Practice sheet for adding and subtracting fractions with like denominators.
Worksheet titled "Adding and Subtracting Fractions" with 12 math problems involving fractions with like denominators.
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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
Here are the step-by-step solutions for each problem. Since all fractions in each problem have the same denominator (the bottom number), we can simply add or subtract the numerators (the top numbers) and keep the denominator the same. Then, we simplify the result if possible.
1. $\frac{23}{6} - \frac{5}{6}$
* Subtract the tops: $23 - 5 = 18$
* Keep the bottom: $6$
* Result: $\frac{18}{6}$
* Simplify: $18 \div 6 = 3$
* Answer: 3
2. $\frac{21}{8} - \frac{3}{8}$
* Subtract the tops: $21 - 3 = 18$
* Keep the bottom: $8$
* Result: $\frac{18}{8}$
* Simplify: Both numbers are even, so divide by 2. $\frac{9}{4}$
* Convert to mixed number: $9 \div 4 = 2$ with a remainder of $1$. So, $2 \frac{1}{4}$.
* Answer: $2 \frac{1}{4}$ (or $\frac{9}{4}$)
3. $\frac{21}{4} + \frac{17}{4}$
* Add the tops: $21 + 17 = 38$
* Keep the bottom: $4$
* Result: $\frac{38}{4}$
* Simplify: Divide by 2. $\frac{19}{2}$
* Convert to mixed number: $19 \div 2 = 9$ with a remainder of $1$. So, $9 \frac{1}{2}$.
* Answer: $9 \frac{1}{2}$ (or $\frac{19}{2}$)
4. $\frac{17}{9} - \frac{17}{9}$
* Subtract the tops: $17 - 17 = 0$
* Result: $\frac{0}{9}$
* Answer: 0
5. $\frac{23}{9} + \frac{17}{9}$
* Add the tops: $23 + 17 = 40$
* Keep the bottom: $9$
* Result: $\frac{40}{9}$
* Convert to mixed number: $40 \div 9 = 4$ with a remainder of $4$ ($9 \times 4 = 36$).
* Answer: $4 \frac{4}{9}$
6. $\frac{7}{3} - \frac{1}{3}$
* Subtract the tops: $7 - 1 = 6$
* Keep the bottom: $3$
* Result: $\frac{6}{3}$
* Simplify: $6 \div 3 = 2$
* Answer: 2
7. $\frac{1}{6} + \frac{13}{6}$
* Add the tops: $1 + 13 = 14$
* Keep the bottom: $6$
* Result: $\frac{14}{6}$
* Simplify: Divide by 2. $\frac{7}{3}$
* Convert to mixed number: $7 \div 3 = 2$ with a remainder of $1$.
* Answer: $2 \frac{1}{3}$
8. $\frac{23}{2} - \frac{19}{2}$
* Subtract the tops: $23 - 19 = 4$
* Keep the bottom: $2$
* Result: $\frac{4}{2}$
* Simplify: $4 \div 2 = 2$
* Answer: 2
9. $\frac{20}{7} - \frac{15}{7}$
* Subtract the tops: $20 - 15 = 5$
* Keep the bottom: $7$
* Answer: $\frac{5}{7}$
10. $\frac{13}{6} - \frac{5}{6}$
* Subtract the tops: $13 - 5 = 8$
* Keep the bottom: $6$
* Result: $\frac{8}{6}$
* Simplify: Divide by 2. $\frac{4}{3}$
* Convert to mixed number: $4 \div 3 = 1$ with a remainder of $1$.
* Answer: $1 \frac{1}{3}$
11. $\frac{17}{8} + \frac{3}{8}$
* Add the tops: $17 + 3 = 20$
* Keep the bottom: $8$
* Result: $\frac{20}{8}$
* Simplify: Divide by 4. $\frac{5}{2}$
* Convert to mixed number: $5 \div 2 = 2$ with a remainder of $1$.
