Adding Fractions Worksheets, with different - delegacion.uc3m.es - Free Printable

To solve the given problems involving adding fractions, we need to follow these steps:

1. Find a Common Denominator: If the denominators of the fractions are different, we need to find a common denominator so that we can add the fractions easily.
2. Adjust the Fractions: Rewrite each fraction with the common denominator.
3. Add the Numerators: Add the numerators of the fractions while keeping the common denominator.
4. Simplify the Result: Simplify the resulting fraction if possible.

Let's solve each problem step by step.

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Problem 1: \( \frac{1}{2} + \frac{1}{4} \)

- Step 1: Find a common denominator.
- The denominators are 2 and 4. The least common denominator (LCD) is 4.

- Step 2: Adjust the fractions.
- \( \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \)
- \( \frac{1}{4} \) remains \( \frac{1}{4} \).

- Step 3: Add the numerators.
- \( \frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4} \)

- Step 4: Simplify (if needed).
- \( \frac{3}{4} \) is already in simplest form.

Answer: \( \frac{3}{4} \)

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Problem 2: \( \frac{1}{5} + \frac{7}{10} \)

- Step 1: Find a common denominator.
- The denominators are 5 and 10. The LCD is 10.

- Step 2: Adjust the fractions.
- \( \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10} \)
- \( \frac{7}{10} \) remains \( \frac{7}{10} \).

- Step 3: Add the numerators.
- \( \frac{2}{10} + \frac{7}{10} = \frac{2 + 7}{10} = \frac{9}{10} \)

- Step 4: Simplify (if needed).
- \( \frac{9}{10} \) is already in simplest form.

Answer: \( \frac{9}{10} \)

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Problem 3: \( \frac{1}{6} + \frac{2}{18} \)

- Step 1: Find a common denominator.
- The denominators are 6 and 18. The LCD is 18.

- Step 2: Adjust the fractions.
- \( \frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18} \)
- \( \frac{2}{18} \) remains \( \frac{2}{18} \).

- Step 3: Add the numerators.
- \( \frac{3}{18} + \frac{2}{18} = \frac{3 + 2}{18} = \frac{5}{18} \)

- Step 4: Simplify (if needed).
- \( \frac{5}{18} \) is already in simplest form.

Answer: \( \frac{5}{18} \)

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Problem 4: \( \frac{1}{4} + \frac{2}{12} \)

- Step 1: Find a common denominator.
- The denominators are 4 and 12. The LCD is 12.

- Step 2: Adjust the fractions.
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
- \( \frac{2}{12} \) 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 (if needed).
- \( \frac{5}{12} \) is already in simplest form.

Answer: \( \frac{5}{12} \)

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Problem 5: \( \frac{1}{5} + \frac{3}{15} \)

- Step 1: Find a common denominator.
- The denominators are 5 and 15. The LCD is 15.

- Step 2: Adjust the fractions.
- \( \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15} \)
- \( \frac{3}{15} \) remains \( \frac{3}{15} \).

- Step 3: Add the numerators.
- \( \frac{3}{15} + \frac{3}{15} = \frac{3 + 3}{15} = \frac{6}{15} \)

- Step 4: Simplify (if needed).
- \( \frac{6}{15} \) simplifies to \( \frac{2}{5} \) (divide numerator and denominator by 3).

Answer: \( \frac{2}{5} \)

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Problem 6: \( \frac{1}{8} + \frac{3}{4} \)

- Step 1: Find a common denominator.
- The denominators are 8 and 4. The LCD is 8.

- Step 2: Adjust the fractions.
- \( \frac{1}{8} \) remains \( \frac{1}{8} \)
- \( \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \).

- Step 3: Add the numerators.
- \( \frac{1}{8} + \frac{6}{8} = \frac{1 + 6}{8} = \frac{7}{8} \)

- Step 4: Simplify (if needed).
- \( \frac{7}{8} \) is already in simplest form.

Answer: \( \frac{7}{8} \)

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Problem 7: \( \frac{1}{2} + \frac{3}{8} \)

- Step 1: Find a common denominator.
- The denominators are 2 and 8. The LCD is 8.

- Step 2: Adjust the fractions.
- \( \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \)
- \( \frac{3}{8} \) remains \( \frac{3}{8} \).

- Step 3: Add the numerators.
- \( \frac{4}{8} + \frac{3}{8} = \frac{4 + 3}{8} = \frac{7}{8} \)

- Step 4: Simplify (if needed).
- \( \frac{7}{8} \) is already in simplest form.

Answer: \( \frac{7}{8} \)

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Problem 8: \( \frac{6}{7} + \frac{2}{21} \)

- Step 1: Find a common denominator.
- The denominators are 7 and 21. The LCD is 21.

- Step 2: Adjust the fractions.
- \( \frac{6}{7} = \frac{6 \times 3}{7 \times 3} = \frac{18}{21} \)
- \( \frac{2}{21} \) remains \( \frac{2}{21} \).

- Step 3: Add the numerators.
- \( \frac{18}{21} + \frac{2}{21} = \frac{18 + 2}{21} = \frac{20}{21} \)

- Step 4: Simplify (if needed).
- \( \frac{20}{21} \) is already in simplest form.

Answer: \( \frac{20}{21} \)

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Problem 9: \( \frac{1}{3} + \frac{2}{9} \)

- Step 1: Find a common denominator.
- The denominators are 3 and 9. The LCD is 9.

- Step 2: Adjust the fractions.
- \( \frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9} \)
- \( \frac{2}{9} \) 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 (if needed).
- \( \frac{5}{9} \) is already in simplest form.

Answer: \( \frac{5}{9} \)

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Problem 10: \( \frac{5}{16} + \frac{1}{4} \)

- Step 1: Find a common denominator.
- The denominators are 16 and 4. The LCD is 16.

- Step 2: Adjust the fractions.
- \( \frac{5}{16} \) remains \( \frac{5}{16} \)
- \( \frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16} \).

- Step 3: Add the numerators.
- \( \frac{5}{16} + \frac{4}{16} = \frac{5 + 4}{16} = \frac{9}{16} \)

- Step 4: Simplify (if needed).
- \( \frac{9}{16} \) is already in simplest form.

Answer: \( \frac{9}{16} \)

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Final Answers

1. \( \frac{3}{4} \)
2. \( \frac{9}{10} \)
3. \( \frac{5}{18} \)
4. \( \frac{5}{12} \)
5. \( \frac{2}{5} \)
6. \( \frac{7}{8} \)
7. \( \frac{7}{8} \)
8. \( \frac{20}{21} \)
9. \( \frac{5}{9} \)
10. \( \frac{9}{16} \)

\boxed{\frac{3}{4}, \frac{9}{10}, \frac{5}{18}, \frac{5}{12}, \frac{2}{5}, \frac{7}{8}, \frac{7}{8}, \frac{20}{21}, \frac{5}{9}, \frac{9}{16}}