Subtracting Fractions & Mixed Numbers - Worksheets - Free Printable

To solve the problems involving subtracting mixed numbers with unlike denominators, we need to follow these steps:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Rewrite the fractions with the common denominator.
4. Subtract the numerators while keeping the denominator the same.
5. Simplify the result, if possible, and convert back to a mixed number if necessary.

Let's solve each problem step by step.

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Problem a: \( 6 \frac{1}{2} - 3 \frac{7}{8} \)

1. Convert to improper fractions:
- \( 6 \frac{1}{2} = 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} \)
- \( 3 \frac{7}{8} = 3 + \frac{7}{8} = \frac{24}{8} + \frac{7}{8} = \frac{31}{8} \)

2. Find a common denominator:
- The denominators are 2 and 8. The least common denominator (LCD) is 8.

3. Rewrite the fractions with the common denominator:
- \( \frac{13}{2} = \frac{13 \times 4}{2 \times 4} = \frac{52}{8} \)
- \( \frac{31}{8} \) remains \( \frac{31}{8} \)

4. Subtract the fractions:
- \( \frac{52}{8} - \frac{31}{8} = \frac{52 - 31}{8} = \frac{21}{8} \)

5. Convert back to a mixed number:
- \( \frac{21}{8} = 2 \frac{5}{8} \)

Answer: \( 2 \frac{5}{8} \)

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Problem b: \( 9 \frac{4}{5} - 5 \frac{3}{5} \)

1. Convert to improper fractions:
- \( 9 \frac{4}{5} = 9 + \frac{4}{5} = \frac{45}{5} + \frac{4}{5} = \frac{49}{5} \)
- \( 5 \frac{3}{5} = 5 + \frac{3}{5} = \frac{25}{5} + \frac{3}{5} = \frac{28}{5} \)

2. Find a common denominator:
- The denominators are both 5, so no change is needed.

3. Subtract the fractions:
- \( \frac{49}{5} - \frac{28}{5} = \frac{49 - 28}{5} = \frac{21}{5} \)

4. Convert back to a mixed number:
- \( \frac{21}{5} = 4 \frac{1}{5} \)

Answer: \( 4 \frac{1}{5} \)

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Problem c: \( 7 \frac{5}{6} - 2 \frac{1}{3} \)

1. Convert to improper fractions:
- \( 7 \frac{5}{6} = 7 + \frac{5}{6} = \frac{42}{6} + \frac{5}{6} = \frac{47}{6} \)
- \( 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \)

2. Find a common denominator:
- The denominators are 6 and 3. The LCD is 6.

3. Rewrite the fractions with the common denominator:
- \( \frac{47}{6} \) remains \( \frac{47}{6} \)
- \( \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \)

4. Subtract the fractions:
- \( \frac{47}{6} - \frac{14}{6} = \frac{47 - 14}{6} = \frac{33}{6} \)

5. Simplify and convert back to a mixed number:
- \( \frac{33}{6} = \frac{11}{2} = 5 \frac{1}{2} \)

Answer: \( 5 \frac{1}{2} \)

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Problem d: \( 5 \frac{7}{9} - 3 \frac{1}{3} \)

1. Convert to improper fractions:
- \( 5 \frac{7}{9} = 5 + \frac{7}{9} = \frac{45}{9} + \frac{7}{9} = \frac{52}{9} \)
- \( 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \)

2. Find a common denominator:
- The denominators are 9 and 3. The LCD is 9.

3. Rewrite the fractions with the common denominator:
- \( \frac{52}{9} \) remains \( \frac{52}{9} \)
- \( \frac{10}{3} = \frac{10 \times 3}{3 \times 3} = \frac{30}{9} \)

4. Subtract the fractions:
- \( \frac{52}{9} - \frac{30}{9} = \frac{52 - 30}{9} = \frac{22}{9} \)

5. Convert back to a mixed number:
- \( \frac{22}{9} = 2 \frac{4}{9} \)

Answer: \( 2 \frac{4}{9} \)

