Practice your fraction skills with this set of 12 addition and subtraction problems featuring like denominators.
Math worksheet featuring 12 problems on adding and subtracting fractions with like denominators for elementary students.
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Show Answer Key & Explanations
Step-by-step solution for: Operations With Fractions Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Operations With Fractions Worksheet
To solve the problems involving adding and subtracting fractions, we need to follow these steps:
1. Ensure the denominators are the same: If the denominators are the same, we can directly add or subtract the numerators.
2. Simplify the result: After performing the operation, simplify the resulting fraction if possible.
Let's solve each problem step by step.
---
- Denominators are the same (both are 6).
- Subtract the numerators: \( 23 - 5 = 18 \).
- The result is \( \frac{18}{6} \).
- Simplify: \( \frac{18}{6} = 3 \).
Answer: \( 3 \)
---
- Denominators are the same (both are 8).
- Subtract the numerators: \( 21 - 3 = 18 \).
- The result is \( \frac{18}{8} \).
- Simplify: \( \frac{18}{8} = \frac{9}{4} \).
Answer: \( \frac{9}{4} \)
---
- Denominators are the same (both are 4).
- Add the numerators: \( 21 + 17 = 38 \).
- The result is \( \frac{38}{4} \).
- Simplify: \( \frac{38}{4} = \frac{19}{2} \).
Answer: \( \frac{19}{2} \)
---
- Denominators are the same (both are 9).
- Subtract the numerators: \( 17 - 17 = 0 \).
- The result is \( \frac{0}{9} \).
- Simplify: \( \frac{0}{9} = 0 \).
Answer: \( 0 \)
---
- Denominators are the same (both are 9).
- Add the numerators: \( 23 + 17 = 40 \).
- The result is \( \frac{40}{9} \).
- This fraction is already in simplest form.
Answer: \( \frac{40}{9} \)
---
- Denominators are the same (both are 3).
- Subtract the numerators: \( 7 - 1 = 6 \).
- The result is \( \frac{6}{3} \).
- Simplify: \( \frac{6}{3} = 2 \).
Answer: \( 2 \)
---
- Denominators are the same (both are 6).
- Add the numerators: \( 1 + 13 = 14 \).
- The result is \( \frac{14}{6} \).
- Simplify: \( \frac{14}{6} = \frac{7}{3} \).
Answer: \( \frac{7}{3} \)
---
- Denominators are the same (both are 2).
- Subtract the numerators: \( 23 - 19 = 4 \).
- The result is \( \frac{4}{2} \).
- Simplify: \( \frac{4}{2} = 2 \).
Answer: \( 2 \)
---
- Denominators are the same (both are 7).
- Subtract the numerators: \( 20 - 15 = 5 \).
- The result is \( \frac{5}{7} \).
- This fraction is already in simplest form.
Answer: \( \frac{5}{7} \)
---
- Denominators are the same (both are 6).
- Subtract the numerators: \( 13 - 5 = 8 \).
- The result is \( \frac{8}{6} \).
- Simplify: \( \frac{8}{6} = \frac{4}{3} \).
Answer: \( \frac{4}{3} \)
---
- Denominators are the same (both are 8).
- Add the numerators: \( 17 + 3 = 20 \).
- The result is \( \frac{20}{8} \).
- Simplify: \( \frac{20}{8} = \frac{5}{2} \).
Answer: \( \frac{5}{2} \)
---
- Denominators are the same (both are 10).
- Add the numerators: \( 17 + 13 = 30 \).
- The result is \( \frac{30}{10} \).
- Simplify: \( \frac{30}{10} = 3 \).
Answer: \( 3 \)
---
\[
\boxed{
\begin{array}{lll}
1. & 3 & \\
2. & \frac{9}{4} & \\
3. & \frac{19}{2} & \\
4. & 0 & \\
5. & \frac{40}{9} & \\
6. & 2 & \\
7. & \frac{7}{3} & \\
8. & 2 & \\
9. & \frac{5}{7} & \\
10. & \frac{4}{3} & \\
11. & \frac{5}{2} & \\
12. & 3 &
\end{array}
}
\]
1. Ensure the denominators are the same: If the denominators are the same, we can directly add or subtract the numerators.
2. Simplify the result: After performing the operation, simplify the resulting fraction if possible.
Let's solve each problem step by step.
---
Problem 1: \( \frac{23}{6} - \frac{5}{6} \)
- Denominators are the same (both are 6).
