Free educational worksheet for practicing addition of fractions with unlike denominators.
Worksheet for adding three fractions with unlike denominators, featuring instructions and 20 practice problems from www.edu-games.org.
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Step-by-step solution for: Free adding 3 fractions with unlike denominators worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Free adding 3 fractions with unlike denominators worksheets ...
Here are the step-by-step solutions for the 20 fraction addition problems.
General Method:
1. Find a common denominator (a number that all bottom numbers can divide into).
2. Change each fraction so they have that same bottom number.
3. Add the top numbers together.
4. Simplify the result if possible (reduce the fraction or turn it into a mixed number).
---
1. $\frac{1}{4} + \frac{2}{4} + \frac{1}{6}$
* Common denominator for 4 and 6 is 12.
* $\frac{1}{4} = \frac{3}{12}$, $\frac{2}{4} = \frac{6}{12}$, $\frac{1}{6} = \frac{2}{12}$
* Add tops: $3 + 6 + 2 = 11$
* Result: $\frac{11}{12}$
2. $\frac{1}{2} + \frac{1}{2} + \frac{1}{4}$
* Common denominator is 4.
* $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{4} = \frac{1}{4}$
* Add tops: $2 + 2 + 1 = 5$
* Result: $\frac{5}{4}$ which simplifies to $1 \frac{1}{4}$
3. $\frac{4}{8} + \frac{4}{8} + \frac{3}{4}$
* Common denominator is 8.
* $\frac{3}{4} = \frac{6}{8}$
* Add tops: $4 + 4 + 6 = 14$
* Result: $\frac{14}{8}$ which simplifies to $\frac{7}{4}$ or $1 \frac{3}{4}$
4. $\frac{4}{8} + \frac{3}{6} + \frac{1}{2}$
* Common denominator is 24 (or simplify first: $\frac{1}{2} + \frac{1}{2} + \frac{1}{2}$). Let's use 24 to be safe.
* $\frac{4}{8} = \frac{12}{24}$, $\frac{3}{6} = \frac{12}{24}$, $\frac{1}{2} = \frac{12}{24}$
* Add tops: $12 + 12 + 12 = 36$
* Result: $\frac{36}{24}$ which simplifies to $\frac{3}{2}$ or $1 \frac{1}{2}$
5. $\frac{1}{8} + \frac{3}{6} + \frac{1}{6}$
* Common denominator for 8 and 6 is 24.
* $\frac{1}{8} = \frac{3}{24}$, $\frac{3}{6} = \frac{12}{24}$, $\frac{1}{6} = \frac{4}{24}$
* Add tops: $3 + 12 + 4 = 19$
* Result: $\frac{19}{24}$
6. $\frac{1}{2} + \frac{1}{6} + \frac{2}{6}$
* Common denominator is 6.
* $\frac{1}{2} = \frac{3}{6}$
* Add tops: $3 + 1 + 2 = 6$
* Result: $\frac{6}{6} =$ $1$
7. $\frac{1}{2} + \frac{2}{4} + \frac{4}{6}$
* Common denominator for 2, 4, 6 is 12.
* $\frac{1}{2} = \frac{6}{12}$, $\frac{2}{4} = \frac{6}{12}$, $\frac{4}{6} = \frac{8}{12}$
* Add tops: $6 + 6 + 8 = 20$
* Result: $\frac{20}{12}$ which simplifies to $\frac{5}{3}$ or $1 \frac{2}{3}$
8. $\frac{3}{4} + \frac{1}{6} + \frac{3}{4}$
* Common denominator for 4 and 6 is 12.
* $\frac{3}{4} = \frac{9}{12}$, $\frac{1}{6} = \frac{2}{12}$, $\frac{3}{4} = \frac{9}{12}$
* Add tops: $9 + 2 + 9 = 20$
* Result: $\frac{20}{12}$ which simplifies to $\frac{5}{3}$ or $1 \frac{2}{3}$
9. $\frac{1}{2} + \frac{3}{8} + \frac{2}{4}$
* Common denominator is 8.
* $\frac{1}{2} = \frac{4}{8}$, $\frac{2}{4} = \frac{4}{8}$
* Add tops: $4 + 3 + 4 = 11$
* Result: $\frac{11}{8}$ which simplifies to $1 \frac{3}{8}$
10. $\frac{1}{2} + \frac{2}{8} + \frac{1}{2}$
* Common denominator is 8.
