Operating Fractions (A) Worksheet | Printable Maths Worksheets - Free Printable

Let's solve each section of the "Operating Fractions (A)" worksheet step by step, with explanations.

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Section A: Add or Subtract. Simplify Answers

#### 1) $ \frac{1}{7} + \frac{3}{7} $
- Same denominator → add numerators:
$$
\frac{1+3}{7} = \frac{4}{7}
$$
✔ Answer: $ \frac{4}{7} $

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#### 2) $ \frac{2}{5} + \frac{8}{15} $
- Find LCM of 5 and 15 → 15
- Convert $ \frac{2}{5} = \frac{6}{15} $
- Now add:
$$
\frac{6}{15} + \frac{8}{15} = \frac{14}{15}
$$
✔ Answer: $ \frac{14}{15} $

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#### 3) $ \frac{2}{3} + \frac{1}{4} $
- LCM of 3 and 4 is 12
- $ \frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12} $
- Add:
$$
\frac{8}{12} + \frac{3}{12} = \frac{11}{12}
$$
✔ Answer: $ \frac{11}{12} $

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#### 4) $ \frac{3}{10} - \frac{1}{10} $
- Same denominator:
$$
\frac{3-1}{10} = \frac{2}{10} = \frac{1}{5}
$$
✔ Answer: $ \frac{1}{5} $

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#### 5) $ \frac{11}{24} - \frac{3}{8} $
- Convert $ \frac{3}{8} = \frac{9}{24} $
- Subtract:
$$
\frac{11}{24} - \frac{9}{24} = \frac{2}{24} = \frac{1}{12}
$$
✔ Answer: $ \frac{1}{12} $

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#### 6) $ \frac{5}{6} - \frac{1}{16} $
- LCM of 6 and 16 is 48
- $ \frac{5}{6} = \frac{40}{48}, \quad \frac{1}{16} = \frac{3}{48} $
- Subtract:
$$
\frac{40}{48} - \frac{3}{48} = \frac{37}{48}
$$
✔ Answer: $ \frac{37}{48} $

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✔ Section A Summary:

1. $ \frac{4}{7} $
2. $ \frac{14}{15} $
3. $ \frac{11}{12} $
4. $ \frac{1}{5} $
5. $ \frac{1}{12} $
6. $ \frac{37}{48} $

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Section B: Multiply or Divide. Simplify Answers

#### 1) $ \frac{2}{7} \times \frac{3}{5} $
- Multiply numerators and denominators:
$$
\frac{2 \times 3}{7 \times 5} = \frac{6}{35}
$$
✔ Answer: $ \frac{6}{35} $

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#### 2) $ \frac{5}{8} \times \frac{2}{3} $
- $ \frac{5 \times 2}{8 \times 3} = \frac{10}{24} = \frac{5}{12} $
✔ Answer: $ \frac{5}{12} $

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#### 3) $ \frac{8}{9} \times \frac{3}{10} $
- $ \frac{8 \times 3}{9 \times 10} = \frac{24}{90} = \frac{4}{15} $
✔ Answer: $ \frac{4}{15} $

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#### 4) $ \frac{9}{11} \div \frac{5}{6} $
- Multiply by reciprocal:
$$
\frac{9}{11} \times \frac{6}{5} = \frac{54}{55}
$$
✔ Answer: $ \frac{54}{55} $

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#### 5) $ \frac{3}{8} \div \frac{5}{12} $
- $ \frac{3}{8} \times \frac{12}{5} = \frac{36}{40} = \frac{9}{10} $
✔ Answer: $ \frac{9}{10} $

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#### 6) $ \frac{8}{12} \div 4 $
- First simplify $ \frac{8}{12} = \frac{2}{3} $
- Then divide: $ \frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6} $
✔ Answer: $ \frac{1}{6} $

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✔ Section B Summary:

1. $ \frac{6}{35} $
2. $ \frac{5}{12} $
3. $ \frac{4}{15} $
4. $ \frac{54}{55} $
5. $ \frac{9}{10} $
6. $ \frac{1}{6} $

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Section C: Simplify and Leave as Mixed Numbers

