Fraction addition worksheet with unlike denominators for practice.

To solve the given problems involving the addition of fractions with unlike denominators, 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 both denominators.
2. Adjust the Fractions: Rewrite each fraction with the common denominator by multiplying both the numerator and the denominator by the necessary factor.
3. Add the Numerators: Add the numerators of the adjusted fractions while keeping the common denominator.
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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Problem 1: \( \frac{5}{6} + \frac{4}{5} \)

- Step 1: Find the LCD
- Denominators: 6 and 5
- LCD = 30

- Step 2: Adjust the fractions
- \( \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \)
- \( \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \)

- Step 3: Add the numerators
- \( \frac{25}{30} + \frac{24}{30} = \frac{25 + 24}{30} = \frac{49}{30} \)

- Step 4: Simplify
- \( \frac{49}{30} \) is already in simplest form.

Answer: \( \frac{49}{30} \)

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Problem 2: \( \frac{5}{8} + \frac{4}{6} \)

- Step 1: Find the LCD
- Denominators: 8 and 6
- LCD = 24

- Step 2: Adjust the fractions
- \( \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \)
- \( \frac{4}{6} = \frac{4 \times 4}{6 \times 4} = \frac{16}{24} \)

- Step 3: Add the numerators
- \( \frac{15}{24} + \frac{16}{24} = \frac{15 + 16}{24} = \frac{31}{24} \)

- Step 4: Simplify
- \( \frac{31}{24} \) is already in simplest form.

Answer: \( \frac{31}{24} \)

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Problem 3: \( \frac{5}{6} + \frac{4}{9} \)

- Step 1: Find the LCD
- Denominators: 6 and 9
- LCD = 18

- Step 2: Adjust the fractions
- \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \)
- \( \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} \)

- Step 3: Add the numerators
- \( \frac{15}{18} + \frac{8}{18} = \frac{15 + 8}{18} = \frac{23}{18} \)

- Step 4: Simplify
- \( \frac{23}{18} \) is already in simplest form.

Answer: \( \frac{23}{18} \)

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Problem 4: \( \frac{1}{4} + \frac{2}{7} \)

- Step 1: Find the LCD
- Denominators: 4 and 7
- LCD = 28

- Step 2: Adjust the fractions
- \( \frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28} \)
- \( \frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28} \)

- Step 3: Add the numerators
- \( \frac{7}{28} + \frac{8}{28} = \frac{7 + 8}{28} = \frac{15}{28} \)

- Step 4: Simplify
- \( \frac{15}{28} \) is already in simplest form.

Answer: \( \frac{15}{28} \)

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Problem 5: \( \frac{7}{7} + \frac{4}{6} \)

- Step 1: Simplify \( \frac{7}{7} \)
- \( \frac{7}{7} = 1 \)

- Step 2: Simplify \( \frac{4}{6} \)
- \( \frac{4}{6} = \frac{2}{3} \)

- Step 3: Add the fractions
- \( 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \)

Answer: \( \frac{5}{3} \)

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Problem 6: \( \frac{5}{4} + \frac{3}{9} \)

- Step 1: Simplify \( \frac{3}{9} \)
- \( \frac{3}{9} = \frac{1}{3} \)

- Step 2: Find the LCD
- Denominators: 4 and 3
- LCD = 12

- Step 3: Adjust the fractions
- \( \frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12} \)
- \( \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)

- Step 4: Add the numerators
- \( \frac{15}{12} + \frac{4}{12} = \frac{15 + 4}{12} = \frac{19}{12} \)

Answer: \( \frac{19}{12} \)

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Problem 7: \( \frac{9}{4} + \frac{9}{8} \)

- Step 1: Find the LCD
- Denominators: 4 and 8
- LCD = 8

- Step 2: Adjust the fractions
- \( \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \)
- \( \frac{9}{8} = \frac{9}{8} \)

- Step 3: Add the numerators
- \( \frac{18}{8} + \frac{9}{8} = \frac{18 + 9}{8} = \frac{27}{8} \)

Answer: \( \frac{27}{8} \)

