Adding and Subtracting Fractions worksheet with 12 problems requiring students to solve and simplify answers.
Worksheet titled "Adding and Subtracting Fractions" with 12 math problems involving fractions, mixed numbers, and operations, from Math Monks.
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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) $\frac{3}{5} + \frac{5}{7}$
* Find a common denominator for 5 and 7, which is 35.
* Convert fractions: $\frac{3 \times 7}{35} + \frac{5 \times 5}{35} = \frac{21}{35} + \frac{25}{35}$.
* Add numerators: $21 + 25 = 46$.
* Result: $\frac{46}{35}$ or $1 \frac{11}{35}$.
2) $\frac{5}{7} - \frac{8}{21}$
* The common denominator is 21.
* Convert $\frac{5}{7}$ to $\frac{15}{21}$.
* Subtract: $\frac{15}{21} - \frac{8}{21} = \frac{7}{21}$.
* Simplify: Divide top and bottom by 7 to get $\frac{1}{3}$.
3) $1 \frac{1}{4} + 3 \frac{2}{5}$
* Add whole numbers: $1 + 3 = 4$.
* Find common denominator for fractions (4 and 5 is 20).
* Convert: $\frac{1}{4} = \frac{5}{20}$ and $\frac{2}{5} = \frac{8}{20}$.
* Add fractions: $\frac{5}{20} + \frac{8}{20} = \frac{13}{20}$.
* Combine: $4 \frac{13}{20}$.
4) $4 \frac{3}{7} - 3 \frac{2}{3}$
* Subtract whole numbers: $4 - 3 = 1$.
* Find common denominator for fractions (7 and 3 is 21).
* Convert: $\frac{3}{7} = \frac{9}{21}$ and $\frac{2}{3} = \frac{14}{21}$.
* Subtract fractions: $\frac{9}{21} - \frac{14}{21}$. Since 9 is smaller than 14, we borrow 1 from the whole number.
* New calculation: $1$ becomes $0$, and we add $\frac{21}{21}$ to $\frac{9}{21}$ to get $\frac{30}{21}$.
* Now subtract: $\frac{30}{21} - \frac{14}{21} = \frac{16}{21}$.
* Result: $\frac{16}{21}$.
5) $\frac{3}{4} + \frac{2}{3}$
* Common denominator is 12.
* Convert: $\frac{9}{12} + \frac{8}{12}$.
* Add: $\frac{17}{12}$.
* Convert to mixed number: $1 \frac{5}{12}$.
6) $\frac{8}{9} - \frac{2}{6}$
* First, simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* Problem becomes $\frac{8}{9} - \frac{1}{3}$.
* Common denominator is 9. Convert $\frac{1}{3}$ to $\frac{3}{9}$.
* Subtract: $\frac{8}{9} - \frac{3}{9} = \frac{5}{9}$.
7) $\frac{9}{2} + \frac{1}{4}$
* Common denominator is 4.
* Convert $\frac{9}{2}$ to $\frac{18}{4}$.
* Add: $\frac{18}{4} + \frac{1}{4} = \frac{19}{4}$.
* Convert to mixed number: $4 \frac{3}{4}$.
8) $\frac{5}{7} - 2 \frac{1}{4}$
* This is a small number minus a larger number, so the answer will be negative.
* Let's do $2 \frac{1}{4} - \frac{5}{7}$ first.
* Common denominator is 28.
* $2 \frac{1}{4} = 2 \frac{7}{28}$.
* $\frac{5}{7} = \frac{20}{28}$.
* Borrow from the whole number 2: $1 \frac{35}{28} - \frac{20}{28} = 1 \frac{15}{28}$.
* Since we swapped the order, make it negative: $-1 \frac{15}{28}$.
9) $\frac{5}{6} + 2 \frac{3}{4}$
* Keep the whole number 2 aside for now.
* Common denominator for 6 and 4 is 12.
* Convert: $\frac{5}{6} = \frac{10}{12}$ and $\frac{3}{4} = \frac{9}{12}$.
* Add fractions: $\frac{10}{12} + \frac{9}{12} = \frac{19}{12}$.
* Convert improper fraction: $\frac{19}{12} = 1 \frac{7}{12}$.
* Add the whole number 2 back: $2 + 1 \frac{7}{12} = 3 \frac{7}{12}$.
10) $2 \frac{2}{3} - 1 \frac{2}{9}$
* Subtract whole numbers: $2 - 1 = 1$.
* Common denominator for 3 and 9 is 9.
* Convert $\frac{2}{3}$ to $\frac{6}{9}$.
* Subtract fractions: $\frac{6}{9} - \frac{2}{9} = \frac{4}{9}$.
* Combine with whole number: $1 \frac{4}{9}$.
11) $\frac{1}{3} + 5 \frac{2}{5}$
* Keep the whole number 5 aside.
* Common denominator for 3 and 5 is 15.
* Convert: $\frac{1}{3} = \frac{5}{15}$ and $\frac{2}{5} = \frac{6}{15}$.
* Add fractions: $\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$.
* Combine with whole number: $5 \frac{11}{15}$.
12) $\frac{7}{9} - \frac{2}{3}$
* Common denominator is 9.
* Convert $\frac{2}{3}$ to $\frac{6}{9}$.
* Subtract: $\frac{7}{9} - \frac{6}{9} = \frac{1}{9}$.
Final Answer:
1) $1 \frac{11}{35}$
2) $\frac{1}{3}$
3) $4 \frac{13}{20}$
4) $\frac{16}{21}$
5) $1 \frac{5}{12}$
6) $\frac{5}{9}$
7) $4 \frac{3}{4}$
8) $-1 \frac{15}{28}$
9) $3 \frac{7}{12}$
10) $1 \frac{4}{9}$
11) $5 \frac{11}{15}$
12) $\frac{1}{9}$
1) $\frac{3}{5} + \frac{5}{7}$
* Find a common denominator for 5 and 7, which is 35.
