Let's solve each of these
adding unlike fractions problems step by step. The key to adding unlike fractions is to find a
common denominator, convert the fractions, and then add.
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1. $\frac{3}{9} + \frac{1}{3}$
- Simplify $\frac{3}{9} = \frac{1}{3}$
- So: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$
✔ Answer: $\frac{2}{3}$
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2. $\frac{5}{9} + \frac{1}{2}$
- Find LCM of 9 and 2 → 18
- Convert:
- $\frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18}$
- $\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}$
- Add: $\frac{10}{18} + \frac{9}{18} = \frac{19}{18}$
- Simplify: $\frac{19}{18} = 1\frac{1}{18}$
✔ Answer: $1\frac{1}{18}$
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3. $\frac{1}{6} + \frac{6}{12}$
- Simplify $\frac{6}{12} = \frac{1}{2}$
- Now: $\frac{1}{6} + \frac{1}{2}$
- LCM of 6 and 2 is 6
- $\frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}$
✔ Answer: $\frac{2}{3}$
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4. $\frac{3}{4} + \frac{2}{5}$
- LCM of 4 and 5 is 20
- $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$
- $\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$
- Add: $\frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1\frac{3}{20}$
✔ Answer: $1\frac{3}{20}$
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5. $\frac{2}{9} + \frac{2}{3}$
- LCM of 9 and 3 is 9
- $\frac{2}{3} = \frac{6}{9}$
- Add: $\frac{2}{9} + \frac{6}{9} = \frac{8}{9}$
✔ Answer: $\frac{8}{9}$
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6. $\frac{1}{5} + \frac{1}{6}$
- LCM of 5 and 6 is 30
- $\frac{1}{5} = \frac{6}{30}$
- $\frac{1}{6} = \frac{5}{30}$
- Add: $\frac{6}{30} + \frac{5}{30} = \frac{11}{30}$
✔ Answer: $\frac{11}{30}$
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7. $\frac{2}{3} + \frac{5}{9}$
- LCM of 3 and 9 is 9
- $\frac{2}{3} = \frac{6}{9}$
- Add: $\frac{6}{9} + \frac{5}{9} = \frac{11}{9} = 1\frac{2}{9}$
✔ Answer: $1\frac{2}{9}$
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8. $\frac{1}{4} + \frac{5}{8}$
- LCM of 4 and 8 is 8
- $\frac{1}{4} = \frac{2}{8}$
- Add: $\frac{2}{8} + \frac{5}{8} = \frac{7}{8}$
✔ Answer: $\frac{7}{8}$
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9. $\frac{9}{10} + \frac{1}{5}$
- LCM of 10 and 5 is 10
- $\frac{1}{5} = \frac{2}{10}$
- Add: $\frac{9}{10} + \frac{2}{10} = \frac{11}{10} = 1\frac{1}{10}$
✔ Answer: $1\frac{1}{10}$
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10. $\frac{1}{6} + \frac{2}{3}$
- LCM of 6 and 3 is 6
- $\frac{2}{3} = \frac{4}{6}$
- Add: $\frac{1}{6} + \frac{4}{6} = \frac{5}{6}$
✔ Answer: $\frac{5}{6}$
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1. $\frac{3}{9} + \frac{1}{3}$ | $\frac{2}{3}$ |
| 2. $\frac{5}{9} + \frac{1}{2}$ | $1\frac{1}{18}$ |
| 3. $\frac{1}{6} + \frac{6}{12}$ | $\frac{2}{3}$ |
| 4. $\frac{3}{4} + \frac{2}{5}$ | $1\frac{3}{20}$ |
| 5. $\frac{2}{9} + \frac{2}{3}$ | $\frac{8}{9}$ |
| 6. $\frac{1}{5} + \frac{1}{6}$ | $\frac{11}{30}$ |
| 7. $\frac{2}{3} + \frac{5}{9}$ | $1\frac{2}{9}$ |
| 8. $\frac{1}{4} + \frac{5}{8}$ | $\frac{7}{8}$ |
| 9. $\frac{9}{10} + \frac{1}{5}$ | $1\frac{1}{10}$ |
|10. $\frac{1}{6} + \frac{2}{3}$ | $\frac{5}{6}$ |
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🔍 Summary of Steps for Adding Unlike Fractions:
1. Find the
Least Common Denominator (LCD).
2. Convert each fraction to an equivalent fraction with the LCD.
3. Add the numerators, keep the denominator.
4. Simplify the result (reduce or write as mixed number if needed).
Let me know if you'd like this as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of unike denominators.
