Free Printable 5th Grade Math Worksheets (with Answers!) — Mashup Math - Free Printable

Let's solve each part of the worksheet step by step.

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Part 1: Multiply and write your answers in the simplest form

#### 1. $ \frac{2}{9} \times \frac{6}{3} $

- First, simplify $ \frac{6}{3} = 2 $
- Now: $ \frac{2}{9} \times 2 = \frac{4}{9} $
- ✔ Answer: $ \boxed{\frac{4}{9}} $

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#### 2. $ \frac{3}{7} \times \frac{14}{6} $

- Simplify before multiplying:
- $ \frac{14}{6} = \frac{7}{3} $ (divide numerator and denominator by 2)
- So: $ \frac{3}{7} \times \frac{7}{3} $
- Cancel out common factors:
- $ \frac{3}{7} \times \frac{7}{3} = \frac{3 \times 7}{7 \times 3} = 1 $
- ✔ Answer: $ \boxed{1} $

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#### 3. $ \frac{2}{5} \times \frac{10}{14} $

- Simplify $ \frac{10}{14} = \frac{5}{7} $
- Now: $ \frac{2}{5} \times \frac{5}{7} $
- Cancel $ 5 $: $ \frac{2}{\cancel{5}} \times \frac{\cancel{5}}{7} = \frac{2}{7} $
- ✔ Answer: $ \boxed{\frac{2}{7}} $

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#### 4. $ \frac{8}{9} \times \frac{18}{12} $

- Simplify $ \frac{18}{12} = \frac{3}{2} $
- Now: $ \frac{8}{9} \times \frac{3}{2} $
- Simplify crosswise:
- $ 8 $ and $ 2 $: divide both by 2 → $ 4 $ and $ 1 $
- $ 3 $ and $ 9 $: divide both by 3 → $ 1 $ and $ 3 $
- So: $ \frac{4}{3} \times \frac{1}{1} = \frac{4}{3} $
- Convert to mixed number: $ \frac{4}{3} = 1 \frac{1}{3} $
- ✔ Answer: $ \boxed{1 \frac{1}{3}} $

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Part 2: Convert improper fractions to mixed numbers

#### 1. $ \frac{50}{7} $

- Divide: $ 50 \div 7 = 7 $ remainder $ 1 $
- So: $ 7 \frac{1}{7} $
- ✔ Answer: $ \boxed{7 \frac{1}{7}} $

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#### 2. $ \frac{31}{5} $

- $ 31 \div 5 = 6 $ remainder $ 1 $
- So: $ 6 \frac{1}{5} $
- ✔ Answer: $ \boxed{6 \frac{1}{5}} $

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#### 3. $ \frac{83}{9} $

- $ 83 \div 9 = 9 $ remainder $ 2 $
- So: $ 9 \frac{2}{9} $
- ✔ Answer: $ \boxed{9 \frac{2}{9}} $

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#### 4. $ \frac{19}{4} $

- $ 19 \div 4 = 4 $ remainder $ 3 $
- So: $ 4 \frac{3}{4} $
- ✔ Answer: $ \boxed{4 \frac{3}{4}} $

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Part 3: Compare with <, >, or =

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

- Find a common denominator: LCM of 5 and 2 is 10
- $ \frac{3}{5} = \frac{6}{10}, \quad \frac{1}{2} = \frac{5}{10} $
- $ \frac{6}{10} > \frac{5}{10} $
- ✔ Answer: $ \boxed{>} $

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#### 2. $ \frac{5}{8} \quad \text{○} \quad \frac{8}{16} $

- Simplify $ \frac{8}{16} = \frac{1}{2} $
- Compare $ \frac{5}{8} $ and $ \frac{1}{2} $
- $ \frac{1}{2} = \frac{4}{8} $, so $ \frac{5}{8} > \frac{4}{8} $
- ✔ Answer: $ \boxed{>} $

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#### 3. $ \frac{1}{3} \quad \text{○} \quad \frac{3}{9} $

- Simplify $ \frac{3}{9} = \frac{1}{3} $
- So: $ \frac{1}{3} = \frac{1}{3} $
- ✔ Answer: $ \boxed{=} $

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#### 4. $ \frac{1}{8} \quad \text{○} \quad \frac{3}{4} $

- Convert $ \frac{3}{4} $ to eighths: $ \frac{3}{4} = \frac{6}{8} $
- $ \frac{1}{8} < \frac{6}{8} $
- ✔ Answer: $ \boxed{<} $

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✔ Final Answers:

#### Multiplication:
1. $ \frac{4}{9} $
2. $ 1 $
3. $ \frac{2}{7} $
4. $ 1 \frac{1}{3} $

#### Convert to Mixed Numbers:
1. $ 7 \frac{1}{7} $
2. $ 6 \frac{1}{5} $
3. $ 9 \frac{2}{9} $
4. $ 4 \frac{3}{4} $

#### Compare:
1. $ \frac{3}{5} > \frac{1}{2} $
2. $ \frac{5}{8} > \frac{8}{16} $
3. $ \frac{1}{3} = \frac{3}{9} $
4. $ \frac{1}{8} < \frac{3}{4} $

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