Math worksheet for practicing addition and subtraction of mixed fractions.
Worksheet titled "Adding and Subtracting Mixed Fractions" with 12 math problems involving addition and subtraction of mixed numbers.
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Step-by-step solution for: Adding and Subtracting Fractions Worksheets with Answer Key
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Show Answer Key & Explanations
Step-by-step solution for: Adding and Subtracting Fractions Worksheets with Answer Key
Here are the step-by-step solutions for each problem on the worksheet.
1) $7 \frac{1}{2} + 1 \frac{7}{8}$
* First, find a common denominator for the fractions $\frac{1}{2}$ and $\frac{7}{8}$. The common denominator is 8.
* Convert $\frac{1}{2}$ to eighths: $\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$.
* Add the whole numbers: $7 + 1 = 8$.
* Add the fractions: $\frac{4}{8} + \frac{7}{8} = \frac{11}{8}$.
* Since $\frac{11}{8}$ is an improper fraction, convert it to a mixed number: $1 \frac{3}{8}$.
* Add this to the whole number sum: $8 + 1 \frac{3}{8} = 9 \frac{3}{8}$.
2) $9 \frac{1}{6} - 4 \frac{1}{2}$
* Find a common denominator for 6 and 2, which is 6.
* Convert $\frac{1}{2}$ to sixths: $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
* The problem is now $9 \frac{1}{6} - 4 \frac{3}{6}$.
* You cannot subtract $\frac{3}{6}$ from $\frac{1}{6}$, so you must borrow from the whole number 9.
* Change 9 to 8 and add $\frac{6}{6}$ to the fraction: $\frac{1}{6} + \frac{6}{6} = \frac{7}{6}$.
* Now subtract: $8 \frac{7}{6} - 4 \frac{3}{6}$.
* Whole numbers: $8 - 4 = 4$.
* Fractions: $\frac{7}{6} - \frac{3}{6} = \frac{4}{6}$.
* Simplify $\frac{4}{6}$ by dividing top and bottom by 2: $\frac{2}{3}$.
* Answer: $4 \frac{2}{3}$.
3) $6 \frac{1}{3} + 2 \frac{5}{6}$
* Common denominator for 3 and 6 is 6.
* Convert $\frac{1}{3}$: $\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$.
* Add whole numbers: $6 + 2 = 8$.
* Add fractions: $\frac{2}{6} + \frac{5}{6} = \frac{7}{6}$.
* Convert $\frac{7}{6}$ to $1 \frac{1}{6}$.
* Add to whole number sum: $8 + 1 \frac{1}{6} = 9 \frac{1}{6}$.
4) $4 \frac{4}{5} - 3 \frac{1}{6}$
* Common denominator for 5 and 6 is 30.
* Convert fractions: $\frac{4}{5} = \frac{24}{30}$ and $\frac{1}{6} = \frac{5}{30}$.
* Subtract whole numbers: $4 - 3 = 1$.
* Subtract fractions: $\frac{24}{30} - \frac{5}{30} = \frac{19}{30}$.
* Answer: $1 \frac{19}{30}$.
5) $2 \frac{1}{2} + 3 \frac{1}{4}$
* Common denominator for 2 and 4 is 4.
* Convert $\frac{1}{2}$: $\frac{2}{4}$.
* Add whole numbers: $2 + 3 = 5$.
* Add fractions: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.
* Answer: $5 \frac{3}{4}$.
6) $4 \frac{4}{7} - 2 \frac{2}{5}$
* Common denominator for 7 and 5 is 35.
* Convert fractions: $\frac{4}{7} = \frac{20}{35}$ and $\frac{2}{5} = \frac{14}{35}$.
* Subtract whole numbers: $4 - 2 = 2$.
* Subtract fractions: $\frac{20}{35} - \frac{14}{35} = \frac{6}{35}$.
* Answer: $2 \frac{6}{35}$.
7) $3 \frac{7}{12} + 2 \frac{1}{8}$
* Common denominator for 12 and 8 is 24.
* Convert fractions: $\frac{7}{12} = \frac{14}{24}$ and $\frac{1}{8} = \frac{3}{24}$.
* Add whole numbers: $3 + 2 = 5$.
* Add fractions: $\frac{14}{24} + \frac{3}{24} = \frac{17}{24}$.
* Answer: $5 \frac{17}{24}$.
