Four Operations Fractions Worksheet (with answers) | Teaching ... - Free Printable

Let's solve each part of the challenge step by step and simplify the answers to their simplest form.

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a) $\frac{2}{8} + \frac{1}{8}$

- Same denominator: add numerators
- $\frac{2+1}{8} = \frac{3}{8}$
- Already simplified

✔ Answer: $\boxed{\frac{3}{8}}$

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b) $\frac{2}{8} - \frac{1}{8}$

- Same denominator: subtract numerators
- $\frac{2-1}{8} = \frac{1}{8}$

✔ Answer: $\boxed{\frac{1}{8}}$

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c) $\frac{1}{8} \times \frac{1}{2}$

- Multiply numerators and denominators:
- $\frac{1 \times 1}{8 \times 2} = \frac{1}{16}$

✔ Answer: $\boxed{\frac{1}{16}}$

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d) $\frac{2}{8} \div \frac{1}{8}$

- Dividing fractions: multiply by reciprocal
- $\frac{2}{8} \div \frac{1}{8} = \frac{2}{8} \times \frac{8}{1} = \frac{2 \times 8}{8 \times 1} = \frac{16}{8} = 2$

✔ Answer: $\boxed{2}$

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e) $\frac{2}{6} \div 2$

- Divide a fraction by a whole number: write 2 as $\frac{2}{1}$
- $\frac{2}{6} \div \frac{2}{1} = \frac{2}{6} \times \frac{1}{2} = \frac{2 \times 1}{6 \times 2} = \frac{2}{12} = \frac{1}{6}$

✔ Answer: $\boxed{\frac{1}{6}}$

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f) $\frac{2}{8} \times 3$

- Write 3 as $\frac{3}{1}$
- $\frac{2}{8} \times \frac{3}{1} = \frac{6}{8} = \frac{3}{4}$ (simplify by dividing numerator and denominator by 2)

✔ Answer: $\boxed{\frac{3}{4}}$

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g) $1\frac{2}{8} + \frac{7}{8}$

- First, convert mixed number to improper fraction:
- $1\frac{2}{8} = \frac{8}{8} + \frac{2}{8} = \frac{10}{8}$
- Now add: $\frac{10}{8} + \frac{7}{8} = \frac{17}{8}$
- Convert back: $\frac{17}{8} = 2\frac{1}{8}$

✔ Answer: $\boxed{2\frac{1}{8}}$

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h) $\frac{2}{8} \div \frac{3}{5}$

- Multiply by reciprocal:
- $\frac{2}{8} \times \frac{5}{3} = \frac{10}{24} = \frac{5}{12}$ (divide numerator and denominator by 2)

✔ Answer: $\boxed{\frac{5}{12}}$

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i) $3\frac{5}{12} - \frac{1}{6}$

- Convert mixed number to improper fraction:
- $3\frac{5}{12} = \frac{3 \times 12 + 5}{12} = \frac{36 + 5}{12} = \frac{41}{12}$
- Now subtract: $\frac{41}{12} - \frac{1}{6}$
- Common denominator: LCD of 12 and 6 is 12
- $\frac{1}{6} = \frac{2}{12}$
- $\frac{41}{12} - \frac{2}{12} = \frac{39}{12} = \frac{13}{4}$ (simplify by dividing by 3)
- Convert to mixed number: $\frac{13}{4} = 3\frac{1}{4}$

✔ Answer: $\boxed{3\frac{1}{4}}$

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j) $\frac{3}{7} \times \frac{12}{63}$

- Multiply numerators and denominators:
- $\frac{3 \times 12}{7 \times 63} = \frac{36}{441}$
- Simplify:
- Find GCF of 36 and 441.
- Factors: 36 = $2^2 \times 3^2$, 441 = $21^2 = 3^2 \times 7^2$
- GCF = $3^2 = 9$
- $\frac{36 \div 9}{441 \div 9} = \frac{4}{49}$

✔ Answer: $\boxed{\frac{4}{49}}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| a) | $\frac{3}{8}$ |
| b) | $\frac{1}{8}$ |
| c) | $\frac{1}{16}$ |
| d) | $2$ |
| e) | $\frac{1}{6}$ |
| f) | $\frac{3}{4}$ |
| g) | $2\frac{1}{8}$ |
| h) | $\frac{5}{12}$ |
| i) | $3\frac{1}{4}$ |
| j) | $\frac{4}{49}$ |

All answers are in simplest form. 🎉