Fractions Worksheets | Fractions Math Sheets - Free Printable

Problem Overview:

The task involves solving problems related to adding and subtracting fractions, simplifying the answers, and converting improper fractions to mixed numbers where possible. The worksheet is divided into three sections:

1. Section A: Basic addition and subtraction of fractions.
2. Section B: More complex addition and subtraction of fractions.
3. Section C: Addition and subtraction involving mixed numbers and improper fractions.

I will solve each section step by step.

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Section A: Solve

#### 1) $ \frac{1}{8} + \frac{1}{8} $
- Both fractions have the same denominator (8).
- Add the numerators: $ 1 + 1 = 2 $.
- Result: $ \frac{2}{8} $.
- Simplify: $ \frac{2}{8} = \frac{1}{4} $.
- Answer: $ \frac{1}{4} $.

#### 2) $ \frac{3}{5} - \frac{1}{5} $
- Both fractions have the same denominator (5).
- Subtract the numerators: $ 3 - 1 = 2 $.
- Result: $ \frac{2}{5} $.
- Answer: $ \frac{2}{5} $.

#### 3) $ \frac{1}{7} - \frac{1}{14} $
- Find a common denominator: The least common multiple (LCM) of 7 and 14 is 14.
- Rewrite $ \frac{1}{7} $ as $ \frac{2}{14} $.
- Subtract: $ \frac{2}{14} - \frac{1}{14} = \frac{1}{14} $.
- Answer: $ \frac{1}{14} $.

#### 4) $ \frac{1}{15} + \frac{1}{15} $
- Both fractions have the same denominator (15).
- Add the numerators: $ 1 + 1 = 2 $.
- Result: $ \frac{2}{15} $.
- Answer: $ \frac{2}{15} $.

#### 5) $ \frac{1}{40} + \frac{1}{2} $
- Find a common denominator: The LCM of 40 and 2 is 40.
- Rewrite $ \frac{1}{2} $ as $ \frac{20}{40} $.
- Add: $ \frac{1}{40} + \frac{20}{40} = \frac{21}{40} $.
- Answer: $ \frac{21}{40} $.

#### 6) $ \frac{1}{7} - \frac{1}{11} $
- Find a common denominator: The LCM of 7 and 11 is 77.
- Rewrite $ \frac{1}{7} $ as $ \frac{11}{77} $ and $ \frac{1}{11} $ as $ \frac{7}{77} $.
- Subtract: $ \frac{11}{77} - \frac{7}{77} = \frac{4}{77} $.
- Answer: $ \frac{4}{77} $.

#### 7) $ \frac{1}{15} + \frac{1}{2} $
- Find a common denominator: The LCM of 15 and 2 is 30.
- Rewrite $ \frac{1}{15} $ as $ \frac{2}{30} $ and $ \frac{1}{2} $ as $ \frac{15}{30} $.
- Add: $ \frac{2}{30} + \frac{15}{30} = \frac{17}{30} $.
- Answer: $ \frac{17}{30} $.

#### 8) $ \frac{1}{9} - \frac{1}{19} $
- Find a common denominator: The LCM of 9 and 19 is 171.
- Rewrite $ \frac{1}{9} $ as $ \frac{19}{171} $ and $ \frac{1}{19} $ as $ \frac{9}{171} $.
- Subtract: $ \frac{19}{171} - \frac{9}{171} = \frac{10}{171} $.
- Answer: $ \frac{10}{171} $.

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Section B: Solve

#### 1) $ \frac{1}{10} + \frac{2}{5} $
- Find a common denominator: The LCM of 10 and 5 is 10.
- Rewrite $ \frac{2}{5} $ as $ \frac{4}{10} $.
- Add: $ \frac{1}{10} + \frac{4}{10} = \frac{5}{10} $.
- Simplify: $ \frac{5}{10} = \frac{1}{2} $.
- Answer: $ \frac{1}{2} $.

#### 2) $ \frac{1}{3} - \frac{1}{21} $
- Find a common denominator: The LCM of 3 and 21 is 21.
- Rewrite $ \frac{1}{3} $ as $ \frac{7}{21} $.
- Subtract: $ \frac{7}{21} - \frac{1}{21} = \frac{6}{21} $.
- Simplify: $ \frac{6}{21} = \frac{2}{7} $.
- Answer: $ \frac{2}{7} $.

