Fraction arithmetic practice worksheet with 12 problems covering addition, subtraction, multiplication, and division of fractions.

Here's the complete solution to all 12 fraction problems, with step-by-step explanations.

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Problem 1:

$\frac{17}{3} + \frac{3}{17}$

These fractions have different denominators. Find the Least Common Denominator (LCD) of 3 and 17 → since they are both prime, LCD = $3 \times 17 = 51$.

Convert each fraction:

- $\frac{17}{3} = \frac{17 \times 17}{3 \times 17} = \frac{289}{51}$
- $\frac{3}{17} = \frac{3 \times 3}{17 \times 3} = \frac{9}{51}$

Add:

$\frac{289}{51} + \frac{9}{51} = \frac{298}{51}$

✔ Answer: $\boxed{\frac{298}{51}}$ (or as a mixed number: $5\frac{43}{51}$)

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Problem 2:

$\frac{7}{2} + \frac{11}{13}$

LCD of 2 and 13 is 26.

Convert:

- $\frac{7}{2} = \frac{7 \times 13}{2 \times 13} = \frac{91}{26}$
- $\frac{11}{13} = \frac{11 \times 2}{13 \times 2} = \frac{22}{26}$

Add:

$\frac{91}{26} + \frac{22}{26} = \frac{113}{26}$

✔ Answer: $\boxed{\frac{113}{26}}$ (or $4\frac{9}{26}$)

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Problem 3:

$\frac{3}{2} + \frac{20}{3}$

LCD of 2 and 3 is 6.

Convert:

- $\frac{3}{2} = \frac{9}{6}$
- $\frac{20}{3} = \frac{40}{6}$

Add:

$\frac{9}{6} + \frac{40}{6} = \frac{49}{6}$

✔ Answer: $\boxed{\frac{49}{6}}$ (or $8\frac{1}{6}$)

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Problem 4:

$\frac{13}{14} - \frac{12}{22}$

First, simplify $\frac{12}{22} = \frac{6}{11}$

Now subtract: $\frac{13}{14} - \frac{6}{11}$

LCD of 14 and 11 is 154.

Convert:

- $\frac{13}{14} = \frac{13 \times 11}{14 \times 11} = \frac{143}{154}$
- $\frac{6}{11} = \frac{6 \times 14}{11 \times 14} = \frac{84}{154}$

Subtract:

$\frac{143}{154} - \frac{84}{154} = \frac{59}{154}$

✔ Answer: $\boxed{\frac{59}{154}}$

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Problem 5:

$\frac{9}{10} - \frac{3}{15}$

Simplify $\frac{3}{15} = \frac{1}{5}$

Now: $\frac{9}{10} - \frac{1}{5}$

LCD of 10 and 5 is 10.

Convert:

- $\frac{1}{5} = \frac{2}{10}$

Subtract:

$\frac{9}{10} - \frac{2}{10} = \frac{7}{10}$

✔ Answer: $\boxed{\frac{7}{10}}$

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Problem 6:

$\frac{18}{19} - \frac{5}{6}$

LCD of 19 and 6 is 114.

Convert:

- $\frac{18}{19} = \frac{18 \times 6}{19 \times 6} = \frac{108}{114}$
- $\frac{5}{6} = \frac{5 \times 19}{6 \times 19} = \frac{95}{114}$

Subtract:

$\frac{108}{114} - \frac{95}{114} = \frac{13}{114}$

✔ Answer: $\boxed{\frac{13}{114}}$

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Problem 7:

$\frac{12}{15} \times \frac{6}{20}$

Multiply numerators and denominators:

$\frac{12 \times 6}{15 \times 20} = \frac{72}{300}$

Simplify: divide numerator and denominator by 12 → $\frac{6}{25}$

(Or simplify before multiplying: $\frac{12}{15} = \frac{4}{5}, \frac{6}{20} = \frac{3}{10}$ → $\frac{4}{5} \times \frac{3}{10} = \frac{12}{50} = \frac{6}{25}$)

✔ Answer: $\boxed{\frac{6}{25}}$

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Problem 8:

$\frac{23}{18} \times \frac{16}{21}$

Multiply: $\frac{23 \times 16}{18 \times 21} = \frac{368}{378}$

Simplify: divide numerator and denominator by 2 → $\frac{184}{189}$

Check if further simplification possible: GCF of 184 and 189 is 1 → done.

✔ Answer: $\boxed{\frac{184}{189}}$

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Problem 9:

$\frac{9}{14} \times \frac{22}{24}$

Simplify first: $\frac{22}{24} = \frac{11}{12}$

Now: $\frac{9}{14} \times \frac{11}{12} = \frac{99}{168}$

Simplify: divide numerator and denominator by 3 → $\frac{33}{56}$

✔ Answer: $\boxed{\frac{33}{56}}$

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Problem 10:

$\frac{26}{52} \div \frac{12}{13}$

Dividing fractions: multiply by reciprocal.

First, simplify $\frac{26}{52} = \frac{1}{2}$

So: $\frac{1}{2} \div \frac{12}{13} = \frac{1}{2} \times \frac{13}{12} = \frac{13}{24}$

✔ Answer: $\boxed{\frac{13}{24}}$

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Problem 11:

$\frac{5}{96} \div \frac{3}{64}$

Multiply by reciprocal: $\frac{5}{96} \times \frac{64}{3}$

Simplify before multiplying:

- 64 and 96: both divisible by 32 → $\frac{64}{96} = \frac{2}{3}$

So: $\frac{5}{96} \times \frac{64}{3} = \frac{5 \times 64}{96 \times 3} = \frac{5 \times 2}{3 \times 3} = \frac{10}{9}$

✔ Answer: $\boxed{\frac{10}{9}}$ (or $1\frac{1}{9}$)

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Problem 12:

$\frac{27}{21} \div \frac{44}{14}$

Simplify first:

- $\frac{27}{21} = \frac{9}{7}$
- $\frac{44}{14} = \frac{22}{7}$

Now: $\frac{9}{7} \div \frac{22}{7} = \frac{9}{7} \times \frac{7}{22} = \frac{9 \times 7}{7 \times 22}$

Cancel 7s: $\frac{9}{22}$

✔ Answer: $\boxed{\frac{9}{22}}$

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## ✔ Final Answers Summary:

1. $\boxed{\frac{298}{51}}$
2. $\boxed{\frac{113}{26}}$
3. $\boxed{\frac{49}{6}}$
4. $\boxed{\frac{59}{154}}$
5. $\boxed{\frac{7}{10}}$
6. $\boxed{\frac{13}{114}}$
7. $\boxed{\frac{6}{25}}$
8. $\boxed{\frac{184}{189}}$
9. $\boxed{\frac{33}{56}}$
10. $\boxed{\frac{13}{24}}$
11. $\boxed{\frac{10}{9}}$
12. $\boxed{\frac{9}{22}}$

Let me know if you’d like these as mixed numbers or decimals too!