#### 1) $ 12 + \frac{8}{11} $
- Already a mixed number: $ 12 \frac{8}{11} $
✔ Answer: $ 12 \frac{8}{11} $

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#### 2) $ \frac{7}{15} \times 9 $
- $ \frac{7}{15} \times 9 = \frac{63}{15} = \frac{21}{5} $
- Convert to mixed number: $ 4 \frac{1}{5} $
✔ Answer: $ 4 \frac{1}{5} $

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#### 3) $ 12 - \frac{8}{3} $
- Convert 12 to fraction: $ \frac{36}{3} $
- $ \frac{36}{3} - \frac{8}{3} = \frac{28}{3} $
- Convert to mixed: $ 9 \frac{1}{3} $
✔ Answer: $ 9 \frac{1}{3} $

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#### 4) $ 1\frac{2}{3} - \frac{2}{9} $
- Convert $ 1\frac{2}{3} = \frac{5}{3} $
- $ \frac{5}{3} = \frac{15}{9}, \quad \frac{15}{9} - \frac{2}{9} = \frac{13}{9} $
- $ \frac{13}{9} = 1 \frac{4}{9} $
✔ Answer: $ 1 \frac{4}{9} $

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#### 5) $ \frac{12}{5} + \frac{4}{6} $
- Simplify $ \frac{4}{6} = \frac{2}{3} $
- LCM of 5 and 3 is 15
- $ \frac{12}{5} = \frac{36}{15}, \quad \frac{2}{3} = \frac{10}{15} $
- Add: $ \frac{46}{15} = 3 \frac{1}{15} $
✔ Answer: $ 3 \frac{1}{15} $

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#### 6) $ 10 \div \frac{4}{7} $
- $ 10 \times \frac{7}{4} = \frac{70}{4} = \frac{35}{2} = 17 \frac{1}{2} $
✔ Answer: $ 17 \frac{1}{2} $

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✔ Section C Summary:

1. $ 12 \frac{8}{11} $
2. $ 4 \frac{1}{5} $
3. $ 9 \frac{1}{3} $
4. $ 1 \frac{4}{9} $
5. $ 3 \frac{1}{15} $
6. $ 17 \frac{1}{2} $

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Extension Problem:

Solve:
$$
\frac{2}{10} \left[ \left( \frac{1}{12} + \frac{3}{4} \right) \div \frac{4}{7} \right]
$$

#### Step 1: Simplify inside parentheses
$ \frac{1}{12} + \frac{3}{4} $
- LCM of 12 and 4 is 12
- $ \frac{3}{4} = \frac{9}{12} $
- $ \frac{1}{12} + \frac{9}{12} = \frac{10}{12} = \frac{5}{6} $

#### Step 2: Divide by $ \frac{4}{7} $
$$
\frac{5}{6} \div \frac{4}{7} = \frac{5}{6} \times \frac{7}{4} = \frac{35}{24}
$$

#### Step 3: Multiply by $ \frac{2}{10} $
- $ \frac{2}{10} = \frac{1}{5} $
- $ \frac{1}{5} \times \frac{35}{24} = \frac{35}{120} = \frac{7}{24} $

✔ Final Answer: $ \frac{7}{24} $

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✔ Final Answers:

#### Section A:
1. $ \frac{4}{7} $
2. $ \frac{14}{15} $
3. $ \frac{11}{12} $
4. $ \frac{1}{5} $
5. $ \frac{1}{12} $
6. $ \frac{37}{48} $

#### Section B:
1. $ \frac{6}{35} $
2. $ \frac{5}{12} $
3. $ \frac{4}{15} $
4. $ \frac{54}{55} $
5. $ \frac{9}{10} $
6. $ \frac{1}{6} $

#### Section C:
1. $ 12 \frac{8}{11} $
2. $ 4 \frac{1}{5} $
3. $ 9 \frac{1}{3} $
4. $ 1 \frac{4}{9} $
5. $ 3 \frac{1}{15} $
6. $ 17 \frac{1}{2} $

#### Extension:
$$
\boxed{\frac{7}{24}}
$$

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