#### 3) $ \frac{1}{4} + \frac{5}{12} $
- Find a common denominator: The LCM of 4 and 12 is 12.
- Rewrite $ \frac{1}{4} $ as $ \frac{3}{12} $.
- Add: $ \frac{3}{12} + \frac{5}{12} = \frac{8}{12} $.
- Simplify: $ \frac{8}{12} = \frac{2}{3} $.
- Answer: $ \frac{2}{3} $.

#### 4) $ \frac{1}{18} - \frac{7}{18} $
- Both fractions have the same denominator (18).
- Subtract the numerators: $ 1 - 7 = -6 $.
- Result: $ \frac{-6}{18} $.
- Simplify: $ \frac{-6}{18} = \frac{-1}{3} $.
- Answer: $ -\frac{1}{3} $.

#### 5) $ \frac{3}{7} - \frac{2}{5} $
- Find a common denominator: The LCM of 7 and 5 is 35.
- Rewrite $ \frac{3}{7} $ as $ \frac{15}{35} $ and $ \frac{2}{5} $ as $ \frac{14}{35} $.
- Subtract: $ \frac{15}{35} - \frac{14}{35} = \frac{1}{35} $.
- Answer: $ \frac{1}{35} $.

#### 6) $ \frac{3}{10} + \frac{6}{7} $
- Find a common denominator: The LCM of 10 and 7 is 70.
- Rewrite $ \frac{3}{10} $ as $ \frac{21}{70} $ and $ \frac{6}{7} $ as $ \frac{60}{70} $.
- Add: $ \frac{21}{70} + \frac{60}{70} = \frac{81}{70} $.
- Convert to a mixed number: $ \frac{81}{70} = 1 \frac{11}{70} $.
- Answer: $ 1 \frac{11}{70} $.

#### 7) $ \frac{7}{11} + \frac{2}{5} $
- Find a common denominator: The LCM of 11 and 5 is 55.
- Rewrite $ \frac{7}{11} $ as $ \frac{35}{55} $ and $ \frac{2}{5} $ as $ \frac{22}{55} $.
- Add: $ \frac{35}{55} + \frac{22}{55} = \frac{57}{55} $.
- Convert to a mixed number: $ \frac{57}{55} = 1 \frac{2}{55} $.
- Answer: $ 1 \frac{2}{55} $.

#### 8) $ \frac{4}{5} - \frac{6}{15} $
- Simplify $ \frac{6}{15} $: $ \frac{6}{15} = \frac{2}{5} $.
- Now subtract: $ \frac{4}{5} - \frac{2}{5} = \frac{2}{5} $.
- Answer: $ \frac{2}{5} $.

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Section C: Add and Subtract Mixed Numbers and Improper Fractions

#### 1) $ 3 + \frac{56}{8} $
- Simplify $ \frac{56}{8} $: $ \frac{56}{8} = 7 $.
- Add: $ 3 + 7 = 10 $.
- Answer: $ 10 $.

#### 2) $ 2 \frac{1}{3} + 3 \frac{1}{2} $
- Convert mixed numbers to improper fractions:
- $ 2 \frac{1}{3} = \frac{7}{3} $.
- $ 3 \frac{1}{2} = \frac{7}{2} $.
- Find a common denominator: The LCM of 3 and 2 is 6.
- Rewrite $ \frac{7}{3} $ as $ \frac{14}{6} $ and $ \frac{7}{2} $ as $ \frac{21}{6} $.
- Add: $ \frac{14}{6} + \frac{21}{6} = \frac{35}{6} $.
- Convert to a mixed number: $ \frac{35}{6} = 5 \frac{5}{6} $.
- Answer: $ 5 \frac{5}{6} $.

#### 3) $ \frac{17}{8} - 1 $
- Convert 1 to a fraction with denominator 8: $ 1 = \frac{8}{8} $.
- Subtract: $ \frac{17}{8} - \frac{8}{8} = \frac{9}{8} $.
- Convert to a mixed number: $ \frac{9}{8} = 1 \frac{1}{8} $.
- Answer: $ 1 \frac{1}{8} $.