8) $5 \frac{1}{5} - 3 \frac{5}{7}$
* Common denominator for 5 and 7 is 35.
* Convert fractions: $\frac{1}{5} = \frac{7}{35}$ and $\frac{5}{7} = \frac{25}{35}$.
* Problem: $5 \frac{7}{35} - 3 \frac{25}{35}$.
* Cannot subtract $\frac{25}{35}$ from $\frac{7}{35}$, so borrow from 5.
* Change 5 to 4 and add $\frac{35}{35}$ to fraction: $\frac{7}{35} + \frac{35}{35} = \frac{42}{35}$.
* New problem: $4 \frac{42}{35} - 3 \frac{25}{35}$.
* Subtract whole numbers: $4 - 3 = 1$.
* Subtract fractions: $\frac{42}{35} - \frac{25}{35} = \frac{17}{35}$.
* Answer: $1 \frac{17}{35}$.
9) $4 \frac{2}{5} + 3 \frac{5}{6}$
* Common denominator for 5 and 6 is 30.
* Convert fractions: $\frac{2}{5} = \frac{12}{30}$ and $\frac{5}{6} = \frac{25}{30}$.
* Add whole numbers: $4 + 3 = 7$.
* Add fractions: $\frac{12}{30} + \frac{25}{30} = \frac{37}{30}$.
* Convert improper fraction: $\frac{37}{30} = 1 \frac{7}{30}$.
* Add to whole number sum: $7 + 1 \frac{7}{30} = 8 \frac{7}{30}$.
10) $3 \frac{1}{10} - 1 \frac{6}{8}$
* First, simplify $\frac{6}{8}$ to $\frac{3}{4}$ to make it easier (optional, but helpful). Let's stick to denominators 10 and 8 first. Common denominator is 40.
* Convert fractions: $\frac{1}{10} = \frac{4}{40}$ and $\frac{6}{8} = \frac{30}{40}$.
* Problem: $3 \frac{4}{40} - 1 \frac{30}{40}$.
* Borrow from 3: Change 3 to 2, add $\frac{40}{40}$ to fraction. $\frac{4}{40} + \frac{40}{40} = \frac{44}{40}$.
* New problem: $2 \frac{44}{40} - 1 \frac{30}{40}$.
* Subtract whole numbers: $2 - 1 = 1$.
* Subtract fractions: $\frac{44}{40} - \frac{30}{40} = \frac{14}{40}$.
* Simplify $\frac{14}{40}$ by dividing by 2: $\frac{7}{20}$.
* Answer: $1 \frac{7}{20}$.
11) $6 \frac{7}{8} + 9 \frac{3}{9}$
* First, simplify $\frac{3}{9}$ to $\frac{1}{3}$.
* Common denominator for 8 and 3 is 24.
* Convert fractions: $\frac{7}{8} = \frac{21}{24}$ and $\frac{1}{3} = \frac{8}{24}$.
* Add whole numbers: $6 + 9 = 15$.
* Add fractions: $\frac{21}{24} + \frac{8}{24} = \frac{29}{24}$.
* Convert improper fraction: $\frac{29}{24} = 1 \frac{5}{24}$.
* Add to whole number sum: $15 + 1 \frac{5}{24} = 16 \frac{5}{24}$.
12) $7 \frac{1}{2} - 4 \frac{7}{8}$
* Common denominator for 2 and 8 is 8.
* Convert $\frac{1}{2}$: $\frac{4}{8}$.
* Problem: $7 \frac{4}{8} - 4 \frac{7}{8}$.
* Borrow from 7: Change 7 to 6, add $\frac{8}{8}$ to fraction. $\frac{4}{8} + \frac{8}{8} = \frac{12}{8}$.
* New problem: $6 \frac{12}{8} - 4 \frac{7}{8}$.
* Subtract whole numbers: $6 - 4 = 2$.
* Subtract fractions: $\frac{12}{8} - \frac{7}{8} = \frac{5}{8}$.
* Answer: $2 \frac{5}{8}$.
