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 the 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 first: $\frac{4}{6} = \frac{2}{3}$
- 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 = 8×9, no common factors)
- 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: $\frac{3}{6} = \frac{1}{2}$
- Now: $\frac{1}{2} + \frac{2}{9}$
- 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 1 Answers:

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

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

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

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

- Simplify: $\frac{2}{4} = \frac{1}{2}$
- Compare $\frac{2}{3}$ and $\frac{1}{2}$
- LCD = 6:
- $\frac{2}{3} = \frac{4}{6}$
- $\frac{1}{2} = \frac{3}{6}$
- Since $\frac{4}{6} > \frac{3}{6}$ → $\frac{2}{3} > \frac{2}{4}$
- Answer: $\boxed{>}$

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

- LCD = 10:
- $\frac{3}{5} = \frac{6}{10}$
- $\frac{1}{2} = \frac{5}{10}$
- $\frac{6}{10} > \frac{5}{10}$ → $\frac{3}{5} > \frac{1}{2}$
- Answer: $\boxed{>}$

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

- Same numerator: 5
- Smaller denominator means larger fraction
- $6 < 9$ → $\frac{5}{6} > \frac{5}{9}$
- Or LCD = 18:
- $\frac{5}{6} = \frac{15}{18}$
- $\frac{5}{9} = \frac{10}{18}$
- $\frac{15}{18} > \frac{10}{18}$
- Answer: $\boxed{>}$

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

- Same numerator: 4
- $9 > 5$ → smaller denominator → larger fraction
- So $\frac{4}{9} < \frac{4}{5}$
- Or LCD = 45:
- $\frac{4}{9} = \frac{20}{45}$
- $\frac{4}{5} = \frac{36}{45}$
- $\frac{20}{45} < \frac{36}{45}$
- Answer: $\boxed{<}$

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

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

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

- LCD = 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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✔ Part 2 Answers:

1. $>$
2. $>$
3. $>$
4. $<$
5. $=$
6. $>$

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✔ Final Answers Summary:

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

#### Comparison Problems:
1. $>$
2. $>$
3. $>$
4. $<$
5. $=$
6. $>$

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