- Subtract the numerators: \( 23 - 5 = 18 \).
- The result is \( \frac{18}{6} \).
- Simplify: \( \frac{18}{6} = 3 \).
Answer: \( 3 \)
---
Problem 2: \( \frac{21}{8} - \frac{3}{8} \)
- Denominators are the same (both are 8).
- Subtract the numerators: \( 21 - 3 = 18 \).
- The result is \( \frac{18}{8} \).
- Simplify: \( \frac{18}{8} = \frac{9}{4} \).
Answer: \( \frac{9}{4} \)
---
Problem 3: \( \frac{21}{4} + \frac{17}{4} \)
- Denominators are the same (both are 4).
- Add the numerators: \( 21 + 17 = 38 \).
- The result is \( \frac{38}{4} \).
- Simplify: \( \frac{38}{4} = \frac{19}{2} \).
Answer: \( \frac{19}{2} \)
---
Problem 4: \( \frac{17}{9} - \frac{17}{9} \)
- Denominators are the same (both are 9).
- Subtract the numerators: \( 17 - 17 = 0 \).
- The result is \( \frac{0}{9} \).
- Simplify: \( \frac{0}{9} = 0 \).
Answer: \( 0 \)
---
Problem 5: \( \frac{23}{9} + \frac{17}{9} \)
- Denominators are the same (both are 9).
- Add the numerators: \( 23 + 17 = 40 \).
- The result is \( \frac{40}{9} \).
- This fraction is already in simplest form.
Answer: \( \frac{40}{9} \)
---
Problem 6: \( \frac{7}{3} - \frac{1}{3} \)
- Denominators are the same (both are 3).
- Subtract the numerators: \( 7 - 1 = 6 \).
- The result is \( \frac{6}{3} \).
- Simplify: \( \frac{6}{3} = 2 \).
Answer: \( 2 \)
---
Problem 7: \( \frac{1}{6} + \frac{13}{6} \)
- Denominators are the same (both are 6).
- Add the numerators: \( 1 + 13 = 14 \).
- The result is \( \frac{14}{6} \).
- Simplify: \( \frac{14}{6} = \frac{7}{3} \).
Answer: \( \frac{7}{3} \)
---
Problem 8: \( \frac{23}{2} - \frac{19}{2} \)
- Denominators are the same (both are 2).
- Subtract the numerators: \( 23 - 19 = 4 \).
- The result is \( \frac{4}{2} \).
- Simplify: \( \frac{4}{2} = 2 \).
Answer: \( 2 \)
---
Problem 9: \( \frac{20}{7} - \frac{15}{7} \)
- Denominators are the same (both are 7).
- Subtract the numerators: \( 20 - 15 = 5 \).
- The result is \( \frac{5}{7} \).
- This fraction is already in simplest form.
Answer: \( \frac{5}{7} \)
---
Problem 10: \( \frac{13}{6} - \frac{5}{6} \)
- Denominators are the same (both are 6).
- Subtract the numerators: \( 13 - 5 = 8 \).
- The result is \( \frac{8}{6} \).
- Simplify: \( \frac{8}{6} = \frac{4}{3} \).
Answer: \( \frac{4}{3} \)
---
Problem 11: \( \frac{17}{8} + \frac{3}{8} \)
- Denominators are the same (both are 8).
- Add the numerators: \( 17 + 3 = 20 \).
- The result is \( \frac{20}{8} \).
- Simplify: \( \frac{20}{8} = \frac{5}{2} \).
Answer: \( \frac{5}{2} \)
---
Problem 12: \( \frac{17}{10} + \frac{13}{10} \)
- Denominators are the same (both are 10).
- Add the numerators: \( 17 + 13 = 30 \).
- The result is \( \frac{30}{10} \).
- Simplify: \( \frac{30}{10} = 3 \).
Answer: \( 3 \)
---
Final Answers:
\[
\boxed{
\begin{array}{lll}
1. & 3 & \\
2. & \frac{9}{4} & \\
3. & \frac{19}{2} & \\
4. & 0 & \\
5. & \frac{40}{9} & \\
6. & 2 & \\
7. & \frac{7}{3} & \\
8. & 2 & \\
9. & \frac{5}{7} & \\
10. & \frac{4}{3} & \\
11. & \frac{5}{2} & \\
12. & 3 &
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of mixed operations with fractions worksheet.