Final Answer:
1) $9 \frac{3}{8}$
2) $4 \frac{2}{3}$
3) $9 \frac{1}{6}$
4) $1 \frac{19}{30}$
5) $5 \frac{3}{4}$
6) $2 \frac{6}{35}$
7) $5 \frac{17}{24}$
8) $1 \frac{17}{35}$
9) $8 \frac{7}{30}$
10) $1 \frac{7}{20}$
11) $16 \frac{5}{24}$
12) $2 \frac{5}{8}$
1) $7 \frac{1}{2} + 1 \frac{7}{8}$
* First, find a common denominator for the fractions $\frac{1}{2}$ and $\frac{7}{8}$. The common denominator is 8.
* Convert $\frac{1}{2}$ to eighths: $\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$.
* Add the whole numbers: $7 + 1 = 8$.
* Add the fractions: $\frac{4}{8} + \frac{7}{8} = \frac{11}{8}$.
* Since $\frac{11}{8}$ is an improper fraction, convert it to a mixed number: $1 \frac{3}{8}$.
* Add this to the whole number sum: $8 + 1 \frac{3}{8} = 9 \frac{3}{8}$.
2) $9 \frac{1}{6} - 4 \frac{1}{2}$
* Find a common denominator for 6 and 2, which is 6.
* Convert $\frac{1}{2}$ to sixths: $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
* The problem is now $9 \frac{1}{6} - 4 \frac{3}{6}$.
* You cannot subtract $\frac{3}{6}$ from $\frac{1}{6}$, so you must borrow from the whole number 9.
* Change 9 to 8 and add $\frac{6}{6}$ to the fraction: $\frac{1}{6} + \frac{6}{6} = \frac{7}{6}$.
* Now subtract: $8 \frac{7}{6} - 4 \frac{3}{6}$.
* Whole numbers: $8 - 4 = 4$.
* Fractions: $\frac{7}{6} - \frac{3}{6} = \frac{4}{6}$.
* Simplify $\frac{4}{6}$ by dividing top and bottom by 2: $\frac{2}{3}$.
* Answer: $4 \frac{2}{3}$.
3) $6 \frac{1}{3} + 2 \frac{5}{6}$
* Common denominator for 3 and 6 is 6.
* Convert $\frac{1}{3}$: $\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$.
* Add whole numbers: $6 + 2 = 8$.
* Add fractions: $\frac{2}{6} + \frac{5}{6} = \frac{7}{6}$.
* Convert $\frac{7}{6}$ to $1 \frac{1}{6}$.
* Add to whole number sum: $8 + 1 \frac{1}{6} = 9 \frac{1}{6}$.
4) $4 \frac{4}{5} - 3 \frac{1}{6}$
* Common denominator for 5 and 6 is 30.
* Convert fractions: $\frac{4}{5} = \frac{24}{30}$ and $\frac{1}{6} = \frac{5}{30}$.
* Subtract whole numbers: $4 - 3 = 1$.
* Subtract fractions: $\frac{24}{30} - \frac{5}{30} = \frac{19}{30}$.
* Answer: $1 \frac{19}{30}$.
5) $2 \frac{1}{2} + 3 \frac{1}{4}$
* Common denominator for 2 and 4 is 4.
* Convert $\frac{1}{2}$: $\frac{2}{4}$.
* Add whole numbers: $2 + 3 = 5$.
* Add fractions: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.
* Answer: $5 \frac{3}{4}$.
6) $4 \frac{4}{7} - 2 \frac{2}{5}$
* Common denominator for 7 and 5 is 35.
* Convert fractions: $\frac{4}{7} = \frac{20}{35}$ and $\frac{2}{5} = \frac{14}{35}$.
* Subtract whole numbers: $4 - 2 = 2$.
* Subtract fractions: $\frac{20}{35} - \frac{14}{35} = \frac{6}{35}$.
* Answer: $2 \frac{6}{35}$.
7) $3 \frac{7}{12} + 2 \frac{1}{8}$
* Common denominator for 12 and 8 is 24.
* Convert fractions: $\frac{7}{12} = \frac{14}{24}$ and $\frac{1}{8} = \frac{3}{24}$.
* Add whole numbers: $3 + 2 = 5$.
* Add fractions: $\frac{14}{24} + \frac{3}{24} = \frac{17}{24}$.
* Answer: $5 \frac{17}{24}$.
8) $5 \frac{1}{5} - 3 \frac{5}{7}$
* Common denominator for 5 and 7 is 35.
* Convert fractions: $\frac{1}{5} = \frac{7}{35}$ and $\frac{5}{7} = \frac{25}{35}$.