* Answer: $2 \frac{1}{2}$
12. $\frac{17}{10} + \frac{13}{10}$
* Add the tops: $17 + 13 = 30$
* Keep the bottom: $10$
* Result: $\frac{30}{10}$
* Simplify: $30 \div 10 = 3$
* Answer: 3
Final Answer:
1. 3
2. $2 \frac{1}{4}$
3. $9 \frac{1}{2}$
4. 0
5. $4 \frac{4}{9}$
6. 2
7. $2 \frac{1}{3}$
8. 2
9. $\frac{5}{7}$
10. $1 \frac{1}{3}$
11. $2 \frac{1}{2}$
12. 3
1. $\frac{23}{6} - \frac{5}{6}$
* Subtract the tops: $23 - 5 = 18$
* Keep the bottom: $6$
* Result: $\frac{18}{6}$
* Simplify: $18 \div 6 = 3$
* Answer: 3
2. $\frac{21}{8} - \frac{3}{8}$
* Subtract the tops: $21 - 3 = 18$
* Keep the bottom: $8$
* Result: $\frac{18}{8}$
* Simplify: Both numbers are even, so divide by 2. $\frac{9}{4}$
* Convert to mixed number: $9 \div 4 = 2$ with a remainder of $1$. So, $2 \frac{1}{4}$.
* Answer: $2 \frac{1}{4}$ (or $\frac{9}{4}$)
3. $\frac{21}{4} + \frac{17}{4}$
* Add the tops: $21 + 17 = 38$
* Keep the bottom: $4$
* Result: $\frac{38}{4}$
* Simplify: Divide by 2. $\frac{19}{2}$
* Convert to mixed number: $19 \div 2 = 9$ with a remainder of $1$. So, $9 \frac{1}{2}$.
* Answer: $9 \frac{1}{2}$ (or $\frac{19}{2}$)
4. $\frac{17}{9} - \frac{17}{9}$
* Subtract the tops: $17 - 17 = 0$
* Result: $\frac{0}{9}$
* Answer: 0
5. $\frac{23}{9} + \frac{17}{9}$
* Add the tops: $23 + 17 = 40$
* Keep the bottom: $9$
* Result: $\frac{40}{9}$
* Convert to mixed number: $40 \div 9 = 4$ with a remainder of $4$ ($9 \times 4 = 36$).
* Answer: $4 \frac{4}{9}$
6. $\frac{7}{3} - \frac{1}{3}$
* Subtract the tops: $7 - 1 = 6$
* Keep the bottom: $3$
* Result: $\frac{6}{3}$
* Simplify: $6 \div 3 = 2$
* Answer: 2
7. $\frac{1}{6} + \frac{13}{6}$
* Add the tops: $1 + 13 = 14$
* Keep the bottom: $6$
* Result: $\frac{14}{6}$
* Simplify: Divide by 2. $\frac{7}{3}$
* Convert to mixed number: $7 \div 3 = 2$ with a remainder of $1$.
* Answer: $2 \frac{1}{3}$
8. $\frac{23}{2} - \frac{19}{2}$
* Subtract the tops: $23 - 19 = 4$
* Keep the bottom: $2$
* Result: $\frac{4}{2}$
* Simplify: $4 \div 2 = 2$
* Answer: 2
9. $\frac{20}{7} - \frac{15}{7}$
* Subtract the tops: $20 - 15 = 5$
* Keep the bottom: $7$
* Answer: $\frac{5}{7}$
10. $\frac{13}{6} - \frac{5}{6}$
* Subtract the tops: $13 - 5 = 8$
* Keep the bottom: $6$
* Result: $\frac{8}{6}$
* Simplify: Divide by 2. $\frac{4}{3}$
* Convert to mixed number: $4 \div 3 = 1$ with a remainder of $1$.
* Answer: $1 \frac{1}{3}$
11. $\frac{17}{8} + \frac{3}{8}$
* Add the tops: $17 + 3 = 20$
* Keep the bottom: $8$
* Result: $\frac{20}{8}$
* Simplify: Divide by 4. $\frac{5}{2}$
* Convert to mixed number: $5 \div 2 = 2$ with a remainder of $1$.
* Answer: $2 \frac{1}{2}$
12. $\frac{17}{10} + \frac{13}{10}$
* Add the tops: $17 + 13 = 30$
* Keep the bottom: $10$
* Result: $\frac{30}{10}$
* Simplify: $30 \div 10 = 3$
* Answer: 3
Final Answer:
1. 3
2. $2 \frac{1}{4}$
3. $9 \frac{1}{2}$
4. 0
5. $4 \frac{4}{9}$
6. 2
7. $2 \frac{1}{3}$
8. 2
9. $\frac{5}{7}$
10. $1 \frac{1}{3}$
11. $2 \frac{1}{2}$
12. 3
Parent Tip: Review the logic above to help your child master the concept of operation of fractions worksheet.