* $\frac{1}{2} = \frac{4}{8}$, $\frac{1}{2} = \frac{4}{8}$
* Add tops: $4 + 2 + 4 = 10$
* Result: $\frac{10}{8}$ which simplifies to $\frac{5}{4}$ or $1 \frac{1}{4}$
11. $\frac{1}{8} + \frac{4}{8} + \frac{4}{8}$
* Denominators are already the same.
* Add tops: $1 + 4 + 4 = 9$
* Result: $\frac{9}{8}$ which simplifies to $1 \frac{1}{8}$
12. $\frac{1}{6} + \frac{4}{6} + \frac{3}{4}$
* Common denominator for 6 and 4 is 12.
* $\frac{1}{6} = \frac{2}{12}$, $\frac{4}{6} = \frac{8}{12}$, $\frac{3}{4} = \frac{9}{12}$
* Add tops: $2 + 8 + 9 = 19$
* Result: $\frac{19}{12}$ which simplifies to $1 \frac{7}{12}$
13. $\frac{1}{2} + \frac{1}{2} + \frac{1}{2}$
* Add tops: $1 + 1 + 1 = 3$
* Result: $\frac{3}{2}$ which simplifies to $1 \frac{1}{2}$
14. $\frac{5}{8} + \frac{3}{6} + \frac{1}{2}$
* Common denominator is 24.
* $\frac{5}{8} = \frac{15}{24}$, $\frac{3}{6} = \frac{12}{24}$, $\frac{1}{2} = \frac{12}{24}$
* Add tops: $15 + 12 + 12 = 39$
* Result: $\frac{39}{24}$ which simplifies to $\frac{13}{8}$ or $1 \frac{5}{8}$
15. $\frac{1}{2} + \frac{1}{2} + \frac{2}{4}$
* Common denominator is 4.
* $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{2} = \frac{2}{4}$
* Add tops: $2 + 2 + 2 = 6$
* Result: $\frac{6}{4}$ which simplifies to $\frac{3}{2}$ or $1 \frac{1}{2}$
16. $\frac{1}{2} + \frac{1}{6} + \frac{4}{6}$
* Common denominator is 6.
* $\frac{1}{2} = \frac{3}{6}$
* Add tops: $3 + 1 + 4 = 8$
* Result: $\frac{8}{6}$ which simplifies to $\frac{4}{3}$ or $1 \frac{1}{3}$
17. $\frac{3}{6} + \frac{2}{8} + \frac{1}{6}$
* Combine the sixths first: $\frac{3}{6} + \frac{1}{6} = \frac{4}{6}$.
* Now add $\frac{4}{6} + \frac{2}{8}$. Common denominator for 6 and 8 is 24.
* $\frac{4}{6} = \frac{16}{24}$, $\frac{2}{8} = \frac{6}{24}$
* Add tops: $16 + 6 = 22$
* Result: $\frac{22}{24}$ which simplifies to $\frac{11}{12}$
18. $\frac{1}{2} + \frac{2}{4} + \frac{1}{2}$
* Common denominator is 4.
* $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{2} = \frac{2}{4}$
* Add tops: $2 + 2 + 2 = 6$
* Result: $\frac{6}{4}$ which simplifies to $\frac{3}{2}$ or $1 \frac{1}{2}$
19. $\frac{1}{4} + \frac{1}{2} + \frac{5}{8}$
* Common denominator is 8.
* $\frac{1}{4} = \frac{2}{8}$, $\frac{1}{2} = \frac{4}{8}$
* Add tops: $2 + 4 + 5 = 11$
* Result: $\frac{11}{8}$ which simplifies to $1 \frac{3}{8}$
20. $\frac{4}{8} + \frac{1}{2} + \frac{2}{6}$
* Common denominator is 24.
* $\frac{4}{8} = \frac{12}{24}$, $\frac{1}{2} = \frac{12}{24}$, $\frac{2}{6} = \frac{8}{24}$
* Add tops: $12 + 12 + 8 = 32$
* Result: $\frac{32}{24}$ which simplifies to $\frac{4}{3}$ or $1 \frac{1}{3}$
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Final Answer:
1. $\frac{11}{12}$
2. $1 \frac{1}{4}$
3. $1 \frac{3}{4}$
4. $1 \frac{1}{2}$
5. $\frac{19}{24}$
6. $1$
7. $1 \frac{2}{3}$
8. $1 \frac{2}{3}$
9. $1 \frac{3}{8}$
10. $1 \frac{1}{4}$
11. $1 \frac{1}{8}$
12. $1 \frac{7}{12}$
13. $1 \frac{1}{2}$
14. $1 \frac{5}{8}$
15. $1 \frac{1}{2}$
16. $1 \frac{1}{3}$
17. $\frac{11}{12}$
18. $1 \frac{1}{2}$
19. $1 \frac{3}{8}$
20. $1 \frac{1}{3}$
General Method:
1. Find a common denominator (a number that all bottom numbers can divide into).
2. Change each fraction so they have that same bottom number.
3. Add the top numbers together.
4. Simplify the result if possible (reduce the fraction or turn it into a mixed number).
---
1. $\frac{1}{4} + \frac{2}{4} + \frac{1}{6}$
* Common denominator for 4 and 6 is 12.
