# Fraction Operations

## Objective

Subtract a mixed number from a mixed number.

## Common Core Standards

### Core Standards

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• 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.

## Criteria for Success

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1. Estimate the difference of two mixed numbers, determining whether that estimate will be greater than or less than the actual difference.
2. Subtract two mixed numbers using a variety of strategies, such as:
1. Converting the mixed numbers to fractions greater than 1 and subtracting like units,
2. Subtracting the corresponding whole number and fractional parts of both the minuend and subtrahend, regrouping a whole if necessary, or
3. Using simplifying strategies, such as going down over a whole or counting up over a whole.
3. Assess the reasonableness of answers based on estimates (MP.1).

## Tips for Teachers

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Before the Problem Set, you could have students play a modified version of “Rolling Fractions” found on p. 63 of the Georgia Standards of Excellence Curriculum Frameworks: Mathematics GSE Fourth Grade Unit 4: Operations with Fractions. You should modify it by having students subtract a fraction from a mixed number and not a mixed number from a mixed number. You may also modify it by giving students more denominators to choose from in #1 of the directions (e.g., include all denominators students are expected to work with in Grade 4, including 2, 3, 4, 5, 6, 8, 10, and 12).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

1. Solve.
1. 3 thousands 5 tens – 1 thousand 2 tens = ___________
2. 3 dogs 5 puppies – 1 orange 2 puppies = ___________
3. 3 ones 5 eighths – 1 one 2 eighths = ___________
2. What do you notice about the problems in #1? What do you wonder?

### Problem 2

Solve.

a.   ${3{2\over3}-1{1\over3}}$

b.   $4\frac{3}{4}-2\frac{1}{4}$

c.   ${6{7\over10}-2{7\over10}}$

### Problem 3

Solve.

a.   ${5-1{2\over5}}$

b.   ${6{7\over10}-2{8\over10}}$

c.   ${9{2\over6}-3{5\over6}}$

### Problem 4

Solve.

a.   ${4{3\over8}-3{6\over8}}$

b.   ${11{3\over12}-9{11\over12}}$

## Discussion of Problem Set

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• Can you accurately subtract mixed numbers by subtracting the fraction first, or must you always subtract the whole numbers first?
• When subtracting mixed numbers, what is the advantage of subtracting the whole numbers first?
• Which strategy do you prefer to use? What are the advantages and disadvantages of that strategy?
• How can subtracting a mixed number from a mixed number be similar to subtracting a fraction from a mixed number?
• If you were unsure of any answer on this Problem Set, what could you do to see if your answer is reasonable? Would drawing a picture or estimating the difference be helpful?

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Solve. Show or explain your work.

1.   ${4{2\over3}-2{1\over3}}$

2.   ${12{5\over8}-11{7\over8}}$

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