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Problem e: \( 8 \frac{9}{12} - 3 \frac{1}{6} \)

1. Simplify the fractions:
- \( \frac{9}{12} = \frac{3}{4} \)
- So, \( 8 \frac{9}{12} = 8 \frac{3}{4} \)

2. Convert to improper fractions:
- \( 8 \frac{3}{4} = 8 + \frac{3}{4} = \frac{32}{4} + \frac{3}{4} = \frac{35}{4} \)
- \( 3 \frac{1}{6} = 3 + \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6} \)

3. Find a common denominator:
- The denominators are 4 and 6. The LCD is 12.

4. Rewrite the fractions with the common denominator:
- \( \frac{35}{4} = \frac{35 \times 3}{4 \times 3} = \frac{105}{12} \)
- \( \frac{19}{6} = \frac{19 \times 2}{6 \times 2} = \frac{38}{12} \)

5. Subtract the fractions:
- \( \frac{105}{12} - \frac{38}{12} = \frac{105 - 38}{12} = \frac{67}{12} \)

6. Convert back to a mixed number:
- \( \frac{67}{12} = 5 \frac{7}{12} \)

Answer: \( 5 \frac{7}{12} \)

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Problem f: \( 1 \frac{1}{4} - \frac{7}{8} \)

1. Convert to improper fractions:
- \( 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \)
- \( \frac{7}{8} \) remains \( \frac{7}{8} \)

2. Find a common denominator:
- The denominators are 4 and 8. The LCD is 8.

3. Rewrite the fractions with the common denominator:
- \( \frac{5}{4} = \frac{5 \times 2}{4 \times 2} = \frac{10}{8} \)
- \( \frac{7}{8} \) remains \( \frac{7}{8} \)

4. Subtract the fractions:
- \( \frac{10}{8} - \frac{7}{8} = \frac{10 - 7}{8} = \frac{3}{8} \)

Answer: \( \frac{3}{8} \)

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Problem g: \( 15 \frac{3}{5} - 3 \frac{1}{2} \)

1. Convert to improper fractions:
- \( 15 \frac{3}{5} = 15 + \frac{3}{5} = \frac{75}{5} + \frac{3}{5} = \frac{78}{5} \)
- \( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \)

2. Find a common denominator:
- The denominators are 5 and 2. The LCD is 10.

3. Rewrite the fractions with the common denominator:
- \( \frac{78}{5} = \frac{78 \times 2}{5 \times 2} = \frac{156}{10} \)
- \( \frac{7}{2} = \frac{7 \times 5}{2 \times 5} = \frac{35}{10} \)

4. Subtract the fractions:
- \( \frac{156}{10} - \frac{35}{10} = \frac{156 - 35}{10} = \frac{121}{10} \)

5. Convert back to a mixed number:
- \( \frac{121}{10} = 12 \frac{1}{10} \)

Answer: \( 12 \frac{1}{10} \)

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Problem h: \( 3 \frac{3}{8} - 2 \frac{1}{4} \)

1. Convert to improper fractions:
- \( 3 \frac{3}{8} = 3 + \frac{3}{8} = \frac{24}{8} + \frac{3}{8} = \frac{27}{8} \)
- \( 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)

2. Find a common denominator:
- The denominators are 8 and 4. The LCD is 8.

3. Rewrite the fractions with the common denominator:
- \( \frac{27}{8} \) remains \( \frac{27}{8} \)
- \( \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \)

4. Subtract the fractions:
- \( \frac{27}{8} - \frac{18}{8} = \frac{27 - 18}{8} = \frac{9}{8} \)

5. Convert back to a mixed number:
- \( \frac{9}{8} = 1 \frac{1}{8} \)

Answer: \( 1 \frac{1}{8} \)

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Problem i: \( 7 \frac{11}{12} - 2 \frac{1}{2} \)

1. Convert to improper fractions:
- \( 7 \frac{11}{12} = 7 + \frac{11}{12} = \frac{84}{12} + \frac{11}{12} = \frac{95}{12} \)
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)

