Grade 5 math worksheet for subtracting mixed numbers with unlike denominators.
Worksheet titled "Subtracting mixed numbers (unlike denominators)" for Grade 5 fractions, featuring 12 problems involving subtraction of mixed numbers with unlike denominators.
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Step-by-step solution for: Subtract mixed numbers (unlike denominators) worksheets | Worsheets library
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Show Answer Key & Explanations
Step-by-step solution for: Subtract mixed numbers (unlike denominators) worksheets | Worsheets library
Here are the step-by-step solutions for each problem on the worksheet.
1. $16 \frac{3}{5} - 10 \frac{2}{5}$
* Subtract the whole numbers: $16 - 10 = 6$
* Subtract the fractions: $\frac{3}{5} - \frac{2}{5} = \frac{1}{5}$
* Combine them: $6 \frac{1}{5}$
2. $7 \frac{5}{12} - 2 \frac{1}{2}$
* Find a common denominator for 12 and 2, which is 12. Convert $\frac{1}{2}$ to $\frac{6}{12}$.
* The problem becomes $7 \frac{5}{12} - 2 \frac{6}{12}$.
* Since 5 is smaller than 6, borrow 1 from the 7. The 7 becomes 6, and add $\frac{12}{12}$ to the fraction: $\frac{5}{12} + \frac{12}{12} = \frac{17}{12}$.
* Now subtract: $6 \frac{17}{12} - 2 \frac{6}{12}$.
* Whole numbers: $6 - 2 = 4$.
* Fractions: $\frac{17}{12} - \frac{6}{12} = \frac{11}{12}$.
* Answer: $4 \frac{11}{12}$
3. $8 \frac{9}{10} - 3 \frac{2}{5}$
* Find a common denominator for 10 and 5, which is 10. Convert $\frac{2}{5}$ to $\frac{4}{10}$.
* The problem becomes $8 \frac{9}{10} - 3 \frac{4}{10}$.
* Subtract whole numbers: $8 - 3 = 5$.
* Subtract fractions: $\frac{9}{10} - \frac{4}{10} = \frac{5}{10}$.
* Simplify the fraction $\frac{5}{10}$ to $\frac{1}{2}$.
* Answer: $5 \frac{1}{2}$
4. $19 \frac{2}{5} - 11 \frac{5}{8}$
* Find a common denominator for 5 and 8, which is 40.
* Convert fractions: $\frac{2}{5} = \frac{16}{40}$ and $\frac{5}{8} = \frac{25}{40}$.
* The problem is $19 \frac{16}{40} - 11 \frac{25}{40}$.
* Borrow 1 from 19 (becomes 18) and add $\frac{40}{40}$ to $\frac{16}{40}$ to get $\frac{56}{40}$.
* Subtract whole numbers: $18 - 11 = 7$.
* Subtract fractions: $\frac{56}{40} - \frac{25}{40} = \frac{31}{40}$.
* Answer: $7 \frac{31}{40}$
5. $13 \frac{1}{8} - 12 \frac{10}{12}$
* First, simplify $\frac{10}{12}$ to $\frac{5}{6}$. The problem is $13 \frac{1}{8} - 12 \frac{5}{6}$.
* Common denominator for 8 and 6 is 24.
* Convert fractions: $\frac{1}{8} = \frac{3}{24}$ and $\frac{5}{6} = \frac{20}{24}$.
* Problem: $13 \frac{3}{24} - 12 \frac{20}{24}$.
* Borrow 1 from 13 (becomes 12). Add $\frac{24}{24}$ to $\frac{3}{24}$ to get $\frac{27}{24}$.
* Subtract whole numbers: $12 - 12 = 0$.
* Subtract fractions: $\frac{27}{24} - \frac{20}{24} = \frac{7}{24}$.
* Answer: $\frac{7}{24}$
6. $18 \frac{1}{2} - 17 \frac{7}{8}$
* Common denominator for 2 and 8 is 8. Convert $\frac{1}{2}$ to $\frac{4}{8}$.
* Problem: $18 \frac{4}{8} - 17 \frac{7}{8}$.
* Borrow 1 from 18 (becomes 17). Add $\frac{8}{8}$ to $\frac{4}{8}$ to get $\frac{12}{8}$.
* Subtract whole numbers: $17 - 17 = 0$.
* Subtract fractions: $\frac{12}{8} - \frac{7}{8} = \frac{5}{8}$.
* Answer: $\frac{5}{8}$
7. $14 \frac{4}{10} - 13 \frac{1}{3}$
* Simplify $\frac{4}{10}$ to $\frac{2}{5}$. Problem: $14 \frac{2}{5} - 13 \frac{1}{3}$.
* Common denominator for 5 and 3 is 15.
* Convert fractions: $\frac{2}{5} = \frac{6}{15}$ and $\frac{1}{3} = \frac{5}{15}$.
* Subtract whole numbers: $14 - 13 = 1$.
* Subtract fractions: $\frac{6}{15} - \frac{5}{15} = \frac{1}{15}$.
