Math worksheet for adding fractions with unlike denominators.

You’ve uploaded a worksheet titled “Operations with Unlike Denominators”, which asks students to add proper fractions with different denominators. To solve these, we need to:

1. Find the Least Common Denominator (LCD) — the smallest number that both denominators divide into evenly.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Add the numerators, keeping the common denominator.
4. Simplify the result if possible (reduce to lowest terms).

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Let’s solve all 18 problems step by step.

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Problem 1:

$\frac{2}{5} + \frac{5}{10}$

- LCD of 5 and 10 is 10.
- $\frac{2}{5} = \frac{4}{10}$
- $\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$ → already simplified.

✔ Answer: $\frac{9}{10}$

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Problem 2:

$\frac{4}{9} + \frac{3}{12}$

- Simplify $\frac{3}{12} = \frac{1}{4}$
- LCD of 9 and 4 is 36
- $\frac{4}{9} = \frac{16}{36}$, $\frac{1}{4} = \frac{9}{36}$
- $\frac{16}{36} + \frac{9}{36} = \frac{25}{36}$

✔ Answer: $\frac{25}{36}$

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Problem 3:

$\frac{1}{4} + \frac{3}{5}$

- LCD of 4 and 5 is 20
- $\frac{1}{4} = \frac{5}{20}$, $\frac{3}{5} = \frac{12}{20}$
- $\frac{5}{20} + \frac{12}{20} = \frac{17}{20}$

✔ Answer: $\frac{17}{20}$

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Problem 4:

$\frac{2}{5} + \frac{1}{3}$

- LCD of 5 and 3 is 15
- $\frac{2}{5} = \frac{6}{15}$, $\frac{1}{3} = \frac{5}{15}$
- $\frac{6}{15} + \frac{5}{15} = \frac{11}{15}$

✔ Answer: $\frac{11}{15}$

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Problem 5:

$\frac{2}{5} + \frac{3}{10}$

- LCD of 5 and 10 is 10
- $\frac{2}{5} = \frac{4}{10}$
- $\frac{4}{10} + \frac{3}{10} = \frac{7}{10}$

✔ Answer: $\frac{7}{10}$

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Problem 6:

$\frac{5}{14} + \frac{3}{7}$

- LCD of 14 and 7 is 14
- $\frac{3}{7} = \frac{6}{14}$
- $\frac{5}{14} + \frac{6}{14} = \frac{11}{14}$

✔ Answer: $\frac{11}{14}$

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Problem 7:

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

- LCD of 9 and 3 is 9
- $\frac{1}{3} = \frac{3}{9}$
- $\frac{5}{9} + \frac{3}{9} = \frac{8}{9}$

✔ Answer: $\frac{8}{9}$

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Problem 8:

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

- LCD of 6 and 9 is 18
- $\frac{1}{6} = \frac{3}{18}$, $\frac{2}{9} = \frac{4}{18}$
- $\frac{3}{18} + \frac{4}{18} = \frac{7}{18}$

✔ Answer: $\frac{7}{18}$

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Problem 9:

$\frac{5}{15} + \frac{3}{5}$

- Simplify $\frac{5}{15} = \frac{1}{3}$
- LCD of 3 and 5 is 15
- $\frac{1}{3} = \frac{5}{15}$, $\frac{3}{5} = \frac{9}{15}$
- $\frac{5}{15} + \frac{9}{15} = \frac{14}{15}$

✔ Answer: $\frac{14}{15}$

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Problem 10:

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

- Simplify $\frac{3}{9} = \frac{1}{3}$
- LCD of 3 and 5 is 15
- $\frac{1}{3} = \frac{5}{15}$, $\frac{1}{5} = \frac{3}{15}$
- $\frac{5}{15} + \frac{3}{15} = \frac{8}{15}$

✔ Answer: $\frac{8}{15}$

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Problem 11:

$\frac{4}{10} + \frac{7}{20}$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- LCD of 5 and 20 is 20
- $\frac{2}{5} = \frac{8}{20}$, $\frac{7}{20}$ stays
- $\frac{8}{20} + \frac{7}{20} = \frac{15}{20} = \frac{3}{4}$ (simplified)

✔ Answer: $\frac{3}{4}$

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Problem 12:

$\frac{3}{10} + \frac{2}{15}$

- LCD of 10 and 15 is 30
- $\frac{3}{10} = \frac{9}{30}$, $\frac{2}{15} = \frac{4}{30}$
- $\frac{9}{30} + \frac{4}{30} = \frac{13}{30}$

✔ Answer: $\frac{13}{30}$

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Problem 13:

$\frac{6}{15} + \frac{3}{20}$

- Simplify $\frac{6}{15} = \frac{2}{5}$
- LCD of 5 and 20 is 20
- $\frac{2}{5} = \frac{8}{20}$, $\frac{3}{20}$ stays
- $\frac{8}{20} + \frac{3}{20} = \frac{11}{20}$

✔ Answer: $\frac{11}{20}$

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Problem 14:

$\frac{1}{4} + \frac{4}{10}$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- LCD of 4 and 5 is 20
- $\frac{1}{4} = \frac{5}{20}$, $\frac{2}{5} = \frac{8}{20}$
- $\frac{5}{20} + \frac{8}{20} = \frac{13}{20}$

✔ Answer: $\frac{13}{20}$

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Problem 15:

$\frac{3}{15} + \frac{7}{12}$

- Simplify $\frac{3}{15} = \frac{1}{5}$
- LCD of 5 and 12 is 60
- $\frac{1}{5} = \frac{12}{60}$, $\frac{7}{12} = \frac{35}{60}$
- $\frac{12}{60} + \frac{35}{60} = \frac{47}{60}$

✔ Answer: $\frac{47}{60}$

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Problem 16:

$\frac{4}{15} + \frac{3}{25}$

- LCD of 15 and 25 is 75
- $\frac{4}{15} = \frac{20}{75}$, $\frac{3}{25} = \frac{9}{75}$
- $\frac{20}{75} + \frac{9}{75} = \frac{29}{75}$

✔ Answer: $\frac{29}{75}$

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Problem 17:

$\frac{4}{10} + \frac{7}{15}$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- LCD of 5 and 15 is 15
- $\frac{2}{5} = \frac{6}{15}$, $\frac{7}{15}$ stays
- $\frac{6}{15} + \frac{7}{15} = \frac{13}{15}$

✔ Answer: $\frac{13}{15}$

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Problem 18:

$\frac{3}{10} + \frac{2}{15}$

- LCD of 10 and 15 is 30
- $\frac{3}{10} = \frac{9}{30}$, $\frac{2}{15} = \frac{4}{30}$
- $\frac{9}{30} + \frac{4}{30} = \frac{13}{30}$

✔ Answer: $\frac{13}{30}$

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## ✔ Final Answers Summary:

1) $\frac{9}{10}$
2) $\frac{25}{36}$
3) $\frac{17}{20}$
4) $\frac{11}{15}$
5) $\frac{7}{10}$
6) $\frac{11}{14}$
7) $\frac{8}{9}$
8) $\frac{7}{18}$
9) $\frac{14}{15}$
10) $\frac{8}{15}$
11) $\frac{3}{4}$
12) $\frac{13}{30}$
13) $\frac{11}{20}$
14) $\frac{13}{20}$
15) $\frac{47}{60}$
16) $\frac{29}{75}$
17) $\frac{13}{15}$
18) $\frac{13}{30}$

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💡 Tip for Students: Always check if you can simplify fractions *before* adding — it often makes finding the LCD easier! And always reduce your final answer if possible.

Let me know if you’d like this as a printable answer key or explained differently!