Adding Subtracting Multiplying and Dividing Fractions Worksheets ... - Free Printable

Here's the complete solution to all 14 fraction problems, with step-by-step explanations for each.

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Problem 1:

$\frac{12}{22} \times \frac{2}{5}$

Multiply numerators and denominators:
= $\frac{12 \times 2}{22 \times 5} = \frac{24}{110}$

Simplify by dividing numerator and denominator by 2:
= $\frac{12}{55}$

✔ Answer: $\boxed{\frac{12}{55}}$

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Problem 2:

$\frac{16}{17} \div \frac{4}{9}$

Dividing fractions: multiply by reciprocal:
= $\frac{16}{17} \times \frac{9}{4}$

Simplify before multiplying: 16 and 4 → 4 and 1
= $\frac{4}{17} \times \frac{9}{1} = \frac{36}{17}$

Convert to mixed number (optional): $2\frac{2}{17}$

✔ Answer: $\boxed{\frac{36}{17}}$ or $\boxed{2\frac{2}{17}}$

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Problem 3:

$\frac{9}{16} + \frac{36}{27}$

First, simplify $\frac{36}{27} = \frac{4}{3}$

Now find LCD of 16 and 3 → 48

Convert:
$\frac{9}{16} = \frac{27}{48}$
$\frac{4}{3} = \frac{64}{48}$

Add:
$\frac{27 + 64}{48} = \frac{91}{48}$

Convert to mixed number: $1\frac{43}{48}$

✔ Answer: $\boxed{\frac{91}{48}}$ or $\boxed{1\frac{43}{48}}$

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Problem 4:

$\frac{9}{34} \div \frac{23}{51}$

Multiply by reciprocal:
= $\frac{9}{34} \times \frac{51}{23}$

Simplify: 51 and 34 → both divisible by 17 → 3 and 2
= $\frac{9}{2} \times \frac{3}{23} = \frac{27}{46}$

✔ Answer: $\boxed{\frac{27}{46}}$

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Problem 5:

$\frac{20}{3} + \frac{24}{11}$

LCD of 3 and 11 is 33

Convert:
$\frac{20}{3} = \frac{220}{33}$
$\frac{24}{11} = \frac{72}{33}$

Add:
$\frac{220 + 72}{33} = \frac{292}{33}$

Convert to mixed number: $8\frac{28}{33}$

✔ Answer: $\boxed{\frac{292}{33}}$ or $\boxed{8\frac{28}{33}}$

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Problem 6:

$\frac{21}{26} - \frac{1}{8}$

LCD of 26 and 8 is 104

Convert:
$\frac{21}{26} = \frac{84}{104}$
$\frac{1}{8} = \frac{13}{104}$

Subtract:
$\frac{84 - 13}{104} = \frac{71}{104}$

Already simplified.

✔ Answer: $\boxed{\frac{71}{104}}$

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Problem 7:

$\frac{17}{5} \times \frac{32}{6}$

Simplify first: $\frac{32}{6} = \frac{16}{3}$

Now:
= $\frac{17}{5} \times \frac{16}{3} = \frac{272}{15}$

Convert to mixed number: $18\frac{2}{15}$

✔ Answer: $\boxed{\frac{272}{15}}$ or $\boxed{18\frac{2}{15}}$

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Problem 8:

$\frac{4}{15} + \frac{9}{16}$

LCD of 15 and 16 is 240

Convert:
$\frac{4}{15} = \frac{64}{240}$
$\frac{9}{16} = \frac{135}{240}$

Add:
$\frac{64 + 135}{240} = \frac{199}{240}$

Already simplified.

✔ Answer: $\boxed{\frac{199}{240}}$

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Problem 9:

$\frac{31}{6} - \frac{8}{7}$

LCD of 6 and 7 is 42

Convert:
$\frac{31}{6} = \frac{217}{42}$
$\frac{8}{7} = \frac{48}{42}$

Subtract:
$\frac{217 - 48}{42} = \frac{169}{42}$

Convert to mixed number: $4\frac{1}{42}$

✔ Answer: $\boxed{\frac{169}{42}}$ or $\boxed{4\frac{1}{42}}$

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Problem 10:

$\frac{11}{14} - \frac{12}{26}$

Simplify $\frac{12}{26} = \frac{6}{13}$

LCD of 14 and 13 is 182

Convert:
$\frac{11}{14} = \frac{143}{182}$
$\frac{6}{13} = \frac{84}{182}$

Subtract:
$\frac{143 - 84}{182} = \frac{59}{182}$

Already simplified.

✔ Answer: $\boxed{\frac{59}{182}}$

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Problem 11:

$\frac{15}{16} \div \frac{19}{3}$

Multiply by reciprocal:
= $\frac{15}{16} \times \frac{3}{19} = \frac{45}{304}$

Already simplified.

✔ Answer: $\boxed{\frac{45}{304}}$

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Problem 12:

$\frac{7}{9} \div \frac{3}{16}$

Multiply by reciprocal:
= $\frac{7}{9} \times \frac{16}{3} = \frac{112}{27}$

Convert to mixed number: $4\frac{4}{27}$

✔ Answer: $\boxed{\frac{112}{27}}$ or $\boxed{4\frac{4}{27}}$

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Problem 13:

$\frac{15}{18} \times \frac{13}{22}$

Simplify $\frac{15}{18} = \frac{5}{6}$

Now:
= $\frac{5}{6} \times \frac{13}{22} = \frac{65}{132}$

Already simplified.

✔ Answer: $\boxed{\frac{65}{132}}$

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Problem 14:

$\frac{12}{21} \div \frac{14}{56}$

Simplify both fractions first:

$\frac{12}{21} = \frac{4}{7}$
$\frac{14}{56} = \frac{1}{4}$

Now divide:
= $\frac{4}{7} \div \frac{1}{4} = \frac{4}{7} \times \frac{4}{1} = \frac{16}{7}$

Convert to mixed number: $2\frac{2}{7}$

✔ Answer: $\boxed{\frac{16}{7}}$ or $\boxed{2\frac{2}{7}}$

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## ✔ Final Answers Summary:

1. $\frac{12}{55}$
2. $\frac{36}{17}$
3. $\frac{91}{48}$
4. $\frac{27}{46}$
5. $\frac{292}{33}$
6. $\frac{71}{104}$
7. $\frac{272}{15}$
8. $\frac{199}{240}$
9. $\frac{169}{42}$
10. $\frac{59}{182}$
11. $\frac{45}{304}$
12. $\frac{112}{27}$
13. $\frac{65}{132}$
14. $\frac{16}{7}$

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