Adding fractions with unlike denominators worksheet for math practice.

To solve the problem of adding fractions with unlike denominators, we need to follow these steps:

1. Find the Least Common Denominator (LCD): The LCD is the smallest number that is a multiple of both denominators.
2. Rewrite each fraction with the LCD as the denominator: This involves multiplying both the numerator and the denominator of each fraction by the appropriate factor to get the equivalent fraction with the LCD.
3. Add the numerators: Once the fractions have the same denominator, add the numerators and keep the denominator the same.
4. Simplify the result if possible: Reduce the fraction to its simplest form.

Let's solve each problem step by step.

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Problem 1: $\frac{1}{4} + \frac{2}{12}$

- Step 1: Find the LCD
- Denominators: 4 and 12
- LCD of 4 and 12 is 12.

- Step 2: Rewrite each fraction with the LCD
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
- $\frac{2}{12}$ remains $\frac{2}{12}$

- Step 3: Add the numerators
- $\frac{3}{12} + \frac{2}{12} = \frac{3 + 2}{12} = \frac{5}{12}$

- Step 4: Simplify
- $\frac{5}{12}$ is already in simplest form.

Answer: $\frac{5}{12}$

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Problem 2: $\frac{2}{6} + \frac{1}{2}$

- Step 1: Find the LCD
- Denominators: 6 and 2
- LCD of 6 and 2 is 6.

- Step 2: Rewrite each fraction with the LCD
- $\frac{2}{6}$ remains $\frac{2}{6}$
- $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

- Step 3: Add the numerators
- $\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}$

- Step 4: Simplify
- $\frac{5}{6}$ is already in simplest form.

Answer: $\frac{5}{6}$

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Problem 3: $\frac{1}{3} + \frac{2}{9}$

- Step 1: Find the LCD
- Denominators: 3 and 9
- LCD of 3 and 9 is 9.

- Step 2: Rewrite each fraction with the LCD
- $\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}$
- $\frac{2}{9}$ remains $\frac{2}{9}$

- Step 3: Add the numerators
- $\frac{3}{9} + \frac{2}{9} = \frac{3 + 2}{9} = \frac{5}{9}$

- Step 4: Simplify
- $\frac{5}{9}$ is already in simplest form.

Answer: $\frac{5}{9}$

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Problem 4: $\frac{5}{8} + \frac{1}{16}$

- Step 1: Find the LCD
- Denominators: 8 and 16
- LCD of 8 and 16 is 16.

- Step 2: Rewrite each fraction with the LCD
- $\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16}$
- $\frac{1}{16}$ remains $\frac{1}{16}$

- Step 3: Add the numerators
- $\frac{10}{16} + \frac{1}{16} = \frac{10 + 1}{16} = \frac{11}{16}$

- Step 4: Simplify
- $\frac{11}{16}$ is already in simplest form.

Answer: $\frac{11}{16}$

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Problem 5: $\frac{2}{9} + \frac{1}{27}$

- Step 1: Find the LCD
- Denominators: 9 and 27
- LCD of 9 and 27 is 27.

- Step 2: Rewrite each fraction with the LCD
- $\frac{2}{9} = \frac{2 \times 3}{9 \times 3} = \frac{6}{27}$
- $\frac{1}{27}$ remains $\frac{1}{27}$

- Step 3: Add the numerators
- $\frac{6}{27} + \frac{1}{27} = \frac{6 + 1}{27} = \frac{7}{27}$

- Step 4: Simplify
- $\frac{7}{27}$ is already in simplest form.

Answer: $\frac{7}{27}$

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Problem 6: $\frac{1}{3} + \frac{3}{21}$

- Step 1: Find the LCD
- Denominators: 3 and 21
- LCD of 3 and 21 is 21.

- Step 2: Rewrite each fraction with the LCD
- $\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}$
- $\frac{3}{21}$ remains $\frac{3}{21}$

- Step 3: Add the numerators
- $\frac{7}{21} + \frac{3}{21} = \frac{7 + 3}{21} = \frac{10}{21}$

- Step 4: Simplify
- $\frac{10}{21}$ is already in simplest form.

Answer: $\frac{10}{21}$

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Problem 7: $\frac{3}{4} + \frac{1}{16}$

- Step 1: Find the LCD
- Denominators: 4 and 16
- LCD of 4 and 16 is 16.

- Step 2: Rewrite each fraction with the LCD
- $\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}$
- $\frac{1}{16}$ remains $\frac{1}{16}$

- Step 3: Add the numerators
- $\frac{12}{16} + \frac{1}{16} = \frac{12 + 1}{16} = \frac{13}{16}$

- Step 4: Simplify
- $\frac{13}{16}$ is already in simplest form.

Answer: $\frac{13}{16}$

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Problem 8: $\frac{1}{5} + \frac{1}{10}$

- Step 1: Find the LCD
- Denominators: 5 and 10
- LCD of 5 and 10 is 10.

- Step 2: Rewrite each fraction with the LCD
- $\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$
- $\frac{1}{10}$ remains $\frac{1}{10}$

- Step 3: Add the numerators
- $\frac{2}{10} + \frac{1}{10} = \frac{2 + 1}{10} = \frac{3}{10}$

- Step 4: Simplify
- $\frac{3}{10}$ is already in simplest form.

Answer: $\frac{3}{10}$

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Problem 9: $\frac{3}{7} + \frac{1}{28}$

- Step 1: Find the LCD
- Denominators: 7 and 28
- LCD of 7 and 28 is 28.

- Step 2: Rewrite each fraction with the LCD
- $\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}$
- $\frac{1}{28}$ remains $\frac{1}{28}$

- Step 3: Add the numerators
- $\frac{12}{28} + \frac{1}{28} = \frac{12 + 1}{28} = \frac{13}{28}$

- Step 4: Simplify
- $\frac{13}{28}$ is already in simplest form.

Answer: $\frac{13}{28}$

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Problem 10: $\frac{3}{5} + \frac{1}{10}$

- Step 1: Find the LCD
- Denominators: 5 and 10
- LCD of 5 and 10 is 10.

- Step 2: Rewrite each fraction with the LCD
- $\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
- $\frac{1}{10}$ remains $\frac{1}{10}$

- Step 3: Add the numerators
- $\frac{6}{10} + \frac{1}{10} = \frac{6 + 1}{10} = \frac{7}{10}$

- Step 4: Simplify
- $\frac{7}{10}$ is already in simplest form.

Answer: $\frac{7}{10}$

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Final Answers:

1. $\frac{5}{12}$
2. $\frac{5}{6}$
3. $\frac{5}{9}$
4. $\frac{11}{16}$
5. $\frac{7}{27}$
6. $\frac{10}{21}$
7. $\frac{13}{16}$
8. $\frac{3}{10}$
9. $\frac{13}{28}$
10. $\frac{7}{10}$

$$
\boxed{\frac{5}{12}, \frac{5}{6}, \frac{5}{9}, \frac{11}{16}, \frac{7}{27}, \frac{10}{21}, \frac{13}{16}, \frac{3}{10}, \frac{13}{28}, \frac{7}{10}}
$$