Subtracting Mixed Numbers Worksheets - 15 Worksheets Library - Free Printable
Educational worksheet: Subtracting Mixed Numbers Worksheets - 15 Worksheets Library. Download and print for classroom or home learning activities.
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Step-by-step solution for: Subtracting Mixed Numbers Worksheets - 15 Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Subtracting Mixed Numbers Worksheets - 15 Worksheets Library
Here are the step-by-step solutions for each problem on the worksheet. To subtract mixed numbers with unlike denominators, we first find a common denominator for the fractions, convert them, and then subtract. If the top fraction is smaller than the bottom fraction, we borrow 1 from the whole number.
1. $3 \frac{1}{3} - 1 \frac{1}{2}$
* Common denominator for 3 and 2 is 6.
* Convert: $3 \frac{2}{6} - 1 \frac{3}{6}$
* Since $\frac{2}{6}$ is smaller than $\frac{3}{6}$, borrow 1 from the 3. The 3 becomes 2, and add $\frac{6}{6}$ to $\frac{2}{6}$ to get $\frac{8}{6}$.
* New equation: $2 \frac{8}{6} - 1 \frac{3}{6}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{8}{6} - \frac{3}{6} = \frac{5}{6}$
* Result: $1 \frac{5}{6}$
2. $4 \frac{3}{5} - 2 \frac{1}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $4 \frac{9}{15} - 2 \frac{5}{15}$
* Subtract wholes: $4 - 2 = 2$
* Subtract fractions: $\frac{9}{15} - \frac{5}{15} = \frac{4}{15}$
* Result: $2 \frac{4}{15}$
3. $3 \frac{1}{2} - 2 \frac{3}{5}$
* Common denominator for 2 and 5 is 10.
* Convert: $3 \frac{5}{10} - 2 \frac{6}{10}$
* Since $\frac{5}{10}$ is smaller than $\frac{6}{10}$, borrow 1 from the 3. The 3 becomes 2, and $\frac{5}{10}$ becomes $\frac{15}{10}$.
* New equation: $2 \frac{15}{10} - 2 \frac{6}{10}$
* Subtract wholes: $2 - 2 = 0$
* Subtract fractions: $\frac{15}{10} - \frac{6}{10} = \frac{9}{10}$
* Result: $\frac{9}{10}$
4. $2 \frac{2}{3} - 1 \frac{3}{5}$
* Common denominator for 3 and 5 is 15.
* Convert: $2 \frac{10}{15} - 1 \frac{9}{15}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{10}{15} - \frac{9}{15} = \frac{1}{15}$
* Result: $1 \frac{1}{15}$
5. $4 \frac{1}{6} - 3 \frac{3}{5}$
* Common denominator for 6 and 5 is 30.
* Convert: $4 \frac{5}{30} - 3 \frac{18}{30}$
* Since $\frac{5}{30}$ is smaller than $\frac{18}{30}$, borrow 1 from the 4. The 4 becomes 3, and $\frac{5}{30}$ becomes $\frac{35}{30}$.
* New equation: $3 \frac{35}{30} - 3 \frac{18}{30}$
* Subtract wholes: $3 - 3 = 0$
* Subtract fractions: $\frac{35}{30} - \frac{18}{30} = \frac{17}{30}$
* Result: $\frac{17}{30}$
6. $2 \frac{3}{4} - 1 \frac{2}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $2 \frac{15}{20} - 1 \frac{8}{20}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$
* Result: $1 \frac{7}{20}$
7. $3 \frac{1}{5} - 2 \frac{2}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $3 \frac{3}{15} - 2 \frac{10}{15}$
* Since $\frac{3}{15}$ is smaller than $\frac{10}{15}$, borrow 1 from the 3. The 3 becomes 2, and $\frac{3}{15}$ becomes $\frac{18}{15}$.
* New equation: $2 \frac{18}{15} - 2 \frac{10}{15}$
* Subtract wholes: $2 - 2 = 0$
* Subtract fractions: $\frac{18}{15} - \frac{10}{15} = \frac{8}{15}$
* Result: $\frac{8}{15}$
8. $5 \frac{1}{3} - 2 \frac{2}{5}$
* Common denominator for 3 and 5 is 15.