* Answer: $1 \frac{1}{15}$
8. $19 \frac{7}{12} - 19 \frac{1}{5}$
* The whole numbers are the same ($19 - 19 = 0$), so we just subtract the fractions.
* Common denominator for 12 and 5 is 60.
* Convert fractions: $\frac{7}{12} = \frac{35}{60}$ and $\frac{1}{5} = \frac{12}{60}$.
* Subtract: $\frac{35}{60} - \frac{12}{60} = \frac{23}{60}$.
* Answer: $\frac{23}{60}$
9. $20 \frac{3}{4} - 18 \frac{2}{3}$
* Common denominator for 4 and 3 is 12.
* Convert fractions: $\frac{3}{4} = \frac{9}{12}$ and $\frac{2}{3} = \frac{8}{12}$.
* Subtract whole numbers: $20 - 18 = 2$.
* Subtract fractions: $\frac{9}{12} - \frac{8}{12} = \frac{1}{12}$.
* Answer: $2 \frac{1}{12}$
10. $19 \frac{7}{10} - 13 \frac{4}{10}$
* Subtract whole numbers: $19 - 13 = 6$.
* Subtract fractions: $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$.
* Answer: $6 \frac{3}{10}$
11. $17 \frac{5}{6} - 1 \frac{3}{5}$
* Common denominator for 6 and 5 is 30.
* Convert fractions: $\frac{5}{6} = \frac{25}{30}$ and $\frac{3}{5} = \frac{18}{30}$.
* Subtract whole numbers: $17 - 1 = 16$.
* Subtract fractions: $\frac{25}{30} - \frac{18}{30} = \frac{7}{30}$.
* Answer: $16 \frac{7}{30}$
12. $9 \frac{1}{5} - 5 \frac{4}{5}$
* Problem: $9 \frac{1}{5} - 5 \frac{4}{5}$.
* Since 1 is smaller than 4, borrow 1 from the 9. The 9 becomes 8.
* Add $\frac{5}{5}$ to $\frac{1}{5}$ to get $\frac{6}{5}$.
* New problem: $8 \frac{6}{5} - 5 \frac{4}{5}$.
* Subtract whole numbers: $8 - 5 = 3$.
* Subtract fractions: $\frac{6}{5} - \frac{4}{5} = \frac{2}{5}$.
* Answer: $3 \frac{2}{5}$
Final Answer:
1. $6 \frac{1}{5}$
2. $4 \frac{11}{12}$
3. $5 \frac{1}{2}$
4. $7 \frac{31}{40}$
5. $\frac{7}{24}$
6. $\frac{5}{8}$
7. $1 \frac{1}{15}$
8. $\frac{23}{60}$
9. $2 \frac{1}{12}$
10. $6 \frac{3}{10}$
11. $16 \frac{7}{30}$
12. $3 \frac{2}{5}$
1. $16 \frac{3}{5} - 10 \frac{2}{5}$
* Subtract the whole numbers: $16 - 10 = 6$
* Subtract the fractions: $\frac{3}{5} - \frac{2}{5} = \frac{1}{5}$
* Combine them: $6 \frac{1}{5}$
2. $7 \frac{5}{12} - 2 \frac{1}{2}$
* Find a common denominator for 12 and 2, which is 12. Convert $\frac{1}{2}$ to $\frac{6}{12}$.
* The problem becomes $7 \frac{5}{12} - 2 \frac{6}{12}$.
* Since 5 is smaller than 6, borrow 1 from the 7. The 7 becomes 6, and add $\frac{12}{12}$ to the fraction: $\frac{5}{12} + \frac{12}{12} = \frac{17}{12}$.
* Now subtract: $6 \frac{17}{12} - 2 \frac{6}{12}$.
* Whole numbers: $6 - 2 = 4$.
* Fractions: $\frac{17}{12} - \frac{6}{12} = \frac{11}{12}$.
* Answer: $4 \frac{11}{12}$
3. $8 \frac{9}{10} - 3 \frac{2}{5}$
* Find a common denominator for 10 and 5, which is 10. Convert $\frac{2}{5}$ to $\frac{4}{10}$.
* The problem becomes $8 \frac{9}{10} - 3 \frac{4}{10}$.
* Subtract whole numbers: $8 - 3 = 5$.
* Subtract fractions: $\frac{9}{10} - \frac{4}{10} = \frac{5}{10}$.
* Simplify the fraction $\frac{5}{10}$ to $\frac{1}{2}$.
* Answer: $5 \frac{1}{2}$
4. $19 \frac{2}{5} - 11 \frac{5}{8}$
* Find a common denominator for 5 and 8, which is 40.
* Convert fractions: $\frac{2}{5} = \frac{16}{40}$ and $\frac{5}{8} = \frac{25}{40}$.
* The problem is $19 \frac{16}{40} - 11 \frac{25}{40}$.
* Borrow 1 from 19 (becomes 18) and add $\frac{40}{40}$ to $\frac{16}{40}$ to get $\frac{56}{40}$.
* Subtract whole numbers: $18 - 11 = 7$.
* Subtract fractions: $\frac{56}{40} - \frac{25}{40} = \frac{31}{40}$.
