Printable 5th Grade Adding and Subtracting Fraction Worksheets ... - Free Printable

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Fraction Review

For each problem below, add or subtract fractions and then simplify results.
1) $ \frac{1}{2} + \frac{1}{3} $
2) $ \frac{5}{6} - \frac{1}{4} $
3) $ \frac{3}{4} + \frac{1}{6} $
4) $ \frac{5}{8} - \frac{1}{3} $
5) $ \frac{7}{10} + \frac{2}{5} $
6) $ \frac{1}{2} + \frac{3}{7} $

The next problems involve solving for $ x $:
7) $ 1\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{3} + \frac{1}{6} \right) $
8) $ 4\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{4} + \frac{1}{2} \right) $
9) $ \frac{2}{3}x = \frac{1}{3} \left( \frac{1}{2} + \frac{1}{3} \right) $
10) $ 5\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{3} + \frac{1}{6} \right) $
11) $ 3\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{4} + \frac{1}{2} \right) $
12) $ 6\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{3} + \frac{1}{6} \right) $

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Let’s go through each problem step by step.

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Part 1: Add or Subtract Fractions

#### 1) $ \frac{1}{2} + \frac{1}{3} $
- Find common denominator: LCM of 2 and 3 is 6
- $ \frac{1}{2} = \frac{3}{6}, \frac{1}{3} = \frac{2}{6} $
- $ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} $
✔ Answer: $ \frac{5}{6} $

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#### 2) $ \frac{5}{6} - \frac{1}{4} $
- LCM of 6 and 4 is 12
- $ \frac{5}{6} = \frac{10}{12}, \frac{1}{4} = \frac{3}{12} $
- $ \frac{10}{12} - \frac{3}{12} = \frac{7}{12} $
✔ Answer: $ \frac{7}{12} $

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#### 3) $ \frac{3}{4} + \frac{1}{6} $
- LCM of 4 and 6 is 12
- $ \frac{3}{4} = \frac{9}{12}, \frac{1}{6} = \frac{2}{12} $
- $ \frac{9}{12} + \frac{2}{12} = \frac{11}{12} $
✔ Answer: $ \frac{11}{12} $

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#### 4) $ \frac{5}{8} - \frac{1}{3} $
- LCM of 8 and 3 is 24
- $ \frac{5}{8} = \frac{15}{24}, \frac{1}{3} = \frac{8}{24} $
- $ \frac{15}{24} - \frac{8}{24} = \frac{7}{24} $
✔ Answer: $ \frac{7}{24} $

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#### 5) $ \frac{7}{10} + \frac{2}{5} $
- $ \frac{2}{5} = \frac{4}{10} $
- $ \frac{7}{10} + \frac{4}{10} = \frac{11}{10} = 1\frac{1}{10} $
✔ Answer: $ \frac{11}{10} $ or $ 1\frac{1}{10} $

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#### 6) $ \frac{1}{2} + \frac{3}{7} $
- LCM of 2 and 7 is 14
- $ \frac{1}{2} = \frac{7}{14}, \frac{3}{7} = \frac{6}{14} $
- $ \frac{7}{14} + \frac{6}{14} = \frac{13}{14} $
✔ Answer: $ \frac{13}{14} $

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Part 2: Solve for $ x $

We'll solve each equation step-by-step.

#### 7) $ 1\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{3} + \frac{1}{6} \right) $

First, simplify right-hand side:
- $ \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} $
- So, $ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $

Now: $ 1\frac{1}{2}x = \frac{1}{4} $

Convert $ 1\frac{1}{2} = \frac{3}{2} $, so:
- $ \frac{3}{2}x = \frac{1}{4} $
- Multiply both sides by $ \frac{2}{3} $:
$ x = \frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6} $

✔ Answer: $ x = \frac{1}{6} $

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#### 8) $ 4\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{4} + \frac{1}{2} \right) $

Right-hand side:
- $ \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} $
- $ \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} $

Left side: $ 4\frac{1}{2} = \frac{9}{2} $, so:
- $ \frac{9}{2}x = \frac{3}{8} $
- $ x = \frac{3}{8} \div \frac{9}{2} = \frac{3}{8} \times \frac{2}{9} = \frac{6}{72} = \frac{1}{12} $

✔ Answer: $ x = \frac{1}{12} $

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#### 9) $ \frac{2}{3}x = \frac{1}{3} \left( \frac{1}{2} + \frac{1}{3} \right) $

Inside parentheses:
- $ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} $
- $ \frac{1}{3} \times \frac{5}{6} = \frac{5}{18} $

So: $ \frac{2}{3}x = \frac{5}{18} $
- $ x = \frac{5}{18} \div \frac{2}{3} = \frac{5}{18} \times \frac{3}{2} = \frac{15}{36} = \frac{5}{12} $

✔ Answer: $ x = \frac{5}{12} $

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#### 10) $ 5\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{3} + \frac{1}{6} \right) $

This is same as problem 7 on the right-hand side:
- $ \frac{1}{3} + \frac{1}{6} = \frac{1}{2} $
- $ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $

Left side: $ 5\frac{1}{2} = \frac{11}{2} $
- $ \frac{11}{2}x = \frac{1}{4} $
- $ x = \frac{1}{4} \div \frac{11}{2} = \frac{1}{4} \times \frac{2}{11} = \frac{2}{44} = \frac{1}{22} $

✔ Answer: $ x = \frac{1}{22} $

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#### 11) $ 3\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{4} + \frac{1}{2} \right) $

Same as problem 8:
- RHS: $ \frac{1}{2} \times \left( \frac{1}{4} + \frac{1}{2} \right) = \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} $
- LHS: $ 3\frac{1}{2} = \frac{7}{2} $
- $ \frac{7}{2}x = \frac{3}{8} $
- $ x = \frac{3}{8} \div \frac{7}{2} = \frac{3}{8} \times \frac{2}{7} = \frac{6}{56} = \frac{3}{28} $

✔ Answer: $ x = \frac{3}{28} $

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#### 12) $ 6\frac{1}{2}x = \frac{1}{2} \left( \frac{1}{3} + \frac{1}{6} \right) $

Again, same RHS as before:
- $ \frac{1}{2} \times \left( \frac{1}{3} + \frac{1}{6} \right) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $

LHS: $ 6\frac{1}{2} = \frac{13}{2} $
- $ \frac{13}{2}x = \frac{1}{4} $
- $ x = \frac{1}{4} \div \frac{13}{2} = \frac{1}{4} \times \frac{2}{13} = \frac{2}{52} = \frac{1}{26} $

✔ Answer: $ x = \frac{1}{26} $

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✔ Final Answers Summary:

Addition/Subtraction:
1) $ \frac{5}{6} $
2) $ \frac{7}{12} $
3) $ \frac{11}{12} $
4) $ \frac{7}{24} $
5) $ \frac{11}{10} $ or $ 1\frac{1}{10} $
6) $ \frac{13}{14} $

Solve for $ x $:
7) $ x = \frac{1}{6} $
8) $ x = \frac{1}{12} $
9) $ x = \frac{5}{12} $
10) $ x = \frac{1}{22} $
11) $ x = \frac{3}{28} $
12) $ x = \frac{1}{26} $

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Let me know if you'd like these formatted as a printable answer sheet or need explanations for any specific steps!