Adding fractions with different denominators - Worksheet No.1 ... - Free Printable

Problem: Adding Fractions with Different Denominators

The task is to add fractions where the denominators are different. To solve these problems, we need to follow these steps:

1. Find a Common Denominator: The least common denominator (LCD) is the smallest number that is a multiple of all the denominators.
2. Adjust the Fractions: Rewrite each fraction with the common denominator by multiplying both the numerator and the denominator by the same number.
3. Add the Numerators: Once the denominators are the same, add the numerators and keep the denominator the same.
4. Simplify the Result: Reduce the resulting fraction to its simplest form if possible.

Let's solve each problem step by step.

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

- Both fractions already have the same denominator (4).
- Add the numerators: $1 + 1 = 2$.
- Result: $\frac{2}{4}$.
- Simplify: $\frac{2}{4} = \frac{1}{2}$.

Answer: $\frac{1}{2}$

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

- Find the LCD of 4 and 5: The LCD is 20.
- Adjust the fractions:
- $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$
- $\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}$
- Add the numerators: $\frac{5}{20} + \frac{12}{20} = \frac{17}{20}$.
- Result: $\frac{17}{20}$.

Answer: $\frac{17}{20}$

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3. $\frac{3}{7} + \frac{2}{7}$

- Both fractions already have the same denominator (7).
- Add the numerators: $3 + 2 = 5$.
- Result: $\frac{5}{7}$.

Answer: $\frac{5}{7}$

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

- Find the LCD of 4 and 5: The LCD is 20.
- Adjust the fractions:
- $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$
- $\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$
- Add the numerators: $\frac{15}{20} + \frac{4}{20} = \frac{19}{20}$.
- Result: $\frac{19}{20}$.

Answer: $\frac{19}{20}$

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5. $\frac{5}{8} + \frac{3}{8}$

- Both fractions already have the same denominator (8).
- Add the numerators: $5 + 3 = 8$.
- Result: $\frac{8}{8} = 1$.

Answer: $1$

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6. $\frac{1}{4} + \frac{1}{6}$

- Find the LCD of 4 and 6: The LCD is 12.
- Adjust the fractions:
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
- $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
- Add the numerators: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$.
- Result: $\frac{5}{12}$.

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

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7. $\frac{5}{16} + \frac{7}{16}$

- Both fractions already have the same denominator (16).
- Add the numerators: $5 + 7 = 12$.
- Result: $\frac{12}{16}$.
- Simplify: $\frac{12}{16} = \frac{3}{4}$.

Answer: $\frac{3}{4}$

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8. $\frac{1}{6} + \frac{1}{8}$

- Find the LCD of 6 and 8: The LCD is 24.
- Adjust the fractions:
- $\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}$
- $\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$
- Add the numerators: $\frac{4}{24} + \frac{3}{24} = \frac{7}{24}$.
- Result: $\frac{7}{24}$.

Answer: $\frac{7}{24}$

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9. $\frac{3}{10} + \frac{9}{10}$

- Both fractions already have the same denominator (10).
- Add the numerators: $3 + 9 = 12$.
- Result: $\frac{12}{10}$.
- Simplify: $\frac{12}{10} = \frac{6}{5}$.

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

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10. $\frac{1}{6} + \frac{3}{4}$

- Find the LCD of 6 and 4: The LCD is 12.
- Adjust the fractions:
- $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
- $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$
- Add the numerators: $\frac{2}{12} + \frac{9}{12} = \frac{11}{12}$.
- Result: $\frac{11}{12}$.

Answer: $\frac{11}{12}$

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11. $\frac{1}{3} + \frac{1}{4}$

- Find the LCD of 3 and 4: The LCD is 12.
- Adjust the fractions:
- $\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
- Add the numerators: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$.
- Result: $\frac{7}{12}$.

Answer: $\frac{7}{12}$

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12. $\frac{5}{6} + \frac{1}{8}$

- Find the LCD of 6 and 8: The LCD is 24.
- Adjust the fractions:
- $\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$
- $\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$
- Add the numerators: $\frac{20}{24} + \frac{3}{24} = \frac{23}{24}$.
- Result: $\frac{23}{24}$.

Answer: $\frac{23}{24}$

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13. $\frac{1}{4} + \frac{2}{3}$

- Find the LCD of 4 and 3: The LCD is 12.
- Adjust the fractions:
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
- $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
- Add the numerators: $\frac{3}{12} + \frac{8}{12} = \frac{11}{12}$.
- Result: $\frac{11}{12}$.

Answer: $\frac{11}{12}$

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14. $\frac{1}{9} + \frac{2}{15}$

- Find the LCD of 9 and 15: The LCD is 45.
- Adjust the fractions:
- $\frac{1}{9} = \frac{1 \times 5}{9 \times 5} = \frac{5}{45}$
- $\frac{2}{15} = \frac{2 \times 3}{15 \times 3} = \frac{6}{45}$
- Add the numerators: $\frac{5}{45} + \frac{6}{45} = \frac{11}{45}$.
- Result: $\frac{11}{45}$.

Answer: $\frac{11}{45}$

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15. $\frac{1}{4} + \frac{1}{5}$

- Find the LCD of 4 and 5: The LCD is 20.
- Adjust the fractions:
- $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$
- $\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$
- Add the numerators: $\frac{5}{20} + \frac{4}{20} = \frac{9}{20}$.
- Result: $\frac{9}{20}$.

Answer: $\frac{9}{20}$

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Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ \frac{1}{2} \\
2. & \ \frac{17}{20} \\
3. & \ \frac{5}{7} \\
4. & \ \frac{19}{20} \\
5. & \ 1 \\
6. & \ \frac{5}{12} \\
7. & \ \frac{3}{4} \\
8. & \ \frac{7}{24} \\
9. & \ \frac{6}{5} \\
10. & \ \frac{11}{12} \\
11. & \ \frac{7}{12} \\
12. & \ \frac{23}{24} \\
13. & \ \frac{11}{12} \\
14. & \ \frac{11}{45} \\
15. & \ \frac{9}{20}
\end{aligned}
}
\]