* Problem: $5 \frac{7}{35} - 3 \frac{25}{35}$.
* Cannot subtract $\frac{25}{35}$ from $\frac{7}{35}$, so borrow from 5.
* Change 5 to 4 and add $\frac{35}{35}$ to fraction: $\frac{7}{35} + \frac{35}{35} = \frac{42}{35}$.
* New problem: $4 \frac{42}{35} - 3 \frac{25}{35}$.
* Subtract whole numbers: $4 - 3 = 1$.
* Subtract fractions: $\frac{42}{35} - \frac{25}{35} = \frac{17}{35}$.
* Answer: $1 \frac{17}{35}$.
9) $4 \frac{2}{5} + 3 \frac{5}{6}$
* Common denominator for 5 and 6 is 30.
* Convert fractions: $\frac{2}{5} = \frac{12}{30}$ and $\frac{5}{6} = \frac{25}{30}$.
* Add whole numbers: $4 + 3 = 7$.
* Add fractions: $\frac{12}{30} + \frac{25}{30} = \frac{37}{30}$.
* Convert improper fraction: $\frac{37}{30} = 1 \frac{7}{30}$.
* Add to whole number sum: $7 + 1 \frac{7}{30} = 8 \frac{7}{30}$.
10) $3 \frac{1}{10} - 1 \frac{6}{8}$
* First, simplify $\frac{6}{8}$ to $\frac{3}{4}$ to make it easier (optional, but helpful). Let's stick to denominators 10 and 8 first. Common denominator is 40.
* Convert fractions: $\frac{1}{10} = \frac{4}{40}$ and $\frac{6}{8} = \frac{30}{40}$.
* Problem: $3 \frac{4}{40} - 1 \frac{30}{40}$.
* Borrow from 3: Change 3 to 2, add $\frac{40}{40}$ to fraction. $\frac{4}{40} + \frac{40}{40} = \frac{44}{40}$.
* New problem: $2 \frac{44}{40} - 1 \frac{30}{40}$.
* Subtract whole numbers: $2 - 1 = 1$.
* Subtract fractions: $\frac{44}{40} - \frac{30}{40} = \frac{14}{40}$.
* Simplify $\frac{14}{40}$ by dividing by 2: $\frac{7}{20}$.
* Answer: $1 \frac{7}{20}$.
11) $6 \frac{7}{8} + 9 \frac{3}{9}$
* First, simplify $\frac{3}{9}$ to $\frac{1}{3}$.
* Common denominator for 8 and 3 is 24.
* Convert fractions: $\frac{7}{8} = \frac{21}{24}$ and $\frac{1}{3} = \frac{8}{24}$.
* Add whole numbers: $6 + 9 = 15$.
* Add fractions: $\frac{21}{24} + \frac{8}{24} = \frac{29}{24}$.
* Convert improper fraction: $\frac{29}{24} = 1 \frac{5}{24}$.
* Add to whole number sum: $15 + 1 \frac{5}{24} = 16 \frac{5}{24}$.
12) $7 \frac{1}{2} - 4 \frac{7}{8}$
* Common denominator for 2 and 8 is 8.
* Convert $\frac{1}{2}$: $\frac{4}{8}$.
* Problem: $7 \frac{4}{8} - 4 \frac{7}{8}$.
* Borrow from 7: Change 7 to 6, add $\frac{8}{8}$ to fraction. $\frac{4}{8} + \frac{8}{8} = \frac{12}{8}$.
* New problem: $6 \frac{12}{8} - 4 \frac{7}{8}$.
* Subtract whole numbers: $6 - 4 = 2$.
* Subtract fractions: $\frac{12}{8} - \frac{7}{8} = \frac{5}{8}$.
* Answer: $2 \frac{5}{8}$.
Final Answer:
1) $9 \frac{3}{8}$
2) $4 \frac{2}{3}$
3) $9 \frac{1}{6}$
4) $1 \frac{19}{30}$
5) $5 \frac{3}{4}$
6) $2 \frac{6}{35}$
7) $5 \frac{17}{24}$
8) $1 \frac{17}{35}$
9) $8 \frac{7}{30}$
10) $1 \frac{7}{20}$
11) $16 \frac{5}{24}$
12) $2 \frac{5}{8}$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting fractions worksheet with answer key.
