Simple Addition of Fractions worksheet for students to solve and simplify.

Explanation:
To add fractions, we need to have the same bottom number (called the denominator). If the denominators are different, we find a common one by finding the least common multiple (LCM) of the two denominators. Then, we change each fraction so they have that common denominator. After that, we add the top numbers (numerators) and keep the same bottom number. Finally, we simplify the answer if possible.

Let’s solve each problem step by step.

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① $ \frac{3}{6} + \frac{2}{8} $

- Find the LCM of 6 and 8.
Multiples of 6: 6, 12, 18, 24, ...
Multiples of 8: 8, 16, 24, ...
LCM = 24

- Convert both fractions:
$ \frac{3}{6} = \frac{3 \times 4}{6 \times 4} = \frac{12}{24} $
$ \frac{2}{8} = \frac{2 \times 3}{8 \times 3} = \frac{6}{24} $

- Add: $ \frac{12}{24} + \frac{6}{24} = \frac{18}{24} $

- Simplify: $ \frac{18}{24} = \frac{3}{4} $

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② $ \frac{5}{8} + \frac{6}{12} $

- LCM of 8 and 12:
8: 8, 16, 24, ...
12: 12, 24, ...
LCM = 24

- Convert:
$ \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} $
$ \frac{6}{12} = \frac{6 \times 2}{12 \times 2} = \frac{12}{24} $

- Add: $ \frac{15}{24} + \frac{12}{24} = \frac{27}{24} $

- Simplify: $ \frac{27}{24} = 1 \frac{3}{24} = 1 \frac{1}{8} $

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③ $ \frac{1}{6} + \frac{2}{5} $

- LCM of 6 and 5: 30

- Convert:
$ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} $
$ \frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30} $

- Add: $ \frac{5}{30} + \frac{12}{30} = \frac{17}{30} $

- Already simplified.

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④ $ \frac{1}{2} + \frac{2}{8} $

- LCM of 2 and 8: 8

- Convert:
$ \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} $
$ \frac{2}{8} $ stays the same

- Add: $ \frac{4}{8} + \frac{2}{8} = \frac{6}{8} $

- Simplify: $ \frac{6}{8} = \frac{3}{4} $

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⑤ $ \frac{8}{2} + \frac{6}{3} $

- First, simplify each fraction:
$ \frac{8}{2} = 4 $
$ \frac{6}{3} = 2 $

- Add: $ 4 + 2 = 6 $

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⑥ $ \frac{4}{6} + \frac{5}{10} $

- Simplify first:
$ \frac{4}{6} = \frac{2}{3} $
$ \frac{5}{10} = \frac{1}{2} $

- LCM of 3 and 2: 6

- Convert:
$ \frac{2}{3} = \frac{4}{6} $
$ \frac{1}{2} = \frac{3}{6} $

- Add: $ \frac{4}{6} + \frac{3}{6} = \frac{7}{6} $

- Simplify: $ \frac{7}{6} = 1 \frac{1}{6} $

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⑦ $ \frac{3}{7} + \frac{8}{14} $

- $ \frac{8}{14} = \frac{4}{7} $

- Now: $ \frac{3}{7} + \frac{4}{7} = \frac{7}{7} = 1 $

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⑧ $ \frac{2}{8} + \frac{3}{7} $

- $ \frac{2}{8} = \frac{1}{4} $

- LCM of 4 and 7: 28

- Convert:
$ \frac{1}{4} = \frac{7}{28} $
$ \frac{3}{7} = \frac{12}{28} $

- Add: $ \frac{7}{28} + \frac{12}{28} = \frac{19}{28} $

- Already simplified.

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⑨ $ \frac{4}{21} + \frac{1}{6} $

- LCM of 21 and 6: 42

- Convert:
$ \frac{4}{21} = \frac{4 \times 2}{21 \times 2} = \frac{8}{42} $
$ \frac{1}{6} = \frac{1 \times 7}{6 \times 7} = \frac{7}{42} $

- Add: $ \frac{8}{42} + \frac{7}{42} = \frac{15}{42} $

- Simplify: $ \frac{15}{42} = \frac{5}{14} $

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⑩ $ \frac{4}{9} + \frac{7}{36} $

- LCM of 9 and 36: 36

- Convert:
$ \frac{4}{9} = \frac{4 \times 4}{9 \times 4} = \frac{16}{36} $

- Add: $ \frac{16}{36} + \frac{7}{36} = \frac{23}{36} $

- Already simplified.

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⑪ $ \frac{2}{3} + \frac{7}{18} $

- LCM of 3 and 18: 18

- Convert:
$ \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} $

- Add: $ \frac{12}{18} + \frac{7}{18} = \frac{19}{18} $

- Simplify: $ \frac{19}{18} = 1 \frac{1}{18} $

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⑫ $ \frac{1}{4} + \frac{5}{12} $

- LCM of 4 and 12: 12

- Convert:
$ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} $

- Add: $ \frac{3}{12} + \frac{5}{12} = \frac{8}{12} $

- Simplify: $ \frac{8}{12} = \frac{2}{3} $

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Final Answer:
① $ \frac{3}{4} $
② $ 1 \frac{1}{8} $
③ $ \frac{17}{30} $
④ $ \frac{3}{4} $
⑤ $ 6 $
⑥ $ 1 \frac{1}{6} $
⑦ $ 1 $
⑧ $ \frac{19}{28} $
⑨ $ \frac{5}{14} $
⑩ $ \frac{23}{36} $
⑪ $ 1 \frac{1}{18} $
⑫ $ \frac{2}{3} $