Operations with Fractions (B) Worksheet | PDF Printable Number ... - Free Printable

Let's solve each problem step-by-step, following the instructions to add, subtract, multiply, divide, and simplify all answers as mixed numbers.

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✔ Section A: Add or Subtract

#### 1) $ 2\frac{1}{5} + \frac{17}{20} $

Convert $ 2\frac{1}{5} $ to improper fraction:
$$
2\frac{1}{5} = \frac{11}{5}
$$

Now find a common denominator (LCM of 5 and 20 is 20):
$$
\frac{11}{5} = \frac{44}{20}, \quad \frac{44}{20} + \frac{17}{20} = \frac{61}{20}
$$

Convert back to mixed number:
$$
\frac{61}{20} = 3\frac{1}{20}
$$

✔ Answer: $ 3\frac{1}{20} $

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#### 2) $ 3\frac{5}{8} + \frac{81}{12} $

Convert $ 3\frac{5}{8} $ to improper:
$$
3\frac{5}{8} = \frac{29}{8}
$$

Simplify $ \frac{81}{12} $:
$$
\frac{81}{12} = \frac{27}{4}
$$

Find LCM of 8 and 4 → 8:
$$
\frac{27}{4} = \frac{54}{8}, \quad \frac{29}{8} + \frac{54}{8} = \frac{83}{8}
$$

Convert:
$$
\frac{83}{8} = 10\frac{3}{8}
$$

✔ Answer: $ 10\frac{3}{8} $

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#### 3) $ 4\frac{5}{6} + 6\frac{1}{2} $

Convert both:
$$
4\frac{5}{6} = \frac{29}{6}, \quad 6\frac{1}{2} = \frac{13}{2}
$$

LCM of 6 and 2 is 6:
$$
\frac{13}{2} = \frac{39}{6}, \quad \frac{29}{6} + \frac{39}{6} = \frac{68}{6} = \frac{34}{3}
$$

Convert:
$$
\frac{34}{3} = 11\frac{1}{3}
$$

✔ Answer: $ 11\frac{1}{3} $

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#### 4) $ 2\frac{1}{3} - \frac{1}{12} $

Convert:
$$
2\frac{1}{3} = \frac{7}{3}
$$

LCM of 3 and 12 is 12:
$$
\frac{7}{3} = \frac{28}{12}, \quad \frac{28}{12} - \frac{1}{12} = \frac{27}{12} = \frac{9}{4}
$$

Convert:
$$
\frac{9}{4} = 2\frac{1}{4}
$$

✔ Answer: $ 2\frac{1}{4} $

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#### 5) $ 3\frac{9}{22} - \frac{3}{2} $

Convert:
$$
3\frac{9}{22} = \frac{75}{22}, \quad \frac{3}{2} = \frac{33}{22}
$$

Subtract:
$$
\frac{75}{22} - \frac{33}{22} = \frac{42}{22} = \frac{21}{11}
$$

Convert:
$$
\frac{21}{11} = 1\frac{10}{11}
$$

✔ Answer: $ 1\frac{10}{11} $

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#### 6) $ 8\frac{3}{4} - 5\frac{2}{7} $

Convert:
$$
8\frac{3}{4} = \frac{35}{4}, \quad 5\frac{2}{7} = \frac{37}{7}
$$

LCM of 4 and 7 is 28:
$$
\frac{35}{4} = \frac{245}{28}, \quad \frac{37}{7} = \frac{148}{28}
$$

Subtract:
$$
\frac{245}{28} - \frac{148}{28} = \frac{97}{28}
$$

Convert:
$$
\frac{97}{28} = 3\frac{13}{28}
$$

✔ Answer: $ 3\frac{13}{28} $

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✔ Section B: Multiply or Divide

#### 1) $ 1\frac{1}{5} \times \frac{1}{2} $

Convert:
$$
1\frac{1}{5} = \frac{6}{5}
$$

Multiply:
$$
\frac{6}{5} \times \frac{1}{2} = \frac{6}{10} = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $ (already simplified)

But it says "leave as mixed number" — but this is less than 1, so:

✔ Answer: $ \frac{3}{5} $ (or $ 0\frac{3}{5} $, but usually just $ \frac{3}{5} $)

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#### 2) $ 2\frac{2}{7} \times \frac{10}{3} $

Convert:
$$
2\frac{2}{7} = \frac{16}{7}
$$

Multiply:
$$
\frac{16}{7} \times \frac{10}{3} = \frac{160}{21}
$$

Convert:
$$
\frac{160}{21} = 7\frac{13}{21}
$$

✔ Answer: $ 7\frac{13}{21} $

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#### 3) $ 1\frac{4}{6} \times 1\frac{1}{20} $

Simplify $ 1\frac{4}{6} = 1\frac{2}{3} = \frac{5}{3} $

$ 1\frac{1}{20} = \frac{21}{20} $

Multiply:
$$
\frac{5}{3} \times \frac{21}{20} = \frac{105}{60} = \frac{7}{4}
$$

Convert:
$$
\frac{7}{4} = 1\frac{3}{4}
$$

✔ Answer: $ 1\frac{3}{4} $

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#### 4) $ 14 \div \frac{35}{6} $

