more or less than 1.

a.     $\frac{2}{3}+\frac{4}{5}$

b.     $\frac{5}{12}+\frac{2}{3}$

c.      $\frac{1}{6}+\frac{3}{8}$

1. Solve for the actual sums in #1 above. Are your answers reasonable? Why or why not?

#### Guiding Questions

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#### 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 The Match Foundation, Inc.

## Discussion of Problem Set

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• Look at #3. Did anyone solve without actually adding ${{5\over8}}$ and ${{1\over2}}$? How were you able to do that?
• Look at #4a. How can you tell, before solving, that the sum is going to be less than $1$
• Look at #4c. What do you notice about these fractions? How did that change the way you added?
• Look at #4d. What do you notice about these fractions? How did that change the way you added?
• Look at #8. What is the sum of your two fractions? Was anyone able to come up with a larger sum? How can we ensure we have the largest sum possible?

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### Problem 1

Solve. Show or explain your work.

${{5\over6}+{1\over3}}$

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 4Exit Ticket, Question #1

Grade 5 Mathematics > Module 3 > Topic B > Lesson 4 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 2

Solve. Show or explain your work.

Patrick drank ${{3\over4}}$ liter of water Monday before jogging. He drank ${{4\over5}}$ liter of water after his jog. How much water did Patrick drink altogether?

#### References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 4Exit Ticket, Question #2

Grade 5 Mathematics > Module 3 > Topic B > Lesson 4 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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