* Convert fractions: $\frac{3 \times 7}{35} + \frac{5 \times 5}{35} = \frac{21}{35} + \frac{25}{35}$.
* Add numerators: $21 + 25 = 46$.
* Result: $\frac{46}{35}$ or $1 \frac{11}{35}$.
2) $\frac{5}{7} - \frac{8}{21}$
* The common denominator is 21.
* Convert $\frac{5}{7}$ to $\frac{15}{21}$.
* Subtract: $\frac{15}{21} - \frac{8}{21} = \frac{7}{21}$.
* Simplify: Divide top and bottom by 7 to get $\frac{1}{3}$.
3) $1 \frac{1}{4} + 3 \frac{2}{5}$
* Add whole numbers: $1 + 3 = 4$.
* Find common denominator for fractions (4 and 5 is 20).
* Convert: $\frac{1}{4} = \frac{5}{20}$ and $\frac{2}{5} = \frac{8}{20}$.
* Add fractions: $\frac{5}{20} + \frac{8}{20} = \frac{13}{20}$.
* Combine: $4 \frac{13}{20}$.
4) $4 \frac{3}{7} - 3 \frac{2}{3}$
* Subtract whole numbers: $4 - 3 = 1$.
* Find common denominator for fractions (7 and 3 is 21).
* Convert: $\frac{3}{7} = \frac{9}{21}$ and $\frac{2}{3} = \frac{14}{21}$.
* Subtract fractions: $\frac{9}{21} - \frac{14}{21}$. Since 9 is smaller than 14, we borrow 1 from the whole number.
* New calculation: $1$ becomes $0$, and we add $\frac{21}{21}$ to $\frac{9}{21}$ to get $\frac{30}{21}$.
* Now subtract: $\frac{30}{21} - \frac{14}{21} = \frac{16}{21}$.
* Result: $\frac{16}{21}$.
5) $\frac{3}{4} + \frac{2}{3}$
* Common denominator is 12.
* Convert: $\frac{9}{12} + \frac{8}{12}$.
* Add: $\frac{17}{12}$.
* Convert to mixed number: $1 \frac{5}{12}$.
6) $\frac{8}{9} - \frac{2}{6}$
* First, simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* Problem becomes $\frac{8}{9} - \frac{1}{3}$.
* Common denominator is 9. Convert $\frac{1}{3}$ to $\frac{3}{9}$.
* Subtract: $\frac{8}{9} - \frac{3}{9} = \frac{5}{9}$.
7) $\frac{9}{2} + \frac{1}{4}$
* Common denominator is 4.
* Convert $\frac{9}{2}$ to $\frac{18}{4}$.
* Add: $\frac{18}{4} + \frac{1}{4} = \frac{19}{4}$.
* Convert to mixed number: $4 \frac{3}{4}$.
8) $\frac{5}{7} - 2 \frac{1}{4}$
* This is a small number minus a larger number, so the answer will be negative.
* Let's do $2 \frac{1}{4} - \frac{5}{7}$ first.
* Common denominator is 28.
* $2 \frac{1}{4} = 2 \frac{7}{28}$.
* $\frac{5}{7} = \frac{20}{28}$.
* Borrow from the whole number 2: $1 \frac{35}{28} - \frac{20}{28} = 1 \frac{15}{28}$.
* Since we swapped the order, make it negative: $-1 \frac{15}{28}$.
9) $\frac{5}{6} + 2 \frac{3}{4}$
* Keep the whole number 2 aside for now.
* Common denominator for 6 and 4 is 12.
* Convert: $\frac{5}{6} = \frac{10}{12}$ and $\frac{3}{4} = \frac{9}{12}$.
* Add fractions: $\frac{10}{12} + \frac{9}{12} = \frac{19}{12}$.
* Convert improper fraction: $\frac{19}{12} = 1 \frac{7}{12}$.
* Add the whole number 2 back: $2 + 1 \frac{7}{12} = 3 \frac{7}{12}$.
10) $2 \frac{2}{3} - 1 \frac{2}{9}$
* Subtract whole numbers: $2 - 1 = 1$.
* Common denominator for 3 and 9 is 9.
* Convert $\frac{2}{3}$ to $\frac{6}{9}$.
* Subtract fractions: $\frac{6}{9} - \frac{2}{9} = \frac{4}{9}$.
* Combine with whole number: $1 \frac{4}{9}$.
11) $\frac{1}{3} + 5 \frac{2}{5}$
* Keep the whole number 5 aside.
* Common denominator for 3 and 5 is 15.
* Convert: $\frac{1}{3} = \frac{5}{15}$ and $\frac{2}{5} = \frac{6}{15}$.
* Add fractions: $\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$.
* Combine with whole number: $5 \frac{11}{15}$.
12) $\frac{7}{9} - \frac{2}{3}$
* Common denominator is 9.
* Convert $\frac{2}{3}$ to $\frac{6}{9}$.
* Subtract: $\frac{7}{9} - \frac{6}{9} = \frac{1}{9}$.
Final Answer:
1) $1 \frac{11}{35}$
2) $\frac{1}{3}$
3) $4 \frac{13}{20}$
4) $\frac{16}{21}$
5) $1 \frac{5}{12}$
6) $\frac{5}{9}$
7) $4 \frac{3}{4}$
8) $-1 \frac{15}{28}$
9) $3 \frac{7}{12}$
10) $1 \frac{4}{9}$
11) $5 \frac{11}{15}$
12) $\frac{1}{9}$
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting fractions with unlike denominators worksheet 5th grade.
