Mixed Numbers Subtraction Worksheet - Free Printable

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

1. $6 \frac{3}{9} - 3 \frac{2}{6}$
* First, simplify the fractions: $\frac{3}{9}$ becomes $\frac{1}{3}$ and $\frac{2}{6}$ becomes $\frac{1}{3}$.
* The problem is now: $6 \frac{1}{3} - 3 \frac{1}{3}$.
* Subtract the whole numbers: $6 - 3 = 3$.
* Subtract the fractions: $\frac{1}{3} - \frac{1}{3} = 0$.
* Answer: $3$

2. $4 \frac{2}{4} - 1 \frac{3}{6}$
* Simplify the fractions: $\frac{2}{4}$ becomes $\frac{1}{2}$ and $\frac{3}{6}$ becomes $\frac{1}{2}$.
* The problem is now: $4 \frac{1}{2} - 1 \frac{1}{2}$.
* Subtract the whole numbers: $4 - 1 = 3$.
* Subtract the fractions: $\frac{1}{2} - \frac{1}{2} = 0$.
* Answer: $3$

3. $5 \frac{6}{10} - 2 \frac{4}{12}$
* Simplify the fractions: $\frac{6}{10}$ becomes $\frac{3}{5}$ and $\frac{4}{12}$ becomes $\frac{1}{3}$.
* Find a common denominator for 5 and 3, which is 15.
* Convert fractions: $\frac{3}{5} = \frac{9}{15}$ and $\frac{1}{3} = \frac{5}{15}$.
* The problem is now: $5 \frac{9}{15} - 2 \frac{5}{15}$.
* Subtract whole numbers: $5 - 2 = 3$.
* Subtract fractions: $\frac{9}{15} - \frac{5}{15} = \frac{4}{15}$.
* Answer: $3 \frac{4}{15}$

4. $3 \frac{12}{2} - 1 \frac{1}{6}$
* Simplify the first fraction: $\frac{12}{2} = 6$. So, $3 \frac{12}{2}$ is actually $3 + 6 = 9$.
* The problem is now: $9 - 1 \frac{1}{6}$.
* Think of 9 as $8 \frac{6}{6}$.
* Subtract: $8 \frac{6}{6} - 1 \frac{1}{6}$.
* Whole numbers: $8 - 1 = 7$.
* Fractions: $\frac{6}{6} - \frac{1}{6} = \frac{5}{6}$.
* Answer: $7 \frac{5}{6}$

5. $6 \frac{2}{5} - 4 \frac{2}{8}$
* Simplify the second fraction: $\frac{2}{8}$ becomes $\frac{1}{4}$.
* Find a common denominator for 5 and 4, which is 20.
* Convert fractions: $\frac{2}{5} = \frac{8}{20}$ and $\frac{1}{4} = \frac{5}{20}$.
* The problem is now: $6 \frac{8}{20} - 4 \frac{5}{20}$.
* Subtract whole numbers: $6 - 4 = 2$.
* Subtract fractions: $\frac{8}{20} - \frac{5}{20} = \frac{3}{20}$.
* Answer: $2 \frac{3}{20}$

6. $8 \frac{3}{8} - 2 \frac{6}{11}$
* Find a common denominator for 8 and 11, which is 88.
* Convert fractions: $\frac{3}{8} = \frac{33}{88}$ and $\frac{6}{11} = \frac{48}{88}$.
* Since $\frac{33}{88}$ is smaller than $\frac{48}{88}$, we need to borrow from the whole number 8.
* Change $8 \frac{33}{88}$ to $7 \frac{121}{88}$ (because $88 + 33 = 121$).
* The problem is now: $7 \frac{121}{88} - 2 \frac{48}{88}$.
* Subtract whole numbers: $7 - 2 = 5$.
* Subtract fractions: $\frac{121}{88} - \frac{48}{88} = \frac{73}{88}$.
* Answer: $5 \frac{73}{88}$

7. $5 \frac{4}{9} - 6 \frac{5}{12}$
* *Note: Usually in these worksheets, the first number is larger. However, strictly following the math:*
* Find a common denominator for 9 and 12, which is 36.
* Convert fractions: $\frac{4}{9} = \frac{16}{36}$ and $\frac{5}{12} = \frac{15}{36}$.
* The problem is $5 \frac{16}{36} - 6 \frac{15}{36}$.
* Since 6 is larger than 5, the answer will be negative.
* $6 \frac{15}{36} - 5 \frac{16}{36}$. Borrow from 6 to make it $5 \frac{51}{36}$.
* $5 \frac{51}{36} - 5 \frac{16}{36} = \frac{35}{36}$.
* Because we subtracted the larger number from the smaller one, the result is negative.
* Answer: $-\frac{35}{36}$
*(If this was a typo in the book and should have been $6 \frac{4}{9} - 5 \frac{5}{12}$, the answer would be $\frac{35}{36}$. If it should have been $5 \frac{4}{9} - 4 \frac{5}{12}$, the answer would be $\frac{23}{36}$. Based strictly on the image text, the answer is negative.)*

