Adding unlike fractions worksheets | Worsheets library - Free Printable

Let's solve each problem on the "Adding Unlike Fractions" worksheet step by step. The goal is to add fractions with different denominators by finding a common denominator, converting the fractions, and then adding.

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Problem 1:

$$
\frac{1}{4} + \frac{2}{9}
$$

- Find the least common denominator (LCD) of 4 and 9 → LCM(4, 9) = 36
- Convert:
$$
\frac{1}{4} = \frac{9}{36}, \quad \frac{2}{9} = \frac{8}{36}
$$
- Add:
$$
\frac{9}{36} + \frac{8}{36} = \frac{17}{36}
$$

✔ Answer: $\boxed{\frac{17}{36}}$

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Problem 2:

$$
\frac{8}{12} + \frac{8}{11}
$$

- LCD of 12 and 11 → 132
- Convert:
$$
\frac{8}{12} = \frac{88}{132}, \quad \frac{8}{11} = \frac{96}{132}
$$
- Add:
$$
\frac{88}{132} + \frac{96}{132} = \frac{184}{132}
$$
- Simplify:
$$
\frac{184}{132} = \frac{46}{33} = 1\frac{13}{33}
$$

✔ Answer: $\boxed{1\frac{13}{33}}$

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Problem 3:

$$
\frac{2}{7} + \frac{8}{10}
$$

- Simplify $\frac{8}{10} = \frac{4}{5}$
- LCD of 7 and 5 → 35
- Convert:
$$
\frac{2}{7} = \frac{10}{35}, \quad \frac{4}{5} = \frac{28}{35}
$$
- Add:
$$
\frac{10}{35} + \frac{28}{35} = \frac{38}{35} = 1\frac{3}{35}
$$

✔ Answer: $\boxed{1\frac{3}{35}}$

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Problem 4:

$$
\frac{1}{6} + \frac{6}{11}
$$

- LCD of 6 and 11 → 66
- Convert:
$$
\frac{1}{6} = \frac{11}{66}, \quad \frac{6}{11} = \frac{36}{66}
$$
- Add:
$$
\frac{11}{66} + \frac{36}{66} = \frac{47}{66}
$$

✔ Answer: $\boxed{\frac{47}{66}}$

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Problem 5:

$$
\frac{5}{9} + \frac{1}{3}
$$

- $\frac{1}{3} = \frac{3}{9}$
- Add:
$$
\frac{5}{9} + \frac{3}{9} = \frac{8}{9}
$$

✔ Answer: $\boxed{\frac{8}{9}}$

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Problem 6:

$$
\frac{9}{12} + \frac{2}{12}
$$

- Same denominator → just add numerators:
$$
\frac{9+2}{12} = \frac{11}{12}
$$

✔ Answer: $\boxed{\frac{11}{12}}$

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Problem 7:

$$
\frac{7}{2} + \frac{1}{4}
$$

- LCD of 2 and 4 → 4
- Convert:
$$
\frac{7}{2} = \frac{14}{4}, \quad \frac{1}{4} = \frac{1}{4}
$$
- Add:
$$
\frac{14}{4} + \frac{1}{4} = \frac{15}{4} = 3\frac{3}{4}
$$

✔ Answer: $\boxed{3\frac{3}{4}}$

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Problem 8:

$$
\frac{1}{2} + \frac{6}{9}
$$

- Simplify $\frac{6}{9} = \frac{2}{3}$
- LCD of 2 and 3 → 6
- Convert:
$$
\frac{1}{2} = \frac{3}{6}, \quad \frac{2}{3} = \frac{4}{6}
$$
- Add:
$$
\frac{3}{6} + \frac{4}{6} = \frac{7}{6} = 1\frac{1}{6}
$$

✔ Answer: $\boxed{1\frac{1}{6}}$

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Problem 9:

$$
\frac{4}{10} + \frac{4}{5}
$$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- $\frac{2}{5} + \frac{4}{5} = \frac{6}{5} = 1\frac{1}{5}$

✔ Answer: $\boxed{1\frac{1}{5}}$

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Problem 10:

$$
\frac{1}{2} + \frac{8}{11}
$$

- LCD of 2 and 11 → 22
- Convert:
$$
\frac{1}{2} = \frac{11}{22}, \quad \frac{8}{11} = \frac{16}{22}
$$
- Add:
$$
\frac{11}{22} + \frac{16}{22} = \frac{27}{22} = 1\frac{5}{22}
$$

✔ Answer: $\boxed{1\frac{5}{22}}$

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Problem 11:

$$
\frac{1}{11} + \frac{2}{12}
$$

- Simplify $\frac{2}{12} = \frac{1}{6}$
- LCD of 11 and 6 → 66
- Convert:
$$
\frac{1}{11} = \frac{6}{66}, \quad \frac{1}{6} = \frac{11}{66}
$$
- Add:
$$
\frac{6}{66} + \frac{11}{66} = \frac{17}{66}
$$

✔ Answer: $\boxed{\frac{17}{66}}$

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Problem 12:

$$
\frac{2}{12} + \frac{2}{4}
$$

- Simplify:
$\frac{2}{12} = \frac{1}{6}$, $\frac{2}{4} = \frac{1}{2}$
- LCD of 6 and 2 → 6
- Convert:
$$
\frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}
$$

✔ Answer: $\boxed{\frac{2}{3}}$

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Problem 13:

$$
\frac{3}{6} + \frac{3}{8}
$$

- Simplify $\frac{3}{6} = \frac{1}{2}$
- LCD of 2 and 8 → 8
- Convert:
$$
\frac{1}{2} = \frac{4}{8}, \quad \frac{3}{8} = \frac{3}{8}
$$
- Add:
$$
\frac{4}{8} + \frac{3}{8} = \frac{7}{8}
$$

✔ Answer: $\boxed{\frac{7}{8}}$

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Problem 14:

$$
\frac{6}{5} + \frac{1}{2}
$$

- LCD of 5 and 2 → 10
- Convert:
$$
\frac{6}{5} = \frac{12}{10}, \quad \frac{1}{2} = \frac{5}{10}
$$
- Add:
$$
\frac{12}{10} + \frac{5}{10} = \frac{17}{10} = 1\frac{7}{10}
$$

✔ Answer: $\boxed{1\frac{7}{10}}$

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✔ Final Answers:

1. $\frac{17}{36}$
2. $1\frac{13}{33}$
3. $1\frac{3}{35}$
4. $\frac{47}{66}$
5. $\frac{8}{9}$
6. $\frac{11}{12}$
7. $3\frac{3}{4}$
8. $1\frac{1}{6}$
9. $1\frac{1}{5}$
10. $1\frac{5}{22}$
11. $\frac{17}{66}$
12. $\frac{2}{3}$
13. $\frac{7}{8}$
14. $1\frac{7}{10}$

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Let me know if you'd like this as a printable PDF or need explanations for any specific steps!