# Addition and Subtraction of Fractions/Decimals

## Objective

Subtract fractions with like denominators.

## Common Core Standards

### Core Standards

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• 5.NF.A — Use equivalent fractions as a strategy to add and subtract fractions.

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• 4.NF.A.2

• 4.NF.B.3

## Criteria for Success

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1. Subtract two fractions with like denominators that does not require regrouping.
2. Subtract two fractions with like denominators that requires regrouping, including subtracting from a whole.
3. Rewrite a fraction as an equivalent mixed number.
4. Simplify a fraction.
5. Assess the reasonableness of an answer using number sense and estimation (MP.1).

## Tips for Teachers

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• Lessons 2 and 3 are intended to address the cluster heading “use equivalent fractions as a strategy to add and subtract fractions” (5.NF.A), which presumably includes adding fractions with like denominators. But, this lesson is arguably more directly aligned to the work of 4.NF.3 where students added and subtracted fractions with like denominators. It is up to your discretion about whether this lesson is needed or not.
• “The term ‘improper’ can be a source of confusion because it implies that this representation is not acceptable, which is false. Instead it is often the preferred representation in algebra. Avoid using this term and instead use ‘fraction’ or ‘fraction greater than one’” (Van de Walle, Teaching Student-Centered Mathematics, 3-5, vol. 2, p. 217). Further, fractions do not always need to be converted from ‘improper’ fractions to mixed numbers, since the need to do so often depends on the context (e.g., in the case of fractional coefficients in algebra, they are often written as fractions greater than one, which are generally easier to manipulate). Thus, while every anchor task below includes the question of whether the difference can be written as a mixed number, you may choose to skip that question for certain tasks so that students don’t get the wrong impression that fractions must always be written as mixed numbers whenever possible.
• “It is possible to over-emphasize the importance of simplifying fractions... There is no mathematical reason why fractions must be written in simplified form, although it may be convenient to do so in some cases” (NF Progression, p. 11). Thus, while each anchor task includes the question of whether the difference can be simplified, you may choose to skip that question for certain tasks so that students get the wrong impression that fractions must always be simplified whenever possible.
• Depending on student need, you might decide to split this lesson over two days.
• As a supplement to the Problem Set, students can play "The Fraction Splat!" by Steve Wyborney. All of lesson 11 and lesson 12 align to this lesson.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Solve.

1. Ms. White made a cake to celebrate Ms. Allen’s birthday. At the end of the day, she brought home ${{5\over8}}$ of the cake. Throughout the week, she ate ${{2\over8}}$ of it. How much of the cake does Ms. White have left?
2. Ms. Cole’s hair was ${{11\over12}}$ of a foot long. She went to the hairdresser and cut off ${{2\over12}}$ of a foot of her hair. How long is Ms. Cole’s hair now?

### Problem 2

Solve. Show your work with an area model or a number line.

a.     ${1-{3\over8}}$

b.     ${1{3\over12}-{7\over12}}$

### Problem 3

Solve. Show or explain your work.

a.     ${4{7\over8}-{3\over8}}$

b.     ${8-{5\over6}}$

c.     ${9{1\over12}-{7\over12}}$

d.     ${5{6\over13}-4{4\over13}}$

e.     ${6-4{5\over16}}$

f.     ${14{7\over18}-12{13\over18}}$

## Discussion of Problem Set

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• Look at #2. What strategies did you use to solve? How can you tell, before actually subtracting, whether you’ll need to regroup?
• Look at #4. How do you regroup a whole when there is no fractional part?
• Look at #5. What strategies did you use to solve?
• What are the simplified solutions to #5a and #5c? What does that make you think about how to add or subtract fractions with unlike denominators?

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Solve. Show or explain your work.

1.     ${{3\over4}-{1\over4}}$

2.      ${3-2{1\over5}}$

3.     ${1{3\over8}-{7\over8}}$

4.     ${7{1\over6}-2{5\over6}}$

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