Addition and subtraction of mixed fractions worksheet | Live ... - Free Printable

To solve the problems involving addition and subtraction of mixed fractions, we need to follow these steps:

1. Convert mixed fractions to improper fractions.
2. Find a common denominator for the fractions.
3. Perform the addition or subtraction.
4. Simplify the result, if necessary, and convert back to a mixed fraction if needed.

Let's solve each problem step by step.

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Problem 1: \( 2 \frac{2}{3} + 4 \frac{1}{6} \)

#### Step 1: Convert mixed fractions to improper fractions
- \( 2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \)
- \( 4 \frac{1}{6} = 4 + \frac{1}{6} = \frac{24}{6} + \frac{1}{6} = \frac{25}{6} \)

#### Step 2: Find a common denominator
The denominators are 3 and 6. The least common denominator (LCD) is 6.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \)
- \( \frac{25}{6} \) remains as it is.

#### Step 4: Add the fractions
\[ \frac{16}{6} + \frac{25}{6} = \frac{16 + 25}{6} = \frac{41}{6} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{41}{6} = 6 \frac{5}{6} \]

Answer:
\[ \boxed{6 \frac{5}{6}} \]

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Problem 2: \( 6 \frac{2}{5} + 2 \frac{3}{10} \)

#### Step 1: Convert mixed fractions to improper fractions
- \( 6 \frac{2}{5} = 6 + \frac{2}{5} = \frac{30}{5} + \frac{2}{5} = \frac{32}{5} \)
- \( 2 \frac{3}{10} = 2 + \frac{3}{10} = \frac{20}{10} + \frac{3}{10} = \frac{23}{10} \)

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

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{32}{5} = \frac{32 \times 2}{5 \times 2} = \frac{64}{10} \)
- \( \frac{23}{10} \) remains as it is.

#### Step 4: Add the fractions
\[ \frac{64}{10} + \frac{23}{10} = \frac{64 + 23}{10} = \frac{87}{10} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{87}{10} = 8 \frac{7}{10} \]

Answer:
\[ \boxed{8 \frac{7}{10}} \]

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Problem 3: \( 5 \frac{2}{7} + 4 \frac{3}{14} \)

#### Step 1: Convert mixed fractions to improper fractions
- \( 5 \frac{2}{7} = 5 + \frac{2}{7} = \frac{35}{7} + \frac{2}{7} = \frac{37}{7} \)
- \( 4 \frac{3}{14} = 4 + \frac{3}{14} = \frac{56}{14} + \frac{3}{14} = \frac{59}{14} \)

#### Step 2: Find a common denominator
The denominators are 7 and 14. The LCD is 14.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{37}{7} = \frac{37 \times 2}{7 \times 2} = \frac{74}{14} \)
- \( \frac{59}{14} \) remains as it is.

#### Step 4: Add the fractions
\[ \frac{74}{14} + \frac{59}{14} = \frac{74 + 59}{14} = \frac{133}{14} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{133}{14} = 9 \frac{7}{14} = 9 \frac{1}{2} \] (simplify \( \frac{7}{14} \) to \( \frac{1}{2} \))

Answer:
\[ \boxed{9 \frac{1}{2}} \]

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Problem 4: \( 8 \frac{3}{4} - 6 \frac{2}{12} \)

#### Step 1: Convert mixed fractions to improper fractions
- \( 8 \frac{3}{4} = 8 + \frac{3}{4} = \frac{32}{4} + \frac{3}{4} = \frac{35}{4} \)
- \( 6 \frac{2}{12} = 6 + \frac{2}{12} = \frac{72}{12} + \frac{2}{12} = \frac{74}{12} \)

#### Step 2: Simplify \( \frac{2}{12} \)
\[ \frac{2}{12} = \frac{1}{6} \]
So, \( 6 \frac{2}{12} = 6 \frac{1}{6} \).

#### Step 3: Convert \( 6 \frac{1}{6} \) to an improper fraction
\[ 6 \frac{1}{6} = \frac{36}{6} + \frac{1}{6} = \frac{37}{6} \]

#### Step 4: Find a common denominator
The denominators are 4 and 6. The LCD is 12.

#### Step 5: Rewrite the fractions with the common denominator
- \( \frac{35}{4} = \frac{35 \times 3}{4 \times 3} = \frac{105}{12} \)
- \( \frac{37}{6} = \frac{37 \times 2}{6 \times 2} = \frac{74}{12} \)

#### Step 6: Subtract the fractions
\[ \frac{105}{12} - \frac{74}{12} = \frac{105 - 74}{12} = \frac{31}{12} \]

#### Step 7: Convert back to a mixed fraction
\[ \frac{31}{12} = 2 \frac{7}{12} \]

Answer:
\[ \boxed{2 \frac{7}{12}} \]

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Problem 5: \( 10 \frac{4}{5} - 5 \frac{4}{15} \)

#### Step 1: Convert mixed fractions to improper fractions
- \( 10 \frac{4}{5} = 10 + \frac{4}{5} = \frac{50}{5} + \frac{4}{5} = \frac{54}{5} \)
- \( 5 \frac{4}{15} = 5 + \frac{4}{15} = \frac{75}{15} + \frac{4}{15} = \frac{79}{15} \)

#### Step 2: Find a common denominator
The denominators are 5 and 15. The LCD is 15.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{54}{5} = \frac{54 \times 3}{5 \times 3} = \frac{162}{15} \)
- \( \frac{79}{15} \) remains as it is.

#### Step 4: Subtract the fractions
\[ \frac{162}{15} - \frac{79}{15} = \frac{162 - 79}{15} = \frac{83}{15} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{83}{15} = 5 \frac{8}{15} \]

Answer:
\[ \boxed{5 \frac{8}{15}} \]

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Final Answers:

1. \( \boxed{6 \frac{5}{6}} \)
2. \( \boxed{8 \frac{7}{10}} \)
3. \( \boxed{9 \frac{1}{2}} \)
4. \( \boxed{2 \frac{7}{12}} \)
5. \( \boxed{5 \frac{8}{15}} \)