Adding Mixed Fractions (A) worksheet featuring 12 problems to practice adding mixed numbers and simplifying to lowest terms.

To solve the problems involving adding mixed fractions, we need to follow these steps:

1. Convert mixed fractions to improper fractions.
2. Find a common denominator for the fractions.
3. Add the fractions.
4. Simplify the result to its lowest terms.
5. Convert back to a mixed fraction if necessary.

Let's solve each problem step by step.

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Problem 1: \( 2 \frac{1}{2} + 1 \frac{3}{5} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)
- \( 1 \frac{3}{5} = 1 + \frac{3}{5} = \frac{5}{5} + \frac{3}{5} = \frac{8}{5} \)

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

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10} \)
- \( \frac{8}{5} = \frac{8 \times 2}{5 \times 2} = \frac{16}{10} \)

#### Step 4: Add the fractions
\[ \frac{25}{10} + \frac{16}{10} = \frac{25 + 16}{10} = \frac{41}{10} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{41}{10} = 4 \frac{1}{10} \]

Answer: \( 4 \frac{1}{10} \)

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Problem 2: \( 1 \frac{1}{5} + 1 \frac{1}{3} \)

#### Step 1: Convert to improper fractions
- \( 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \)
- \( 1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \)

#### Step 2: Find a common denominator
The denominators are 5 and 3. The LCD is 15.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{6}{5} = \frac{6 \times 3}{5 \times 3} = \frac{18}{15} \)
- \( \frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15} \)

#### Step 4: Add the fractions
\[ \frac{18}{15} + \frac{20}{15} = \frac{18 + 20}{15} = \frac{38}{15} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{38}{15} = 2 \frac{8}{15} \]

Answer: \( 2 \frac{8}{15} \)

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Problem 3: \( 2 \frac{1}{4} + 1 \frac{5}{6} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)
- \( 1 \frac{5}{6} = 1 + \frac{5}{6} = \frac{6}{6} + \frac{5}{6} = \frac{11}{6} \)

#### Step 2: Find a common denominator
The denominators are 4 and 6. The LCD is 12.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12} \)
- \( \frac{11}{6} = \frac{11 \times 2}{6 \times 2} = \frac{22}{12} \)

#### Step 4: Add the fractions
\[ \frac{27}{12} + \frac{22}{12} = \frac{27 + 22}{12} = \frac{49}{12} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{49}{12} = 4 \frac{1}{12} \]

Answer: \( 4 \frac{1}{12} \)

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

#### Step 1: Convert to improper fractions
- \( 3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \)
- \( 1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \)

#### Step 2: Add the fractions
\[ \frac{11}{3} + \frac{5}{3} = \frac{11 + 5}{3} = \frac{16}{3} \]

#### Step 3: Convert back to a mixed fraction
\[ \frac{16}{3} = 5 \frac{1}{3} \]

Answer: \( 5 \frac{1}{3} \)

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Problem 5: \( 1 \frac{1}{5} + 2 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \)
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)

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

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{6}{5} = \frac{6 \times 2}{5 \times 2} = \frac{12}{10} \)
- \( \frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10} \)

#### Step 4: Add the fractions
\[ \frac{12}{10} + \frac{25}{10} = \frac{12 + 25}{10} = \frac{37}{10} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{37}{10} = 3 \frac{7}{10} \]

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

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Problem 6: \( 1 \frac{1}{5} + 1 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \)
- \( 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \)

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

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{6}{5} = \frac{6 \times 2}{5 \times 2} = \frac{12}{10} \)
- \( \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \)

#### Step 4: Add the fractions
\[ \frac{12}{10} + \frac{15}{10} = \frac{12 + 15}{10} = \frac{27}{10} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{27}{10} = 2 \frac{7}{10} \]

Answer: \( 2 \frac{7}{10} \)

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Problem 7: \( 1 \frac{1}{2} + 1 \frac{1}{3} \)

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

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

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \)
- \( \frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6} \)

#### Step 4: Add the fractions
\[ \frac{9}{6} + \frac{8}{6} = \frac{9 + 8}{6} = \frac{17}{6} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{17}{6} = 2 \frac{5}{6} \]

Answer: \( 2 \frac{5}{6} \)

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Problem 8: \( 3 \frac{2}{3} + 2 \frac{2}{3} \)

#### Step 1: Convert to improper fractions
- \( 3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \)
- \( 2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \)

#### Step 2: Add the fractions
\[ \frac{11}{3} + \frac{8}{3} = \frac{11 + 8}{3} = \frac{19}{3} \]

#### Step 3: Convert back to a mixed fraction
\[ \frac{19}{3} = 6 \frac{1}{3} \]

Answer: \( 6 \frac{1}{3} \)

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Problem 9: \( 1 \frac{3}{5} + 1 \frac{1}{3} \)

#### Step 1: Convert to improper fractions
- \( 1 \frac{3}{5} = 1 + \frac{3}{5} = \frac{5}{5} + \frac{3}{5} = \frac{8}{5} \)
- \( 1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \)

#### Step 2: Find a common denominator
The denominators are 5 and 3. The LCD is 15.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{8}{5} = \frac{8 \times 3}{5 \times 3} = \frac{24}{15} \)
- \( \frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15} \)

#### Step 4: Add the fractions
\[ \frac{24}{15} + \frac{20}{15} = \frac{24 + 20}{15} = \frac{44}{15} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{44}{15} = 2 \frac{14}{15} \]

Answer: \( 2 \frac{14}{15} \)

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Problem 10: \( 1 \frac{2}{5} + 1 \frac{4}{5} \)

#### Step 1: Convert to improper fractions
- \( 1 \frac{2}{5} = 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \)
- \( 1 \frac{4}{5} = 1 + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{9}{5} \)

#### Step 2: Add the fractions
\[ \frac{7}{5} + \frac{9}{5} = \frac{7 + 9}{5} = \frac{16}{5} \]

#### Step 3: Convert back to a mixed fraction
\[ \frac{16}{5} = 3 \frac{1}{5} \]

Answer: \( 3 \frac{1}{5} \)

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Problem 11: \( 1 \frac{3}{4} + 1 \frac{1}{4} \)

#### Step 1: Convert to improper fractions
- \( 1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \)
- \( 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \)

#### Step 2: Add the fractions
\[ \frac{7}{4} + \frac{5}{4} = \frac{7 + 5}{4} = \frac{12}{4} \]

#### Step 3: Simplify the fraction
\[ \frac{12}{4} = 3 \]

Answer: \( 3 \)

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Problem 12: \( 2 \frac{1}{2} + 5 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)
- \( 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \)

#### Step 2: Add the fractions
\[ \frac{5}{2} + \frac{11}{2} = \frac{5 + 11}{2} = \frac{16}{2} \]

#### Step 3: Simplify the fraction
\[ \frac{16}{2} = 8 \]

Answer: \( 8 \)

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Final Answers

\[
\boxed{
\begin{array}{ccc}
1. & 4 \frac{1}{10} & 5. & 3 \frac{7}{10} & 9. & 2 \frac{14}{15} \\
2. & 2 \frac{8}{15} & 6. & 2 \frac{7}{10} & 10. & 3 \frac{1}{5} \\
3. & 4 \frac{1}{12} & 7. & 2 \frac{5}{6} & 11. & 3 \\
4. & 5 \frac{1}{3} & 8. & 6 \frac{1}{3} & 12. & 8 \\
\end{array}
}
\]