2. Find a common denominator:
- The denominators are 12 and 2. The LCD is 12.

3. Rewrite the fractions with the common denominator:
- \( \frac{95}{12} \) remains \( \frac{95}{12} \)
- \( \frac{5}{2} = \frac{5 \times 6}{2 \times 6} = \frac{30}{12} \)

4. Subtract the fractions:
- \( \frac{95}{12} - \frac{30}{12} = \frac{95 - 30}{12} = \frac{65}{12} \)

5. Convert back to a mixed number:
- \( \frac{65}{12} = 5 \frac{5}{12} \)

Answer: \( 5 \frac{5}{12} \)

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Problem j: \( 19 \frac{3}{5} - 12 \frac{3}{10} \)

1. Convert to improper fractions:
- \( 19 \frac{3}{5} = 19 + \frac{3}{5} = \frac{95}{5} + \frac{3}{5} = \frac{98}{5} \)
- \( 12 \frac{3}{10} = 12 + \frac{3}{10} = \frac{120}{10} + \frac{3}{10} = \frac{123}{10} \)

2. Find a common denominator:
- The denominators are 5 and 10. The LCD is 10.

3. Rewrite the fractions with the common denominator:
- \( \frac{98}{5} = \frac{98 \times 2}{5 \times 2} = \frac{196}{10} \)
- \( \frac{123}{10} \) remains \( \frac{123}{10} \)

4. Subtract the fractions:
- \( \frac{196}{10} - \frac{123}{10} = \frac{196 - 123}{10} = \frac{73}{10} \)

5. Convert back to a mixed number:
- \( \frac{73}{10} = 7 \frac{3}{10} \)

Answer: \( 7 \frac{3}{10} \)

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Problem k: \( 4 \frac{2}{3} - 3 \frac{1}{2} \)

1. Convert to improper fractions:
- \( 4 \frac{2}{3} = 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3} \)
- \( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \)

2. Find a common denominator:
- The denominators are 3 and 2. The LCD is 6.

3. Rewrite the fractions with the common denominator:
- \( \frac{14}{3} = \frac{14 \times 2}{3 \times 2} = \frac{28}{6} \)
- \( \frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6} \)

4. Subtract the fractions:
- \( \frac{28}{6} - \frac{21}{6} = \frac{28 - 21}{6} = \frac{7}{6} \)

5. Convert back to a mixed number:
- \( \frac{7}{6} = 1 \frac{1}{6} \)

Answer: \( 1 \frac{1}{6} \)

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Problem l: \( 5 \frac{5}{12} - 3 \frac{1}{3} \)

1. Convert to improper fractions:
- \( 5 \frac{5}{12} = 5 + \frac{5}{12} = \frac{60}{12} + \frac{5}{12} = \frac{65}{12} \)
- \( 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \)

2. Find a common denominator:
- The denominators are 12 and 3. The LCD is 12.

3. Rewrite the fractions with the common denominator:
- \( \frac{65}{12} \) remains \( \frac{65}{12} \)
- \( \frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12} \)

4. Subtract the fractions:
- \( \frac{65}{12} - \frac{40}{12} = \frac{65 - 40}{12} = \frac{25}{12} \)

5. Convert back to a mixed number:
- \( \frac{25}{12} = 2 \frac{1}{12} \)

Answer: \( 2 \frac{1}{12} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
a. & 2 \frac{5}{8} \\
b. & 4 \frac{1}{5} \\
c. & 5 \frac{1}{2} \\
d. & 2 \frac{4}{9} \\
e. & 5 \frac{7}{12} \\
f. & \frac{3}{8} \\
g. & 12 \frac{1}{10} \\
h. & 1 \frac{1}{8} \\
i. & 5 \frac{5}{12} \\
j. & 7 \frac{3}{10} \\
k. & 1 \frac{1}{6} \\
l. & 2 \frac{1}{12} \\
\end{array}
}
\]