8. $5 \frac{4}{8} - 2 \frac{1}{10}$
* Simplify the first fraction: $\frac{4}{8}$ becomes $\frac{1}{2}$.
* Find a common denominator for 2 and 10, which is 10.
* Convert fractions: $\frac{1}{2} = \frac{5}{10}$. The second fraction is already $\frac{1}{10}$.
* The problem is now: $5 \frac{5}{10} - 2 \frac{1}{10}$.
* Subtract whole numbers: $5 - 2 = 3$.
* Subtract fractions: $\frac{5}{10} - \frac{1}{10} = \frac{4}{10}$.
* Simplify the result: $\frac{4}{10}$ becomes $\frac{2}{5}$.
* Answer: $3 \frac{2}{5}$

9. $3 \frac{1}{6} - 1 \frac{2}{4}$
* Simplify the second fraction: $\frac{2}{4}$ becomes $\frac{1}{2}$.
* Find a common denominator for 6 and 2, which is 6.
* Convert fractions: $\frac{1}{6}$ stays $\frac{1}{6}$. $\frac{1}{2} = \frac{3}{6}$.
* The problem is now: $3 \frac{1}{6} - 1 \frac{3}{6}$.
* We need to borrow because $\frac{1}{6}$ is smaller than $\frac{3}{6}$.
* Change $3 \frac{1}{6}$ to $2 \frac{7}{6}$ (since $6+1=7$).
* Subtract whole numbers: $2 - 1 = 1$.
* Subtract fractions: $\frac{7}{6} - \frac{3}{6} = \frac{4}{6}$.
* Simplify the result: $\frac{4}{6}$ becomes $\frac{2}{3}$.
* Answer: $1 \frac{2}{3}$

10. $7 \frac{2}{8} - 5 \frac{5}{7}$
* Simplify the first fraction: $\frac{2}{8}$ becomes $\frac{1}{4}$.
* Find a common denominator for 4 and 7, which is 28.
* Convert fractions: $\frac{1}{4} = \frac{7}{28}$ and $\frac{5}{7} = \frac{20}{28}$.
* The problem is now: $7 \frac{7}{28} - 5 \frac{20}{28}$.
* We need to borrow because $\frac{7}{28}$ is smaller than $\frac{20}{28}$.
* Change $7 \frac{7}{28}$ to $6 \frac{35}{28}$ (since $28+7=35$).
* Subtract whole numbers: $6 - 5 = 1$.
* Subtract fractions: $\frac{35}{28} - \frac{20}{28} = \frac{15}{28}$.
* Answer: $1 \frac{15}{28}$

11. $8 \frac{6}{8} - 4 \frac{6}{9}$
* Simplify fractions: $\frac{6}{8}$ becomes $\frac{3}{4}$ and $\frac{6}{9}$ becomes $\frac{2}{3}$.
* Find a common denominator for 4 and 3, which is 12.
* Convert fractions: $\frac{3}{4} = \frac{9}{12}$ and $\frac{2}{3} = \frac{8}{12}$.
* The problem is now: $8 \frac{9}{12} - 4 \frac{8}{12}$.
* Subtract whole numbers: $8 - 4 = 4$.
* Subtract fractions: $\frac{9}{12} - \frac{8}{12} = \frac{1}{12}$.
* Answer: $4 \frac{1}{12}$

12. $4 \frac{1}{4} - 2 \frac{3}{12}$
* Simplify the second fraction: $\frac{3}{12}$ becomes $\frac{1}{4}$.
* The problem is now: $4 \frac{1}{4} - 2 \frac{1}{4}$.
* Subtract whole numbers: $4 - 2 = 2$.
* Subtract fractions: $\frac{1}{4} - \frac{1}{4} = 0$.
* Answer: $2$

13. $7 \frac{4}{8} - 5 \frac{3}{6}$
* Simplify fractions: $\frac{4}{8}$ becomes $\frac{1}{2}$ and $\frac{3}{6}$ becomes $\frac{1}{2}$.
* The problem is now: $7 \frac{1}{2} - 5 \frac{1}{2}$.
* Subtract whole numbers: $7 - 5 = 2$.
* Subtract fractions: $\frac{1}{2} - \frac{1}{2} = 0$.
* Answer: $2$

14. $4 \frac{2}{6} - 5 \frac{2}{8}$
* *Note: Similar to #7, the second number is larger.*
* Simplify fractions: $\frac{2}{6}$ becomes $\frac{1}{3}$ and $\frac{2}{8}$ becomes $\frac{1}{4}$.
* Find a common denominator for 3 and 4, which is 12.
* Convert fractions: $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$.
* The problem is $4 \frac{4}{12} - 5 \frac{3}{12}$.
* Since 5 is larger than 4, the answer is negative.
* $5 \frac{3}{12} - 4 \frac{4}{12}$. Borrow from 5 to make it $4 \frac{15}{12}$.
* $4 \frac{15}{12} - 4 \frac{4}{12} = \frac{11}{12}$.
* Because we subtracted the larger number from the smaller one, the result is negative.
* Answer: $-\frac{11}{12}$

Final Answer:
1. 3
2. 3
3. 3 4/15
4. 7 5/6
5. 2 3/20
6. 5 73/88
7. -35/36
8. 3 2/5
9. 1 2/3
10. 1 15/28
11. 4 1/12
12. 2
13. 2
14. -11/12