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Problem 8: \( \frac{6}{2} + \frac{2}{4} \)

- Step 1: Simplify \( \frac{6}{2} \)
- \( \frac{6}{2} = 3 \)

- Step 2: Simplify \( \frac{2}{4} \)
- \( \frac{2}{4} = \frac{1}{2} \)

- Step 3: Add the fractions
- \( 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \)

Answer: \( \frac{7}{2} \)

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Problem 9: \( \frac{5}{5} + \frac{7}{3} \)

- Step 1: Simplify \( \frac{5}{5} \)
- \( \frac{5}{5} = 1 \)

- Step 2: Add the fractions
- \( 1 + \frac{7}{3} = \frac{3}{3} + \frac{7}{3} = \frac{10}{3} \)

Answer: \( \frac{10}{3} \)

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Problem 10: \( \frac{1}{4} + \frac{1}{3} \)

- Step 1: Find the LCD
- Denominators: 4 and 3
- LCD = 12

- Step 2: Adjust the fractions
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
- \( \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)

- Step 3: Add the numerators
- \( \frac{3}{12} + \frac{4}{12} = \frac{3 + 4}{12} = \frac{7}{12} \)

Answer: \( \frac{7}{12} \)

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Problem 11: \( \frac{8}{6} + \frac{3}{8} \)

- Step 1: Simplify \( \frac{8}{6} \)
- \( \frac{8}{6} = \frac{4}{3} \)

- Step 2: Find the LCD
- Denominators: 3 and 8
- LCD = 24

- Step 3: Adjust the fractions
- \( \frac{4}{3} = \frac{4 \times 8}{3 \times 8} = \frac{32}{24} \)
- \( \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \)

- Step 4: Add the numerators
- \( \frac{32}{24} + \frac{9}{24} = \frac{32 + 9}{24} = \frac{41}{24} \)

Answer: \( \frac{41}{24} \)

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Problem 12: \( \frac{5}{7} + \frac{5}{5} \)

- Step 1: Simplify \( \frac{5}{5} \)
- \( \frac{5}{5} = 1 \)

- Step 2: Add the fractions
- \( \frac{5}{7} + 1 = \frac{5}{7} + \frac{7}{7} = \frac{12}{7} \)

Answer: \( \frac{12}{7} \)

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Problem 13: \( \frac{15}{11} + \frac{4}{4} \)

- Step 1: Simplify \( \frac{4}{4} \)
- \( \frac{4}{4} = 1 \)

- Step 2: Add the fractions
- \( \frac{15}{11} + 1 = \frac{15}{11} + \frac{11}{11} = \frac{26}{11} \)

Answer: \( \frac{26}{11} \)

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Problem 14: \( \frac{5}{6} + \frac{1}{9} \)

- Step 1: Find the LCD
- Denominators: 6 and 9
- LCD = 18

- Step 2: Adjust the fractions
- \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \)
- \( \frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18} \)

- Step 3: Add the numerators
- \( \frac{15}{18} + \frac{2}{18} = \frac{15 + 2}{18} = \frac{17}{18} \)

Answer: \( \frac{17}{18} \)

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Problem 15: \( \frac{5}{6} + \frac{2}{8} \)

- Step 1: Simplify \( \frac{2}{8} \)
- \( \frac{2}{8} = \frac{1}{4} \)

- Step 2: Find the LCD
- Denominators: 6 and 4
- LCD = 12

- Step 3: Adjust the fractions
- \( \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \)
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)

- Step 4: Add the numerators
- \( \frac{10}{12} + \frac{3}{12} = \frac{10 + 3}{12} = \frac{13}{12} \)

Answer: \( \frac{13}{12} \)

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Problem 16: \( \frac{5}{6} + \frac{13}{9} \)

- Step 1: Find the LCD
- Denominators: 6 and 9
- LCD = 18

- Step 2: Adjust the fractions
- \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \)
- \( \frac{13}{9} = \frac{13 \times 2}{9 \times 2} = \frac{26}{18} \)

- Step 3: Add the numerators
- \( \frac{15}{18} + \frac{26}{18} = \frac{15 + 26}{18} = \frac{41}{18} \)