Divide by fraction: multiply by reciprocal:
$$
14 \div \frac{35}{6} = 14 \times \frac{6}{35} = \frac{84}{35}
$$

Simplify:
$$
\frac{84}{35} = \frac{12}{5} = 2\frac{2}{5}
$$

✔ Answer: $ 2\frac{2}{5} $

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#### 5) $ 12\frac{3}{7} \div 9 $

Convert:
$$
12\frac{3}{7} = \frac{87}{7}
$$

Divide:
$$
\frac{87}{7} \div 9 = \frac{87}{7} \times \frac{1}{9} = \frac{87}{63}
$$

Simplify:
$$
\frac{87}{63} = \frac{29}{21} = 1\frac{8}{21}
$$

✔ Answer: $ 1\frac{8}{21} $

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#### 6) $ 3\frac{3}{4} \div 5\frac{2}{6} $

Simplify $ 5\frac{2}{6} = 5\frac{1}{3} = \frac{16}{3} $

$ 3\frac{3}{4} = \frac{15}{4} $

Divide:
$$
\frac{15}{4} \div \frac{16}{3} = \frac{15}{4} \times \frac{3}{16} = \frac{45}{64}
$$

Already simplified. Less than 1.

✔ Answer: $ \frac{45}{64} $

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✔ Section C: Calculate

#### 1) $ \frac{50}{12} + \frac{15}{9} $

Simplify:
$$
\frac{50}{12} = \frac{25}{6}, \quad \frac{15}{9} = \frac{5}{3}
$$

LCM of 6 and 3 is 6:
$$
\frac{5}{3} = \frac{10}{6}, \quad \frac{25}{6} + \frac{10}{6} = \frac{35}{6}
$$

Convert:
$$
\frac{35}{6} = 5\frac{5}{6}
$$

✔ Answer: $ 5\frac{5}{6} $

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#### 2) $ 4 \times \frac{13}{7} $

$$
4 \times \frac{13}{7} = \frac{52}{7} = 7\frac{3}{7}
$$

✔ Answer: $ 7\frac{3}{7} $

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#### 3) $ \frac{2}{\frac{16}{11}} $

Divide:
$$
2 \div \frac{16}{11} = 2 \times \frac{11}{16} = \frac{22}{16} = \frac{11}{8} = 1\frac{3}{8}
$$

✔ Answer: $ 1\frac{3}{8} $

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#### 4) $ 25 - \left( \frac{8}{3} + 3\frac{1}{6} \right) $

First, convert $ 3\frac{1}{6} = \frac{19}{6} $

Add:
$$
\frac{8}{3} + \frac{19}{6} = \frac{16}{6} + \frac{19}{6} = \frac{35}{6}
$$

Now:
$$
25 - \frac{35}{6} = \frac{150}{6} - \frac{35}{6} = \frac{115}{6} = 19\frac{1}{6}
$$

✔ Answer: $ 19\frac{1}{6} $

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#### 5) $ 12\frac{1}{2} \left( \frac{17}{5} - 2\frac{7}{10} \right) $

First, $ 12\frac{1}{2} = \frac{25}{2} $

Convert $ 2\frac{7}{10} = \frac{27}{10} $

Now:
$$
\frac{17}{5} - \frac{27}{10} = \frac{34}{10} - \frac{27}{10} = \frac{7}{10}
$$

Now multiply:
$$
\frac{25}{2} \times \frac{7}{10} = \frac{175}{20} = \frac{35}{4} = 8\frac{3}{4}
$$

✔ Answer: $ 8\frac{3}{4} $

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✔ Extension: Solve

$$
\frac{2\frac{2}{6} \times 1\frac{3}{4}}{9\frac{1}{2}}
$$

Step 1: Simplify fractions.

- $ 2\frac{2}{6} = 2\frac{1}{3} = \frac{7}{3} $
- $ 1\frac{3}{4} = \frac{7}{4} $
- $ 9\frac{1}{2} = \frac{19}{2} $

Now numerator:
$$
\frac{7}{3} \times \frac{7}{4} = \frac{49}{12}
$$

Now divide:
$$
\frac{49}{12} \div \frac{19}{2} = \frac{49}{12} \times \frac{2}{19} = \frac{98}{228}
$$

Simplify:
$$
\frac{98}{228} = \frac{49}{114}
$$

This is already simplified.

Since it's less than 1, leave as fraction.

✔ Answer: $ \frac{49}{114} $

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✔ Final Answers Summary

#### Section A
1) $ 3\frac{1}{20} $
2) $ 10\frac{3}{8} $
3) $ 11\frac{1}{3} $
4) $ 2\frac{1}{4} $
5) $ 1\frac{10}{11} $
6) $ 3\frac{13}{28} $

#### Section B
1) $ \frac{3}{5} $
2) $ 7\frac{13}{21} $
3) $ 1\frac{3}{4} $
4) $ 2\frac{2}{5} $
5) $ 1\frac{8}{21} $
6) $ \frac{45}{64} $

#### Section C
1) $ 5\frac{5}{6} $
2) $ 7\frac{3}{7} $
3) $ 1\frac{3}{8} $
4) $ 19\frac{1}{6} $
5) $ 8\frac{3}{4} $

#### Extension
$$
\frac{49}{114}
$$

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