* Convert: $5 \frac{5}{15} - 2 \frac{6}{15}$
* Since $\frac{5}{15}$ is smaller than $\frac{6}{15}$, borrow 1 from the 5. The 5 becomes 4, and $\frac{5}{15}$ becomes $\frac{20}{15}$.
* New equation: $4 \frac{20}{15} - 2 \frac{6}{15}$
* Subtract wholes: $4 - 2 = 2$
* Subtract fractions: $\frac{20}{15} - \frac{6}{15} = \frac{14}{15}$
* Result: $2 \frac{14}{15}$
9. $4 \frac{2}{5} - 2 \frac{3}{4}$
* Common denominator for 5 and 4 is 20.
* Convert: $4 \frac{8}{20} - 2 \frac{15}{20}$
* Since $\frac{8}{20}$ is smaller than $\frac{15}{20}$, borrow 1 from the 4. The 4 becomes 3, and $\frac{8}{20}$ becomes $\frac{28}{20}$.
* New equation: $3 \frac{28}{20} - 2 \frac{15}{20}$
* Subtract wholes: $3 - 2 = 1$
* Subtract fractions: $\frac{28}{20} - \frac{15}{20} = \frac{13}{20}$
* Result: $1 \frac{13}{20}$
10. $3 \frac{3}{5} - 1 \frac{1}{4}$
* Common denominator for 5 and 4 is 20.
* Convert: $3 \frac{12}{20} - 1 \frac{5}{20}$
* Subtract wholes: $3 - 1 = 2$
* Subtract fractions: $\frac{12}{20} - \frac{5}{20} = \frac{7}{20}$
* Result: $2 \frac{7}{20}$
11. $4 \frac{4}{5} - 3 \frac{2}{7}$
* Common denominator for 5 and 7 is 35.
* Convert: $4 \frac{28}{35} - 3 \frac{10}{35}$
* Subtract wholes: $4 - 3 = 1$
* Subtract fractions: $\frac{28}{35} - \frac{10}{35} = \frac{18}{35}$
* Result: $1 \frac{18}{35}$
12. $2 \frac{2}{5} - 1 \frac{1}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $2 \frac{6}{15} - 1 \frac{5}{15}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{6}{15} - \frac{5}{15} = \frac{1}{15}$
* Result: $1 \frac{1}{15}$
13. $3 \frac{3}{5} - 2 \frac{2}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $3 \frac{9}{15} - 2 \frac{10}{15}$
* Since $\frac{9}{15}$ is smaller than $\frac{10}{15}$, borrow 1 from the 3. The 3 becomes 2, and $\frac{9}{15}$ becomes $\frac{24}{15}$.
* New equation: $2 \frac{24}{15} - 2 \frac{10}{15}$
* Subtract wholes: $2 - 2 = 0$
* Subtract fractions: $\frac{24}{15} - \frac{10}{15} = \frac{14}{15}$
* Result: $\frac{14}{15}$
14. $4 \frac{4}{5} - 1 \frac{2}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $4 \frac{12}{15} - 1 \frac{10}{15}$
* Subtract wholes: $4 - 1 = 3$
* Subtract fractions: $\frac{12}{15} - \frac{10}{15} = \frac{2}{15}$
* Result: $3 \frac{2}{15}$
15. $3 \frac{3}{4} - 2 \frac{3}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $3 \frac{15}{20} - 2 \frac{12}{20}$
* Subtract wholes: $3 - 2 = 1$
* Subtract fractions: $\frac{15}{20} - \frac{12}{20} = \frac{3}{20}$
* Result: $1 \frac{3}{20}$
16. $2 \frac{3}{4} - 1 \frac{2}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $2 \frac{15}{20} - 1 \frac{8}{20}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$
* Result: $1 \frac{7}{20}$
Final Answer:
1. $1 \frac{5}{6}$
2. $2 \frac{4}{15}$
3. $\frac{9}{10}$
4. $1 \frac{1}{15}$
5. $\frac{17}{30}$
6. $1 \frac{7}{20}$
7. $\frac{8}{15}$
8. $2 \frac{14}{15}$
9. $1 \frac{13}{20}$
10. $2 \frac{7}{20}$
11. $1 \frac{18}{35}$
12. $1 \frac{1}{15}$
13. $\frac{14}{15}$
14. $3 \frac{2}{15}$
15. $1 \frac{3}{20}$
16. $1 \frac{7}{20}$
1. $3 \frac{1}{3} - 1 \frac{1}{2}$
* Common denominator for 3 and 2 is 6.
