Adding Two Proper Fractions with Equal Denominators, Proper ... - Free Printable

Here are the solutions for the "Adding Two Proper Fractions" worksheet.

How to solve these:
1. Check the bottom numbers (denominators): In every problem on this sheet, the bottom numbers are already the same. This makes it easy!
2. Add the top numbers (numerators): Just add the top numbers together. Keep the bottom number exactly the same.
3. Simplify (if asked): Some problems have two blank spaces (`__ = __`). This means you need to simplify your answer. To simplify, find a number that divides evenly into both the top and bottom numbers. Usually, you can divide by 2 or 3.

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1. $\frac{3}{6} + \frac{1}{6}$
* Add tops: $3 + 1 = 4$. Bottom stays 6. Result: $\frac{4}{6}$.
* Simplify: Divide top and bottom by 2. ($4 \div 2 = 2$, $6 \div 2 = 3$).
* Answer: $\frac{4}{6} = \frac{2}{3}$

2. $\frac{6}{9} + \frac{1}{9}$
* Add tops: $6 + 1 = 7$. Bottom stays 9.
* Answer: $\frac{7}{9}$ (Cannot be simplified)

3. $\frac{1}{3} + \frac{1}{3}$
* Add tops: $1 + 1 = 2$. Bottom stays 3.
* Answer: $\frac{2}{3}$

4. $\frac{2}{5} + \frac{1}{5}$
* Add tops: $2 + 1 = 3$. Bottom stays 5.
* Answer: $\frac{3}{5}$

5. $\frac{6}{8} + \frac{1}{8}$
* Add tops: $6 + 1 = 7$. Bottom stays 8.
* Answer: $\frac{7}{8}$

6. $\frac{1}{5} + \frac{1}{5}$
* Add tops: $1 + 1 = 2$. Bottom stays 5.
* Answer: $\frac{2}{5}$

7. $\frac{7}{9} + \frac{1}{9}$
* Add tops: $7 + 1 = 8$. Bottom stays 9.
* Answer: $\frac{8}{9}$

8. $\frac{2}{7} + \frac{3}{7}$
* Add tops: $2 + 3 = 5$. Bottom stays 7.
* Answer: $\frac{5}{7}$

9. $\frac{2}{6} + \frac{3}{6}$
* Add tops: $2 + 3 = 5$. Bottom stays 6.
* Answer: $\frac{5}{6}$

10. $\frac{2}{6} + \frac{2}{6}$
* Add tops: $2 + 2 = 4$. Bottom stays 6. Result: $\frac{4}{6}$.
* Simplify: Divide top and bottom by 2.
* Answer: $\frac{4}{6} = \frac{2}{3}$

11. $\frac{4}{6} + \frac{1}{6}$
* Add tops: $4 + 1 = 5$. Bottom stays 6.
* Answer: $\frac{5}{6}$

12. $\frac{4}{8} + \frac{2}{8}$
* Add tops: $4 + 2 = 6$. Bottom stays 8. Result: $\frac{6}{8}$.
* Simplify: Divide top and bottom by 2. ($6 \div 2 = 3$, $8 \div 2 = 4$).
* Answer: $\frac{6}{8} = \frac{3}{4}$

13. $\frac{3}{9} + \frac{3}{9}$
* Add tops: $3 + 3 = 6$. Bottom stays 9. Result: $\frac{6}{9}$.
* Simplify: Divide top and bottom by 3. ($6 \div 3 = 2$, $9 \div 3 = 3$).
* Answer: $\frac{6}{9} = \frac{2}{3}$

14. $\frac{2}{8} + \frac{4}{8}$
* Add tops: $2 + 4 = 6$. Bottom stays 8. Result: $\frac{6}{8}$.
* Simplify: Divide top and bottom by 2.
* Answer: $\frac{6}{8} = \frac{3}{4}$

15. $\frac{2}{4} + \frac{1}{4}$
* Add tops: $2 + 1 = 3$. Bottom stays 4.
* Answer: $\frac{3}{4}$

16. $\frac{3}{7} + \frac{1}{7}$
* Add tops: $3 + 1 = 4$. Bottom stays 7.
* Answer: $\frac{4}{7}$

17. $\frac{2}{5} + \frac{2}{5}$
* Add tops: $2 + 2 = 4$. Bottom stays 5.
* Answer: $\frac{4}{5}$

18. $\frac{2}{7} + \frac{1}{7}$
* Add tops: $2 + 1 = 3$. Bottom stays 7.
* Answer: $\frac{3}{7}$

19. $\frac{2}{8} + \frac{5}{8}$
* Add tops: $2 + 5 = 7$. Bottom stays 8.
* Answer: $\frac{7}{8}$

20. $\frac{1}{4} + \frac{1}{4}$
* Add tops: $1 + 1 = 2$. Bottom stays 4. Result: $\frac{2}{4}$.
* Simplify: Divide top and bottom by 2. ($2 \div 2 = 1$, $4 \div 2 = 2$).
* Answer: $\frac{2}{4} = \frac{1}{2}$

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Final Answer:
1. $\frac{4}{6} = \frac{2}{3}$
2. $\frac{7}{9}$
3. $\frac{2}{3}$
4. $\frac{3}{5}$
5. $\frac{7}{8}$
6. $\frac{2}{5}$
7. $\frac{8}{9}$
8. $\frac{5}{7}$
9. $\frac{5}{6}$
10. $\frac{4}{6} = \frac{2}{3}$
11. $\frac{5}{6}$
12. $\frac{6}{8} = \frac{3}{4}$
13. $\frac{6}{9} = \frac{2}{3}$
14. $\frac{6}{8} = \frac{3}{4}$
15. $\frac{3}{4}$
16. $\frac{4}{7}$
17. $\frac{4}{5}$
18. $\frac{3}{7}$
19. $\frac{7}{8}$
20. $\frac{2}{4} = \frac{1}{2}$