Adding Mixed Numbers worksheet with ten equations for practice.

Here are the step-by-step solutions for each problem on the worksheet.

1. $2\frac{1}{3} + 7\frac{1}{5}$
* First, add the whole numbers: $2 + 7 = 9$.
* Next, add the fractions $\frac{1}{3} + \frac{1}{5}$. The common denominator for 3 and 5 is 15.
* Convert the fractions: $\frac{1}{3} = \frac{5}{15}$ and $\frac{1}{5} = \frac{3}{15}$.
* Add them: $\frac{5}{15} + \frac{3}{15} = \frac{8}{15}$.
* Combine the parts: $9\frac{8}{15}$.

2. $5\frac{1}{4} + 1\frac{1}{3}$
* Add whole numbers: $5 + 1 = 6$.
* Add fractions $\frac{1}{4} + \frac{1}{3}$. The common denominator is 12.
* Convert: $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{3} = \frac{4}{12}$.
* Add them: $\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$.
* Combine: $6\frac{7}{12}$.

3. $4\frac{8}{11} + 4\frac{1}{6}$
* Add whole numbers: $4 + 4 = 8$.
* Add fractions $\frac{8}{11} + \frac{1}{6}$. The common denominator is 66 ($11 \times 6$).
* Convert: $\frac{8}{11} = \frac{48}{66}$ and $\frac{1}{6} = \frac{11}{66}$.
* Add them: $\frac{48}{66} + \frac{11}{66} = \frac{59}{66}$.
* Combine: $8\frac{59}{66}$.

4. $3\frac{5}{8} + 5\frac{2}{3}$
* Add whole numbers: $3 + 5 = 8$.
* Add fractions $\frac{5}{8} + \frac{2}{3}$. The common denominator is 24.
* Convert: $\frac{5}{8} = \frac{15}{24}$ and $\frac{2}{3} = \frac{16}{24}$.
* Add them: $\frac{15}{24} + \frac{16}{24} = \frac{31}{24}$.
* Since $\frac{31}{24}$ is an improper fraction, convert it to a mixed number: $1\frac{7}{24}$.
* Add this 1 to the whole number sum: $8 + 1 = 9$.
* Final answer: $9\frac{7}{24}$.

5. $9\frac{1}{3} + 6\frac{3}{8}$
* Add whole numbers: $9 + 6 = 15$.
* Add fractions $\frac{1}{3} + \frac{3}{8}$. The common denominator is 24.
* Convert: $\frac{1}{3} = \frac{8}{24}$ and $\frac{3}{8} = \frac{9}{24}$.
* Add them: $\frac{8}{24} + \frac{9}{24} = \frac{17}{24}$.
* Combine: $15\frac{17}{24}$.

6. $10\frac{6}{7} + 2\frac{2}{9}$
* Add whole numbers: $10 + 2 = 12$.
* Add fractions $\frac{6}{7} + \frac{2}{9}$. The common denominator is 63.
* Convert: $\frac{6}{7} = \frac{54}{63}$ and $\frac{2}{9} = \frac{14}{63}$.
* Add them: $\frac{54}{63} + \frac{14}{63} = \frac{68}{63}$.
* Convert improper fraction: $\frac{68}{63} = 1\frac{5}{63}$.
* Add the 1 to the whole number sum: $12 + 1 = 13$.
* Final answer: $13\frac{5}{63}$.

7. $3\frac{1}{6} + 2\frac{1}{3}$
* Add whole numbers: $3 + 2 = 5$.
* Add fractions $\frac{1}{6} + \frac{1}{3}$. The common denominator is 6.
* Convert: $\frac{1}{3} = \frac{2}{6}$. So, $\frac{1}{6} + \frac{2}{6} = \frac{3}{6}$.
* Simplify the fraction: $\frac{3}{6} = \frac{1}{2}$.
* Combine: $5\frac{1}{2}$.

8. $5\frac{1}{7} + 6\frac{1}{2}$
* Add whole numbers: $5 + 6 = 11$.
* Add fractions $\frac{1}{7} + \frac{1}{2}$. The common denominator is 14.
* Convert: $\frac{1}{7} = \frac{2}{14}$ and $\frac{1}{2} = \frac{7}{14}$.
* Add them: $\frac{2}{14} + \frac{7}{14} = \frac{9}{14}$.
* Combine: $11\frac{9}{14}$.

9. $7\frac{7}{8} + 11\frac{1}{4}$
* Add whole numbers: $7 + 11 = 18$.
* Add fractions $\frac{7}{8} + \frac{1}{4}$. The common denominator is 8.
* Convert: $\frac{1}{4} = \frac{2}{8}$. So, $\frac{7}{8} + \frac{2}{8} = \frac{9}{8}$.
* Convert improper fraction: $\frac{9}{8} = 1\frac{1}{8}$.
* Add the 1 to the whole number sum: $18 + 1 = 19$.
* Final answer: $19\frac{1}{8}$.

10. $8\frac{2}{9} + 4\frac{4}{5}$
* Add whole numbers: $8 + 4 = 12$.
* Add fractions $\frac{2}{9} + \frac{4}{5}$. The common denominator is 45.
* Convert: $\frac{2}{9} = \frac{10}{45}$ and $\frac{4}{5} = \frac{36}{45}$.
* Add them: $\frac{10}{45} + \frac{36}{45} = \frac{46}{45}$.
* Convert improper fraction: $\frac{46}{45} = 1\frac{1}{45}$.
* Add the 1 to the whole number sum: $12 + 1 = 13$.
* Final answer: $13\frac{1}{45}$.

Final Answer:
1. $9\frac{8}{15}$
2. $6\frac{7}{12}$
3. $8\frac{59}{66}$
4. $9\frac{7}{24}$
5. $15\frac{17}{24}$
6. $13\frac{5}{63}$
7. $5\frac{1}{2}$
8. $11\frac{9}{14}$
9. $19\frac{1}{8}$
10. $13\frac{1}{45}$