Add and subtract mixed numbers worksheet for assisted learning.

Problem: Add & Subtract Mixed Numbers

The task involves adding mixed numbers and simplifying the final answers. Let's solve each problem step by step.

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#### 1. \( 4 \frac{1}{5} + 7 \frac{2}{5} \)

- Step 1: Separate the whole numbers and fractions.
\[
4 \frac{1}{5} = 4 + \frac{1}{5}, \quad 7 \frac{2}{5} = 7 + \frac{2}{5}
\]

- Step 2: Add the whole numbers.
\[
4 + 7 = 11
\]

- Step 3: Add the fractions.
\[
\frac{1}{5} + \frac{2}{5} = \frac{1 + 2}{5} = \frac{3}{5}
\]

- Step 4: Combine the results.
\[
11 + \frac{3}{5} = 11 \frac{3}{5}
\]

- Final Answer:
\[
\boxed{11 \frac{3}{5}}
\]

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#### 2. \( 1 \frac{8}{9} + 2 \frac{3}{9} \)

- Step 1: Separate the whole numbers and fractions.
\[
1 \frac{8}{9} = 1 + \frac{8}{9}, \quad 2 \frac{3}{9} = 2 + \frac{3}{9}
\]

- Step 2: Add the whole numbers.
\[
1 + 2 = 3
\]

- Step 3: Add the fractions.
\[
\frac{8}{9} + \frac{3}{9} = \frac{8 + 3}{9} = \frac{11}{9}
\]

- Step 4: Simplify the improper fraction \(\frac{11}{9}\) to a mixed number.
\[
\frac{11}{9} = 1 \frac{2}{9}
\]

- Step 5: Combine the results.
\[
3 + 1 \frac{2}{9} = 4 \frac{2}{9}
\]

- Final Answer:
\[
\boxed{4 \frac{2}{9}}
\]

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#### 3. \( 3 \frac{3}{4} + 8 \frac{3}{4} \)

- Step 1: Separate the whole numbers and fractions.
\[
3 \frac{3}{4} = 3 + \frac{3}{4}, \quad 8 \frac{3}{4} = 8 + \frac{3}{4}
\]

- Step 2: Add the whole numbers.
\[
3 + 8 = 11
\]

- Step 3: Add the fractions.
\[
\frac{3}{4} + \frac{3}{4} = \frac{3 + 3}{4} = \frac{6}{4}
\]

- Step 4: Simplify the improper fraction \(\frac{6}{4}\).
\[
\frac{6}{4} = \frac{3}{2} = 1 \frac{1}{2}
\]

- Step 5: Combine the results.
\[
11 + 1 \frac{1}{2} = 12 \frac{1}{2}
\]

- Final Answer:
\[
\boxed{12 \frac{1}{2}}
\]

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#### 4. \( 1 \frac{6}{7} + 1 \frac{5}{7} \)

- Step 1: Separate the whole numbers and fractions.
\[
1 \frac{6}{7} = 1 + \frac{6}{7}, \quad 1 \frac{5}{7} = 1 + \frac{5}{7}
\]

- Step 2: Add the whole numbers.
\[
1 + 1 = 2
\]

- Step 3: Add the fractions.
\[
\frac{6}{7} + \frac{5}{7} = \frac{6 + 5}{7} = \frac{11}{7}
\]

- Step 4: Simplify the improper fraction \(\frac{11}{7}\) to a mixed number.
\[
\frac{11}{7} = 1 \frac{4}{7}
\]

- Step 5: Combine the results.
\[
2 + 1 \frac{4}{7} = 3 \frac{4}{7}
\]

- Final Answer:
\[
\boxed{3 \frac{4}{7}}
\]

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#### 5. \( 5 \frac{2}{6} + 8 \frac{1}{6} \)

- Step 1: Separate the whole numbers and fractions.
\[
5 \frac{2}{6} = 5 + \frac{2}{6}, \quad 8 \frac{1}{6} = 8 + \frac{1}{6}
\]

- Step 2: Add the whole numbers.
\[
5 + 8 = 13
\]

- Step 3: Add the fractions.
\[
\frac{2}{6} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6}
\]

- Step 4: Simplify the fraction \(\frac{3}{6}\).
\[
\frac{3}{6} = \frac{1}{2}
\]

- Step 5: Combine the results.
\[
13 + \frac{1}{2} = 13 \frac{1}{2}
\]

- Final Answer:
\[
\boxed{13 \frac{1}{2}}
\]

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Final Answers:

1. \( \boxed{11 \frac{3}{5}} \)
2. \( \boxed{4 \frac{2}{9}} \)
3. \( \boxed{12 \frac{1}{2}} \)
4. \( \boxed{3 \frac{4}{7}} \)
5. \( \boxed{13 \frac{1}{2}} \)