Let's solve each of these fraction addition problems step by step. The key to adding fractions is to
find a common denominator, then add the numerators while keeping the denominator the same.
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1. $ \frac{1}{3} + \frac{1}{12} $
- The least common denominator (LCD) of 3 and 12 is
12.
- Convert $ \frac{1}{3} $ to twelfths:
$ \frac{1}{3} = \frac{4}{12} $
- Now add:
$ \frac{4}{12} + \frac{1}{12} = \frac{5}{12} $
✔ Answer: $ \frac{5}{12} $
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2. $ \frac{1}{5} + \frac{3}{15} $
- LCD of 5 and 15 is
15.
- Convert $ \frac{1}{5} $:
$ \frac{1}{5} = \frac{3}{15} $
- Add:
$ \frac{3}{15} + \frac{3}{15} = \frac{6}{15} $
- Simplify:
$ \frac{6}{15} = \frac{2}{5} $
✔ Answer: $ \frac{2}{5} $
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3. $ \frac{1}{4} + \frac{1}{8} $
- LCD of 4 and 8 is
8.
- Convert $ \frac{1}{4} $:
$ \frac{1}{4} = \frac{2}{8} $
- Add:
$ \frac{2}{8} + \frac{1}{8} = \frac{3}{8} $
✔ Answer: $ \frac{3}{8} $
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4. $ \frac{1}{8} + \frac{2}{16} $
- LCD of 8 and 16 is
16.
- Convert $ \frac{1}{8} $:
$ \frac{1}{8} = \frac{2}{16} $
- Add:
$ \frac{2}{16} + \frac{2}{16} = \frac{4}{16} $
- Simplify:
$ \frac{4}{16} = \frac{1}{4} $
✔ Answer: $ \frac{1}{4} $
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5. $ \frac{2}{9} + \frac{3}{18} $
- LCD of 9 and 18 is
18.
- Convert $ \frac{2}{9} $:
$ \frac{2}{9} = \frac{4}{18} $
- Add:
$ \frac{4}{18} + \frac{3}{18} = \frac{7}{18} $
✔ Answer: $ \frac{7}{18} $
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6. $ \frac{1}{4} + \frac{2}{24} $
- LCD of 4 and 24 is
24.
- Convert $ \frac{1}{4} $:
$ \frac{1}{4} = \frac{6}{24} $
- Add:
$ \frac{6}{24} + \frac{2}{24} = \frac{8}{24} $
- Simplify:
$ \frac{8}{24} = \frac{1}{3} $
✔ Answer: $ \frac{1}{3} $
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7. $ \frac{1}{3} + \frac{6}{21} $
- LCD of 3 and 21 is
21.
- Convert $ \frac{1}{3} $:
$ \frac{1}{3} = \frac{7}{21} $
- Add:
$ \frac{7}{21} + \frac{6}{21} = \frac{13}{21} $
✔ Answer: $ \frac{13}{21} $
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8. $ \frac{3}{7} + \frac{2}{28} $
- LCD of 7 and 28 is
28.
- Convert $ \frac{3}{7} $:
$ \frac{3}{7} = \frac{12}{28} $
- Add:
$ \frac{12}{28} + \frac{2}{28} = \frac{14}{28} $
- Simplify:
$ \frac{14}{28} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $
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9. $ \frac{1}{6} + \frac{1}{24} $
- LCD of 6 and 24 is
24.
- Convert $ \frac{1}{6} $:
$ \frac{1}{6} = \frac{4}{24} $
- Add:
$ \frac{4}{24} + \frac{1}{24} = \frac{5}{24} $
✔ Answer: $ \frac{5}{24} $
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10. $ \frac{3}{11} + \frac{1}{22} $
- LCD of 11 and 22 is
22.
- Convert $ \frac{3}{11} $:
$ \frac{3}{11} = \frac{6}{22} $
- Add:
$ \frac{6}{22} + \frac{1}{22} = \frac{7}{22} $
✔ Answer: $ \frac{7}{22} $
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✔ Final Answers:
1. $ \frac{5}{12} $
2. $ \frac{2}{5} $
3. $ \frac{3}{8} $
4. $ \frac{1}{4} $
5. $ \frac{7}{18} $
6. $ \frac{1}{3} $
7. $ \frac{13}{21} $
8. $ \frac{1}{2} $
9. $ \frac{5}{24} $
10. $ \frac{7}{22} $
Let me know if you'd like this as a printable worksheet or with visual models!
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting mixed number worksheet 5th grade 10 7a.
