5th Grade Fractions Worksheets - Math Monks - Free Printable

Let's solve the Fractions Worksheet step by step.

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Part 1: Add the fractions and reduce to lowest terms

We'll add each pair of fractions by finding a common denominator, adding the numerators, and simplifying.

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#### 1. $ \frac{5}{7} + \frac{3}{4} $

- LCD of 7 and 4 is 28
- Convert:
- $ \frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28} $
- $ \frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28} $
- Add: $ \frac{20}{28} + \frac{21}{28} = \frac{41}{28} $
- Simplify: $ \frac{41}{28} $ is already in lowest terms (41 is prime).
- Answer: $ \boxed{\frac{41}{28}} $ or $ 1\frac{13}{28} $

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#### 2. $ \frac{4}{3} + \frac{7}{9} $

- LCD of 3 and 9 is 9
- Convert:
- $ \frac{4}{3} = \frac{4 \times 3}{3 \times 3} = \frac{12}{9} $
- $ \frac{7}{9} $ stays same
- Add: $ \frac{12}{9} + \frac{7}{9} = \frac{19}{9} $
- Simplify: $ \frac{19}{9} $ is in lowest terms.
- Answer: $ \boxed{\frac{19}{9}} $ or $ 2\frac{1}{9} $

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#### 3. $ \frac{4}{6} + \frac{1}{3} $

- Simplify $ \frac{4}{6} = \frac{2}{3} $
- Now: $ \frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1 $
- Answer: $ \boxed{1} $

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#### 4. $ \frac{8}{9} + \frac{3}{8} $

- LCD of 9 and 8 is 72
- Convert:
- $ \frac{8}{9} = \frac{8 \times 8}{9 \times 8} = \frac{64}{72} $
- $ \frac{3}{8} = \frac{3 \times 9}{8 \times 9} = \frac{27}{72} $
- Add: $ \frac{64}{72} + \frac{27}{72} = \frac{91}{72} $
- Simplify: $ \frac{91}{72} $ is in lowest terms (91 = 7×13, 72 not divisible by 7 or 13)
- Answer: $ \boxed{\frac{91}{72}} $ or $ 1\frac{19}{72} $

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#### 5. $ \frac{3}{5} + \frac{2}{3} $

- LCD of 5 and 3 is 15
- Convert:
- $ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} $
- $ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} $
- Add: $ \frac{9}{15} + \frac{10}{15} = \frac{19}{15} $
- Simplify: $ \frac{19}{15} $ is in lowest terms.
- Answer: $ \boxed{\frac{19}{15}} $ or $ 1\frac{4}{15} $

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#### 6. $ \frac{3}{6} + \frac{2}{9} $

- Simplify $ \frac{3}{6} = \frac{1}{2} $
- LCD of 2 and 9 is 18
- Convert:
- $ \frac{1}{2} = \frac{9}{18} $
- $ \frac{2}{9} = \frac{4}{18} $
- Add: $ \frac{9}{18} + \frac{4}{18} = \frac{13}{18} $
- Already simplified.
- Answer: $ \boxed{\frac{13}{18}} $

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Part 2: Compare each pair of fractions using <, >, or =

We’ll compare by converting to like denominators or decimals.

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#### 1. $ \frac{2}{3} \quad \square \quad \frac{2}{4} $

- $ \frac{2}{3} \approx 0.666 $, $ \frac{2}{4} = 0.5 $
- So $ \frac{2}{3} > \frac{2}{4} $
- Answer: $ \boxed{>} $

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#### 2. $ \frac{3}{5} \quad \square \quad \frac{1}{2} $

- $ \frac{3}{5} = 0.6 $, $ \frac{1}{2} = 0.5 $
- So $ \frac{3}{5} > \frac{1}{2} $
- Answer: $ \boxed{>} $

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#### 3. $ \frac{5}{6} \quad \square \quad \frac{5}{9} $

- Same numerator: larger denominator → smaller fraction
- $ \frac{5}{6} > \frac{5}{9} $
- Answer: $ \boxed{>} $

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#### 4. $ \frac{4}{9} \quad \square \quad \frac{4}{5} $

- Same numerator: $ \frac{4}{9} < \frac{4}{5} $
- Answer: $ \boxed{<} $

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#### 5. $ \frac{4}{9} \quad \square \quad \frac{8}{18} $

- Simplify $ \frac{8}{18} = \frac{4}{9} $
- So they are equal
- Answer: $ \boxed{=} $

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#### 6. $ \frac{3}{7} \quad \square \quad \frac{5}{14} $

- LCD of 7 and 14 is 14
- $ \frac{3}{7} = \frac{6}{14} $
- $ \frac{5}{14} $ stays same
- $ \frac{6}{14} > \frac{5}{14} $
- So $ \frac{3}{7} > \frac{5}{14} $
- Answer: $ \boxed{>} $

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✔ Final Answers:

#### Addition Section:
1. $ \frac{41}{28} $
2. $ \frac{19}{9} $
3. $ 1 $
4. $ \frac{91}{72} $
5. $ \frac{19}{15} $
6. $ \frac{13}{18} $

#### Comparison Section:
1. $ \frac{2}{3} > \frac{2}{4} $
2. $ \frac{3}{5} > \frac{1}{2} $
3. $ \frac{5}{6} > \frac{5}{9} $
4. $ \frac{4}{9} < \frac{4}{5} $
5. $ \frac{4}{9} = \frac{8}{18} $
6. $ \frac{3}{7} > \frac{5}{14} $

Let me know if you'd like this formatted as a printable answer sheet!