#### 4) $ 7 \frac{3}{5} + 5 $
- Add the whole numbers: $ 7 + 5 = 12 $.
- Keep the fractional part: $ \frac{3}{5} $.
- Combine: $ 12 \frac{3}{5} $.
- Answer: $ 12 \frac{3}{5} $.

#### 5) $ 8 \frac{1}{4} + 6 \frac{3}{8} $
- Convert mixed numbers to improper fractions:
- $ 8 \frac{1}{4} = \frac{33}{4} $.
- $ 6 \frac{3}{8} = \frac{51}{8} $.
- Find a common denominator: The LCM of 4 and 8 is 8.
- Rewrite $ \frac{33}{4} $ as $ \frac{66}{8} $.
- Add: $ \frac{66}{8} + \frac{51}{8} = \frac{117}{8} $.
- Convert to a mixed number: $ \frac{117}{8} = 14 \frac{5}{8} $.
- Answer: $ 14 \frac{5}{8} $.

#### 6) $ \frac{21}{9} - 2 $
- Simplify $ \frac{21}{9} $: $ \frac{21}{9} = \frac{7}{3} $.
- Convert 2 to a fraction with denominator 3: $ 2 = \frac{6}{3} $.
- Subtract: $ \frac{7}{3} - \frac{6}{3} = \frac{1}{3} $.
- Answer: $ \frac{1}{3} $.

#### 7) $ 9 \frac{5}{6} - 4 \frac{7}{9} $
- Convert mixed numbers to improper fractions:
- $ 9 \frac{5}{6} = \frac{59}{6} $.
- $ 4 \frac{7}{9} = \frac{43}{9} $.
- Find a common denominator: The LCM of 6 and 9 is 18.
- Rewrite $ \frac{59}{6} $ as $ \frac{177}{18} $ and $ \frac{43}{9} $ as $ \frac{86}{18} $.
- Subtract: $ \frac{177}{18} - \frac{86}{18} = \frac{91}{18} $.
- Convert to a mixed number: $ \frac{91}{18} = 5 \frac{1}{18} $.
- Answer: $ 5 \frac{1}{18} $.

#### 8) $ 5 \frac{8}{11} + 7 \frac{9}{11} $
- Add the whole numbers: $ 5 + 7 = 12 $.
- Add the fractions: $ \frac{8}{11} + \frac{9}{11} = \frac{17}{11} $.
- Convert $ \frac{17}{11} $ to a mixed number: $ \frac{17}{11} = 1 \frac{6}{11} $.
- Add the whole number parts: $ 12 + 1 = 13 $.
- Combine: $ 13 \frac{6}{11} $.
- Answer: $ 13 \frac{6}{11} $.

#### 9) $ 4 \frac{2}{11} - 3 \frac{9}{11} $
- Subtract the whole numbers: $ 4 - 3 = 1 $.
- Subtract the fractions: $ \frac{2}{11} - \frac{9}{11} = \frac{-7}{11} $.
- Combine: $ 1 - \frac{7}{11} = \frac{11}{11} - \frac{7}{11} = \frac{4}{11} $.
- Answer: $ \frac{4}{11} $.

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Section A:} & 1) \frac{1}{4}, 2) \frac{2}{5}, 3) \frac{1}{14}, 4) \frac{2}{15}, 5) \frac{21}{40}, 6) \frac{4}{77}, 7) \frac{17}{30}, 8) \frac{10}{171} \\
\text{Section B:} & 1) \frac{1}{2}, 2) \frac{2}{7}, 3) \frac{2}{3}, 4) -\frac{1}{3}, 5) \frac{1}{35}, 6) 1 \frac{11}{70}, 7) 1 \frac{2}{55}, 8) \frac{2}{5} \\
\text{Section C:} & 1) 10, 2) 5 \frac{5}{6}, 3) 1 \frac{1}{8}, 4) 12 \frac{3}{5}, 5) 14 \frac{5}{8}, 6) \frac{1}{3}, 7) 5 \frac{1}{18}, 8) 13 \frac{6}{11}, 9) \frac{4}{11}
\end{array}
}
\]