Subtracting Mixed Numbers Worksheet with Ten Problems

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

1) $5 \frac{3}{5} - 2 \frac{1}{10}$
* First, find a common denominator for the fractions $\frac{3}{5}$ and $\frac{1}{10}$. The common denominator is 10.
* Convert $\frac{3}{5}$ to tenths: $\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$.
* Now subtract: $5 \frac{6}{10} - 2 \frac{1}{10}$.
* Subtract whole numbers: $5 - 2 = 3$.
* Subtract fractions: $\frac{6}{10} - \frac{1}{10} = \frac{5}{10}$.
* Simplify the fraction: $\frac{5}{10} = \frac{1}{2}$.
* Result: $3 \frac{1}{2}$.

2) $5 \frac{2}{3} - 4 \frac{2}{4}$
* Find a common denominator for 3 and 4, which is 12.
* Convert fractions: $\frac{2}{3} = \frac{8}{12}$ and $\frac{2}{4} = \frac{6}{12}$.
* Rewrite problem: $5 \frac{8}{12} - 4 \frac{6}{12}$.
* Subtract whole numbers: $5 - 4 = 1$.
* Subtract fractions: $\frac{8}{12} - \frac{6}{12} = \frac{2}{12}$.
* Simplify the fraction: $\frac{2}{12} = \frac{1}{6}$.
* Result: $1 \frac{1}{6}$.

3) $5 \frac{3}{4} - 4 \frac{2}{5}$
* Find a common denominator for 4 and 5, which is 20.
* Convert fractions: $\frac{3}{4} = \frac{15}{20}$ and $\frac{2}{5} = \frac{8}{20}$.
* Rewrite problem: $5 \frac{15}{20} - 4 \frac{8}{20}$.
* Subtract whole numbers: $5 - 4 = 1$.
* Subtract fractions: $\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$.
* Result: $1 \frac{7}{20}$.

4) $9 \frac{3}{5} - 1 \frac{2}{4}$
* Find a common denominator for 5 and 4, which is 20.
* Convert fractions: $\frac{3}{5} = \frac{12}{20}$ and $\frac{2}{4} = \frac{10}{20}$.
* Rewrite problem: $9 \frac{12}{20} - 1 \frac{10}{20}$.
* Subtract whole numbers: $9 - 1 = 8$.
* Subtract fractions: $\frac{12}{20} - \frac{10}{20} = \frac{2}{20}$.
* Simplify the fraction: $\frac{2}{20} = \frac{1}{10}$.
* Result: $8 \frac{1}{10}$.

5) $6 \frac{3}{10} - 1 \frac{1}{4}$
* Find a common denominator for 10 and 4, which is 20.
* Convert fractions: $\frac{3}{10} = \frac{6}{20}$ and $\frac{1}{4} = \frac{5}{20}$.
* Rewrite problem: $6 \frac{6}{20} - 1 \frac{5}{20}$.
* Subtract whole numbers: $6 - 1 = 5$.
* Subtract fractions: $\frac{6}{20} - \frac{5}{20} = \frac{1}{20}$.
* Result: $5 \frac{1}{20}$.

6) $9 \frac{1}{4} - 3 \frac{1}{5}$
* Find a common denominator for 4 and 5, which is 20.
* Convert fractions: $\frac{1}{4} = \frac{5}{20}$ and $\frac{1}{5} = \frac{4}{20}$.
* Rewrite problem: $9 \frac{5}{20} - 3 \frac{4}{20}$.
* Subtract whole numbers: $9 - 3 = 6$.
* Subtract fractions: $\frac{5}{20} - \frac{4}{20} = \frac{1}{20}$.
* Result: $6 \frac{1}{20}$.

7) $9 \frac{1}{3} - 4 \frac{1}{5}$
* Find a common denominator for 3 and 5, which is 15.
* Convert fractions: $\frac{1}{3} = \frac{5}{15}$ and $\frac{1}{5} = \frac{3}{15}$.
* Rewrite problem: $9 \frac{5}{15} - 4 \frac{3}{15}$.
* Subtract whole numbers: $9 - 4 = 5$.
* Subtract fractions: $\frac{5}{15} - \frac{3}{15} = \frac{2}{15}$.
* Result: $5 \frac{2}{15}$.

8) $6 \frac{4}{5} - 1 \frac{1}{4}$
* Find a common denominator for 5 and 4, which is 20.
* Convert fractions: $\frac{4}{5} = \frac{16}{20}$ and $\frac{1}{4} = \frac{5}{20}$.
* Rewrite problem: $6 \frac{16}{20} - 1 \frac{5}{20}$.
* Subtract whole numbers: $6 - 1 = 5$.
* Subtract fractions: $\frac{16}{20} - \frac{5}{20} = \frac{11}{20}$.
* Result: $5 \frac{11}{20}$.

9) $9 \frac{7}{10} - 1 \frac{2}{3}$
* Find a common denominator for 10 and 3, which is 30.
* Convert fractions: $\frac{7}{10} = \frac{21}{30}$ and $\frac{2}{3} = \frac{20}{30}$.
* Rewrite problem: $9 \frac{21}{30} - 1 \frac{20}{30}$.
* Subtract whole numbers: $9 - 1 = 8$.
* Subtract fractions: $\frac{21}{30} - \frac{20}{30} = \frac{1}{30}$.
* Result: $8 \frac{1}{30}$.

10) $6 \frac{2}{4} - 3 \frac{4}{10}$
* Find a common denominator for 4 and 10, which is 20.
* Convert fractions: $\frac{2}{4} = \frac{10}{20}$ and $\frac{4}{10} = \frac{8}{20}$.
* Rewrite problem: $6 \frac{10}{20} - 3 \frac{8}{20}$.
* Subtract whole numbers: $6 - 3 = 3$.
* Subtract fractions: $\frac{10}{20} - \frac{8}{20} = \frac{2}{20}$.
* Simplify the fraction: $\frac{2}{20} = \frac{1}{10}$.
* Result: $3 \frac{1}{10}$.

Final Answer:
1) $3 \frac{1}{2}$
2) $1 \frac{1}{6}$
3) $1 \frac{7}{20}$
4) $8 \frac{1}{10}$
5) $5 \frac{1}{20}$
6) $6 \frac{1}{20}$
7) $5 \frac{2}{15}$
8) $5 \frac{11}{20}$
9) $8 \frac{1}{30}$
10) $3 \frac{1}{10}$