* Convert: $3 \frac{2}{6} - 1 \frac{3}{6}$
* Since $\frac{2}{6}$ is smaller than $\frac{3}{6}$, borrow 1 from the 3. The 3 becomes 2, and add $\frac{6}{6}$ to $\frac{2}{6}$ to get $\frac{8}{6}$.
* New equation: $2 \frac{8}{6} - 1 \frac{3}{6}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{8}{6} - \frac{3}{6} = \frac{5}{6}$
* Result: $1 \frac{5}{6}$
2. $4 \frac{3}{5} - 2 \frac{1}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $4 \frac{9}{15} - 2 \frac{5}{15}$
* Subtract wholes: $4 - 2 = 2$
* Subtract fractions: $\frac{9}{15} - \frac{5}{15} = \frac{4}{15}$
* Result: $2 \frac{4}{15}$
3. $3 \frac{1}{2} - 2 \frac{3}{5}$
* Common denominator for 2 and 5 is 10.
* Convert: $3 \frac{5}{10} - 2 \frac{6}{10}$
* Since $\frac{5}{10}$ is smaller than $\frac{6}{10}$, borrow 1 from the 3. The 3 becomes 2, and $\frac{5}{10}$ becomes $\frac{15}{10}$.
* New equation: $2 \frac{15}{10} - 2 \frac{6}{10}$
* Subtract wholes: $2 - 2 = 0$
* Subtract fractions: $\frac{15}{10} - \frac{6}{10} = \frac{9}{10}$
* Result: $\frac{9}{10}$
4. $2 \frac{2}{3} - 1 \frac{3}{5}$
* Common denominator for 3 and 5 is 15.
* Convert: $2 \frac{10}{15} - 1 \frac{9}{15}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{10}{15} - \frac{9}{15} = \frac{1}{15}$
* Result: $1 \frac{1}{15}$
5. $4 \frac{1}{6} - 3 \frac{3}{5}$
* Common denominator for 6 and 5 is 30.
* Convert: $4 \frac{5}{30} - 3 \frac{18}{30}$
* Since $\frac{5}{30}$ is smaller than $\frac{18}{30}$, borrow 1 from the 4. The 4 becomes 3, and $\frac{5}{30}$ becomes $\frac{35}{30}$.
* New equation: $3 \frac{35}{30} - 3 \frac{18}{30}$
* Subtract wholes: $3 - 3 = 0$
* Subtract fractions: $\frac{35}{30} - \frac{18}{30} = \frac{17}{30}$
* Result: $\frac{17}{30}$
6. $2 \frac{3}{4} - 1 \frac{2}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $2 \frac{15}{20} - 1 \frac{8}{20}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$
* Result: $1 \frac{7}{20}$
7. $3 \frac{1}{5} - 2 \frac{2}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $3 \frac{3}{15} - 2 \frac{10}{15}$
* Since $\frac{3}{15}$ is smaller than $\frac{10}{15}$, borrow 1 from the 3. The 3 becomes 2, and $\frac{3}{15}$ becomes $\frac{18}{15}$.
* New equation: $2 \frac{18}{15} - 2 \frac{10}{15}$
* Subtract wholes: $2 - 2 = 0$
* Subtract fractions: $\frac{18}{15} - \frac{10}{15} = \frac{8}{15}$
* Result: $\frac{8}{15}$
8. $5 \frac{1}{3} - 2 \frac{2}{5}$
* Common denominator for 3 and 5 is 15.
* Convert: $5 \frac{5}{15} - 2 \frac{6}{15}$
* Since $\frac{5}{15}$ is smaller than $\frac{6}{15}$, borrow 1 from the 5. The 5 becomes 4, and $\frac{5}{15}$ becomes $\frac{20}{15}$.