* Answer: $7 \frac{31}{40}$
5. $13 \frac{1}{8} - 12 \frac{10}{12}$
* First, simplify $\frac{10}{12}$ to $\frac{5}{6}$. The problem is $13 \frac{1}{8} - 12 \frac{5}{6}$.
* Common denominator for 8 and 6 is 24.
* Convert fractions: $\frac{1}{8} = \frac{3}{24}$ and $\frac{5}{6} = \frac{20}{24}$.
* Problem: $13 \frac{3}{24} - 12 \frac{20}{24}$.
* Borrow 1 from 13 (becomes 12). Add $\frac{24}{24}$ to $\frac{3}{24}$ to get $\frac{27}{24}$.
* Subtract whole numbers: $12 - 12 = 0$.
* Subtract fractions: $\frac{27}{24} - \frac{20}{24} = \frac{7}{24}$.
* Answer: $\frac{7}{24}$
6. $18 \frac{1}{2} - 17 \frac{7}{8}$
* Common denominator for 2 and 8 is 8. Convert $\frac{1}{2}$ to $\frac{4}{8}$.
* Problem: $18 \frac{4}{8} - 17 \frac{7}{8}$.
* Borrow 1 from 18 (becomes 17). Add $\frac{8}{8}$ to $\frac{4}{8}$ to get $\frac{12}{8}$.
* Subtract whole numbers: $17 - 17 = 0$.
* Subtract fractions: $\frac{12}{8} - \frac{7}{8} = \frac{5}{8}$.
* Answer: $\frac{5}{8}$
7. $14 \frac{4}{10} - 13 \frac{1}{3}$
* Simplify $\frac{4}{10}$ to $\frac{2}{5}$. Problem: $14 \frac{2}{5} - 13 \frac{1}{3}$.
* Common denominator for 5 and 3 is 15.
* Convert fractions: $\frac{2}{5} = \frac{6}{15}$ and $\frac{1}{3} = \frac{5}{15}$.
* Subtract whole numbers: $14 - 13 = 1$.
* Subtract fractions: $\frac{6}{15} - \frac{5}{15} = \frac{1}{15}$.
* Answer: $1 \frac{1}{15}$
8. $19 \frac{7}{12} - 19 \frac{1}{5}$
* The whole numbers are the same ($19 - 19 = 0$), so we just subtract the fractions.
* Common denominator for 12 and 5 is 60.
* Convert fractions: $\frac{7}{12} = \frac{35}{60}$ and $\frac{1}{5} = \frac{12}{60}$.
* Subtract: $\frac{35}{60} - \frac{12}{60} = \frac{23}{60}$.
* Answer: $\frac{23}{60}$
9. $20 \frac{3}{4} - 18 \frac{2}{3}$
* Common denominator for 4 and 3 is 12.
* Convert fractions: $\frac{3}{4} = \frac{9}{12}$ and $\frac{2}{3} = \frac{8}{12}$.
* Subtract whole numbers: $20 - 18 = 2$.
* Subtract fractions: $\frac{9}{12} - \frac{8}{12} = \frac{1}{12}$.
* Answer: $2 \frac{1}{12}$
10. $19 \frac{7}{10} - 13 \frac{4}{10}$
* Subtract whole numbers: $19 - 13 = 6$.
* Subtract fractions: $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$.
* Answer: $6 \frac{3}{10}$
11. $17 \frac{5}{6} - 1 \frac{3}{5}$
* Common denominator for 6 and 5 is 30.
* Convert fractions: $\frac{5}{6} = \frac{25}{30}$ and $\frac{3}{5} = \frac{18}{30}$.
* Subtract whole numbers: $17 - 1 = 16$.
* Subtract fractions: $\frac{25}{30} - \frac{18}{30} = \frac{7}{30}$.
* Answer: $16 \frac{7}{30}$
12. $9 \frac{1}{5} - 5 \frac{4}{5}$
* Problem: $9 \frac{1}{5} - 5 \frac{4}{5}$.
* Since 1 is smaller than 4, borrow 1 from the 9. The 9 becomes 8.
* Add $\frac{5}{5}$ to $\frac{1}{5}$ to get $\frac{6}{5}$.
* New problem: $8 \frac{6}{5} - 5 \frac{4}{5}$.
* Subtract whole numbers: $8 - 5 = 3$.
* Subtract fractions: $\frac{6}{5} - \frac{4}{5} = \frac{2}{5}$.
* Answer: $3 \frac{2}{5}$
Final Answer:
1. $6 \frac{1}{5}$
2. $4 \frac{11}{12}$
3. $5 \frac{1}{2}$
4. $7 \frac{31}{40}$
5. $\frac{7}{24}$
6. $\frac{5}{8}$
7. $1 \frac{1}{15}$
8. $\frac{23}{60}$
9. $2 \frac{1}{12}$
10. $6 \frac{3}{10}$
11. $16 \frac{7}{30}$
12. $3 \frac{2}{5}$
Parent Tip: Review the logic above to help your child master the concept of subtracting fractions borrowing worksheet.