* $\frac{1}{4} = \frac{3}{12}$, $\frac{2}{4} = \frac{6}{12}$, $\frac{1}{6} = \frac{2}{12}$
* Add tops: $3 + 6 + 2 = 11$
* Result: $\frac{11}{12}$
2. $\frac{1}{2} + \frac{1}{2} + \frac{1}{4}$
* Common denominator is 4.
* $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{4} = \frac{1}{4}$
* Add tops: $2 + 2 + 1 = 5$
* Result: $\frac{5}{4}$ which simplifies to $1 \frac{1}{4}$
3. $\frac{4}{8} + \frac{4}{8} + \frac{3}{4}$
* Common denominator is 8.
* $\frac{3}{4} = \frac{6}{8}$
* Add tops: $4 + 4 + 6 = 14$
* Result: $\frac{14}{8}$ which simplifies to $\frac{7}{4}$ or $1 \frac{3}{4}$
4. $\frac{4}{8} + \frac{3}{6} + \frac{1}{2}$
* Common denominator is 24 (or simplify first: $\frac{1}{2} + \frac{1}{2} + \frac{1}{2}$). Let's use 24 to be safe.
* $\frac{4}{8} = \frac{12}{24}$, $\frac{3}{6} = \frac{12}{24}$, $\frac{1}{2} = \frac{12}{24}$
* Add tops: $12 + 12 + 12 = 36$
* Result: $\frac{36}{24}$ which simplifies to $\frac{3}{2}$ or $1 \frac{1}{2}$
5. $\frac{1}{8} + \frac{3}{6} + \frac{1}{6}$
* Common denominator for 8 and 6 is 24.
* $\frac{1}{8} = \frac{3}{24}$, $\frac{3}{6} = \frac{12}{24}$, $\frac{1}{6} = \frac{4}{24}$
* Add tops: $3 + 12 + 4 = 19$
* Result: $\frac{19}{24}$
6. $\frac{1}{2} + \frac{1}{6} + \frac{2}{6}$
* Common denominator is 6.
* $\frac{1}{2} = \frac{3}{6}$
* Add tops: $3 + 1 + 2 = 6$
* Result: $\frac{6}{6} =$ $1$
7. $\frac{1}{2} + \frac{2}{4} + \frac{4}{6}$
* Common denominator for 2, 4, 6 is 12.
* $\frac{1}{2} = \frac{6}{12}$, $\frac{2}{4} = \frac{6}{12}$, $\frac{4}{6} = \frac{8}{12}$
* Add tops: $6 + 6 + 8 = 20$
* Result: $\frac{20}{12}$ which simplifies to $\frac{5}{3}$ or $1 \frac{2}{3}$
8. $\frac{3}{4} + \frac{1}{6} + \frac{3}{4}$
* Common denominator for 4 and 6 is 12.
* $\frac{3}{4} = \frac{9}{12}$, $\frac{1}{6} = \frac{2}{12}$, $\frac{3}{4} = \frac{9}{12}$
* Add tops: $9 + 2 + 9 = 20$
* Result: $\frac{20}{12}$ which simplifies to $\frac{5}{3}$ or $1 \frac{2}{3}$
9. $\frac{1}{2} + \frac{3}{8} + \frac{2}{4}$
* Common denominator is 8.
* $\frac{1}{2} = \frac{4}{8}$, $\frac{2}{4} = \frac{4}{8}$
* Add tops: $4 + 3 + 4 = 11$
* Result: $\frac{11}{8}$ which simplifies to $1 \frac{3}{8}$
10. $\frac{1}{2} + \frac{2}{8} + \frac{1}{2}$
* Common denominator is 8.
* $\frac{1}{2} = \frac{4}{8}$, $\frac{1}{2} = \frac{4}{8}$
* Add tops: $4 + 2 + 4 = 10$
* Result: $\frac{10}{8}$ which simplifies to $\frac{5}{4}$ or $1 \frac{1}{4}$
11. $\frac{1}{8} + \frac{4}{8} + \frac{4}{8}$
* Denominators are already the same.