* New equation: $4 \frac{20}{15} - 2 \frac{6}{15}$
* Subtract wholes: $4 - 2 = 2$
* Subtract fractions: $\frac{20}{15} - \frac{6}{15} = \frac{14}{15}$
* Result: $2 \frac{14}{15}$
9. $4 \frac{2}{5} - 2 \frac{3}{4}$
* Common denominator for 5 and 4 is 20.
* Convert: $4 \frac{8}{20} - 2 \frac{15}{20}$
* Since $\frac{8}{20}$ is smaller than $\frac{15}{20}$, borrow 1 from the 4. The 4 becomes 3, and $\frac{8}{20}$ becomes $\frac{28}{20}$.
* New equation: $3 \frac{28}{20} - 2 \frac{15}{20}$
* Subtract wholes: $3 - 2 = 1$
* Subtract fractions: $\frac{28}{20} - \frac{15}{20} = \frac{13}{20}$
* Result: $1 \frac{13}{20}$
10. $3 \frac{3}{5} - 1 \frac{1}{4}$
* Common denominator for 5 and 4 is 20.
* Convert: $3 \frac{12}{20} - 1 \frac{5}{20}$
* Subtract wholes: $3 - 1 = 2$
* Subtract fractions: $\frac{12}{20} - \frac{5}{20} = \frac{7}{20}$
* Result: $2 \frac{7}{20}$
11. $4 \frac{4}{5} - 3 \frac{2}{7}$
* Common denominator for 5 and 7 is 35.
* Convert: $4 \frac{28}{35} - 3 \frac{10}{35}$
* Subtract wholes: $4 - 3 = 1$
* Subtract fractions: $\frac{28}{35} - \frac{10}{35} = \frac{18}{35}$
* Result: $1 \frac{18}{35}$
12. $2 \frac{2}{5} - 1 \frac{1}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $2 \frac{6}{15} - 1 \frac{5}{15}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{6}{15} - \frac{5}{15} = \frac{1}{15}$
* Result: $1 \frac{1}{15}$
13. $3 \frac{3}{5} - 2 \frac{2}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $3 \frac{9}{15} - 2 \frac{10}{15}$
* Since $\frac{9}{15}$ is smaller than $\frac{10}{15}$, borrow 1 from the 3. The 3 becomes 2, and $\frac{9}{15}$ becomes $\frac{24}{15}$.
* New equation: $2 \frac{24}{15} - 2 \frac{10}{15}$
* Subtract wholes: $2 - 2 = 0$
* Subtract fractions: $\frac{24}{15} - \frac{10}{15} = \frac{14}{15}$
* Result: $\frac{14}{15}$
14. $4 \frac{4}{5} - 1 \frac{2}{3}$
* Common denominator for 5 and 3 is 15.
* Convert: $4 \frac{12}{15} - 1 \frac{10}{15}$
* Subtract wholes: $4 - 1 = 3$
* Subtract fractions: $\frac{12}{15} - \frac{10}{15} = \frac{2}{15}$
* Result: $3 \frac{2}{15}$
15. $3 \frac{3}{4} - 2 \frac{3}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $3 \frac{15}{20} - 2 \frac{12}{20}$
* Subtract wholes: $3 - 2 = 1$
* Subtract fractions: $\frac{15}{20} - \frac{12}{20} = \frac{3}{20}$
* Result: $1 \frac{3}{20}$
16. $2 \frac{3}{4} - 1 \frac{2}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $2 \frac{15}{20} - 1 \frac{8}{20}$
* Subtract wholes: $2 - 1 = 1$
* Subtract fractions: $\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$
* Result: $1 \frac{7}{20}$
Final Answer:
1. $1 \frac{5}{6}$
2. $2 \frac{4}{15}$
3. $\frac{9}{10}$
4. $1 \frac{1}{15}$
5. $\frac{17}{30}$
6. $1 \frac{7}{20}$
7. $\frac{8}{15}$
8. $2 \frac{14}{15}$
9. $1 \frac{13}{20}$
10. $2 \frac{7}{20}$
11. $1 \frac{18}{35}$
12. $1 \frac{1}{15}$
13. $\frac{14}{15}$
14. $3 \frac{2}{15}$
15. $1 \frac{3}{20}$
16. $1 \frac{7}{20}$
Parent Tip: Review the logic above to help your child master the concept of subtracting fractions with whole numbers.