Answer: \( \frac{41}{18} \)

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Problem 17: \( \frac{11}{12} + \frac{11}{4} \)

- Step 1: Find the LCD
- Denominators: 12 and 4
- LCD = 12

- Step 2: Adjust the fractions
- \( \frac{11}{12} = \frac{11}{12} \)
- \( \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \)

- Step 3: Add the numerators
- \( \frac{11}{12} + \frac{33}{12} = \frac{11 + 33}{12} = \frac{44}{12} \)

- Step 4: Simplify
- \( \frac{44}{12} = \frac{11}{3} \)

Answer: \( \frac{11}{3} \)

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Problem 18: \( \frac{5}{6} + \frac{4}{36} \)

- Step 1: Simplify \( \frac{4}{36} \)
- \( \frac{4}{36} = \frac{1}{9} \)

- Step 2: Find the LCD
- Denominators: 6 and 9
- LCD = 18

- Step 3: Adjust the fractions
- \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \)
- \( \frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18} \)

- Step 4: Add the numerators
- \( \frac{15}{18} + \frac{2}{18} = \frac{15 + 2}{18} = \frac{17}{18} \)

Answer: \( \frac{17}{18} \)

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Problem 19: \( \frac{3}{5} + \frac{6}{15} \)

- Step 1: Simplify \( \frac{6}{15} \)
- \( \frac{6}{15} = \frac{2}{5} \)

- Step 2: Add the fractions
- \( \frac{3}{5} + \frac{2}{5} = \frac{3 + 2}{5} = \frac{5}{5} = 1 \)

Answer: \( 1 \)

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Problem 20: \( \frac{5}{6} + \frac{14}{13} \)

- Step 1: Find the LCD
- Denominators: 6 and 13
- LCD = 78

- Step 2: Adjust the fractions
- \( \frac{5}{6} = \frac{5 \times 13}{6 \times 13} = \frac{65}{78} \)
- \( \frac{14}{13} = \frac{14 \times 6}{13 \times 6} = \frac{84}{78} \)

- Step 3: Add the numerators
- \( \frac{65}{78} + \frac{84}{78} = \frac{65 + 84}{78} = \frac{149}{78} \)

Answer: \( \frac{149}{78} \)

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Problem 21: \( \frac{5}{15} + \frac{11}{3} \)

- Step 1: Simplify \( \frac{5}{15} \)
- \( \frac{5}{15} = \frac{1}{3} \)

- Step 2: Add the fractions
- \( \frac{1}{3} + \frac{11}{3} = \frac{1 + 11}{3} = \frac{12}{3} = 4 \)

Answer: \( 4 \)

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Problem 22: \( \frac{2}{4} + \frac{4}{16} \)

- Step 1: Simplify \( \frac{2}{4} \)
- \( \frac{2}{4} = \frac{1}{2} \)

- Step 2: Simplify \( \frac{4}{16} \)
- \( \frac{4}{16} = \frac{1}{4} \)

- Step 3: Find the LCD
- Denominators: 2 and 4
- LCD = 4

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

- Step 5: Add the numerators
- \( \frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4} \)

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

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Final Answers

\[
\boxed{
\begin{aligned}
1. & \frac{49}{30} \\
2. & \frac{31}{24} \\
3. & \frac{23}{18} \\
4. & \frac{15}{28} \\
5. & \frac{5}{3} \\
6. & \frac{19}{12} \\
7. & \frac{27}{8} \\
8. & \frac{7}{2} \\
9. & \frac{10}{3} \\
10. & \frac{7}{12} \\
11. & \frac{41}{24} \\
12. & \frac{12}{7} \\
13. & \frac{26}{11} \\
14. & \frac{17}{18} \\
15. & \frac{13}{12} \\
16. & \frac{41}{18} \\
17. & \frac{11}{3} \\
18. & \frac{17}{18} \\
19. & 1 \\
20. & \frac{149}{78} \\
21. & 4 \\
22. & \frac{3}{4}
\end{aligned}
}
\]