* Add tops: $1 + 4 + 4 = 9$
* Result: $\frac{9}{8}$ which simplifies to $1 \frac{1}{8}$
12. $\frac{1}{6} + \frac{4}{6} + \frac{3}{4}$
* Common denominator for 6 and 4 is 12.
* $\frac{1}{6} = \frac{2}{12}$, $\frac{4}{6} = \frac{8}{12}$, $\frac{3}{4} = \frac{9}{12}$
* Add tops: $2 + 8 + 9 = 19$
* Result: $\frac{19}{12}$ which simplifies to $1 \frac{7}{12}$
13. $\frac{1}{2} + \frac{1}{2} + \frac{1}{2}$
* Add tops: $1 + 1 + 1 = 3$
* Result: $\frac{3}{2}$ which simplifies to $1 \frac{1}{2}$
14. $\frac{5}{8} + \frac{3}{6} + \frac{1}{2}$
* Common denominator is 24.
* $\frac{5}{8} = \frac{15}{24}$, $\frac{3}{6} = \frac{12}{24}$, $\frac{1}{2} = \frac{12}{24}$
* Add tops: $15 + 12 + 12 = 39$
* Result: $\frac{39}{24}$ which simplifies to $\frac{13}{8}$ or $1 \frac{5}{8}$
15. $\frac{1}{2} + \frac{1}{2} + \frac{2}{4}$
* Common denominator is 4.
* $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{2} = \frac{2}{4}$
* Add tops: $2 + 2 + 2 = 6$
* Result: $\frac{6}{4}$ which simplifies to $\frac{3}{2}$ or $1 \frac{1}{2}$
16. $\frac{1}{2} + \frac{1}{6} + \frac{4}{6}$
* Common denominator is 6.
* $\frac{1}{2} = \frac{3}{6}$
* Add tops: $3 + 1 + 4 = 8$
* Result: $\frac{8}{6}$ which simplifies to $\frac{4}{3}$ or $1 \frac{1}{3}$
17. $\frac{3}{6} + \frac{2}{8} + \frac{1}{6}$
* Combine the sixths first: $\frac{3}{6} + \frac{1}{6} = \frac{4}{6}$.
* Now add $\frac{4}{6} + \frac{2}{8}$. Common denominator for 6 and 8 is 24.
* $\frac{4}{6} = \frac{16}{24}$, $\frac{2}{8} = \frac{6}{24}$
* Add tops: $16 + 6 = 22$
* Result: $\frac{22}{24}$ which simplifies to $\frac{11}{12}$
18. $\frac{1}{2} + \frac{2}{4} + \frac{1}{2}$
* Common denominator is 4.
* $\frac{1}{2} = \frac{2}{4}$, $\frac{1}{2} = \frac{2}{4}$
* Add tops: $2 + 2 + 2 = 6$
* Result: $\frac{6}{4}$ which simplifies to $\frac{3}{2}$ or $1 \frac{1}{2}$
19. $\frac{1}{4} + \frac{1}{2} + \frac{5}{8}$
* Common denominator is 8.
* $\frac{1}{4} = \frac{2}{8}$, $\frac{1}{2} = \frac{4}{8}$
* Add tops: $2 + 4 + 5 = 11$
* Result: $\frac{11}{8}$ which simplifies to $1 \frac{3}{8}$
20. $\frac{4}{8} + \frac{1}{2} + \frac{2}{6}$
* Common denominator is 24.
* $\frac{4}{8} = \frac{12}{24}$, $\frac{1}{2} = \frac{12}{24}$, $\frac{2}{6} = \frac{8}{24}$
* Add tops: $12 + 12 + 8 = 32$
* Result: $\frac{32}{24}$ which simplifies to $\frac{4}{3}$ or $1 \frac{1}{3}$
──────────────────────────────────────
Final Answer:
1. $\frac{11}{12}$
2. $1 \frac{1}{4}$
3. $1 \frac{3}{4}$
4. $1 \frac{1}{2}$
5. $\frac{19}{24}$
6. $1$
7. $1 \frac{2}{3}$
8. $1 \frac{2}{3}$
9. $1 \frac{3}{8}$
10. $1 \frac{1}{4}$
11. $1 \frac{1}{8}$
12. $1 \frac{7}{12}$
13. $1 \frac{1}{2}$
14. $1 \frac{5}{8}$
15. $1 \frac{1}{2}$
16. $1 \frac{1}{3}$
17. $\frac{11}{12}$
18. $1 \frac{1}{2}$
19. $1 \frac{3}{8}$
20. $1 \frac{1}{3}$
Parent Tip: Review the logic above to help your child master the concept of math worksheet fractions unlike denominators.
