Worksheet 1, Level 5: Practice finding common denominators with 12 fraction pairs.

Explanation:
We are given 12 fraction addition problems, all requiring a common denominator. That means for each pair of fractions, we need to find the least common denominator (LCD), rewrite both fractions with that denominator, then add the numerators.

Let’s go one by one and solve carefully.

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Question 1:
$\frac{1}{12} + \frac{5}{10}$

- Simplify $\frac{5}{10} = \frac{1}{2}$
- LCD of 12 and 2 is 12.
- $\frac{1}{12} + \frac{6}{12} = \frac{7}{12}$

✔ Answer: $\frac{7}{12}$

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Question 2:
$\frac{1}{12} + \frac{3}{11}$

- Denominators: 12 and 11 → coprime → LCD = $12 \times 11 = 132$
- $\frac{1}{12} = \frac{11}{132}$
$\frac{3}{11} = \frac{36}{132}$
- Sum: $\frac{11 + 36}{132} = \frac{47}{132}$
(47 is prime, doesn’t divide 132 → already simplified)

✔ Answer: $\frac{47}{132}$

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Question 3:
$\frac{1}{12} + \frac{2}{9}$

- LCD of 12 and 9:
Prime factors:
12 = $2^2 \cdot 3$
9 = $3^2$
→ LCD = $2^2 \cdot 3^2 = 4 \cdot 9 = 36$

- $\frac{1}{12} = \frac{3}{36}$
$\frac{2}{9} = \frac{8}{36}$
- Sum: $\frac{11}{36}$

✔ Answer: $\frac{11}{36}$

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Question 4:
$\frac{1}{12} + \frac{5}{12}$

- Same denominator → just add numerators:
$\frac{1+5}{12} = \frac{6}{12} = \frac{1}{2}$

✔ Answer: $\frac{1}{2}$

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Question 5:
$\frac{2}{5} + \frac{4}{7}$

- LCD of 5 and 7 = 35
- $\frac{2}{5} = \frac{14}{35}$
$\frac{4}{7} = \frac{20}{35}$
- Sum: $\frac{34}{35}$

✔ Answer: $\frac{34}{35}$

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Question 6:
$\frac{1}{12} + \frac{7}{20}$

- LCD of 12 and 20:
12 = $2^2 \cdot 3$, 20 = $2^2 \cdot 5$ → LCD = $2^2 \cdot 3 \cdot 5 = 60$

- $\frac{1}{12} = \frac{5}{60}$
$\frac{7}{20} = \frac{21}{60}$
- Sum: $\frac{26}{60} = \frac{13}{30}$ (divide numerator & denominator by 2)

✔ Answer: $\frac{13}{30}$

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Question 7:
$\frac{1}{12} + \frac{5}{16}$

- LCD of 12 and 16:
12 = $2^2 \cdot 3$, 16 = $2^4$ → LCD = $2^4 \cdot 3 = 16 \cdot 3 = 48$

- $\frac{1}{12} = \frac{4}{48}$
$\frac{5}{16} = \frac{15}{48}$
- Sum: $\frac{19}{48}$

✔ Answer: $\frac{19}{48}$

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Question 8:
$\frac{1}{5} + \frac{17}{24}$

- LCD of 5 and 24 = $5 \cdot 24 = 120$ (coprime)
- $\frac{1}{5} = \frac{24}{120}$
$\frac{17}{24} = \frac{85}{120}$
- Sum: $\frac{109}{120}$
(109 is prime; doesn’t divide 120)

✔ Answer: $\frac{109}{120}$

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Question 9:
$\frac{1}{12} + \frac{5}{6}$

- LCD of 12 and 6 = 12
- $\frac{5}{6} = \frac{10}{12}$
- $\frac{1}{12} + \frac{10}{12} = \frac{11}{12}$

✔ Answer: $\frac{11}{12}$

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Question 10:
$\frac{11}{12} + \frac{1}{4}$

- LCD of 12 and 4 = 12
- $\frac{1}{4} = \frac{3}{12}$
- $\frac{11}{12} + \frac{3}{12} = \frac{14}{12} = \frac{7}{6} = 1\frac{1}{6}$
But since the worksheet likely expects improper fraction or simplified fraction, $\frac{7}{6}$ is fine.

✔ Answer: $\frac{7}{6}$

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Question 11:
$\frac{1}{12} + \frac{5}{6}$
Wait — this is same as Question 9! Let’s double-check image description:
It says:
Question 11: $\frac{1}{12}$ and $\frac{5}{6}$ — yes, same as Q9.

So answer is again: $\frac{11}{12}$

✔ Answer: $\frac{11}{12}$

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Question 12:
$\frac{1}{12} + \frac{2}{3}$

- LCD of 12 and 3 = 12
- $\frac{2}{3} = \frac{8}{12}$
- $\frac{1}{12} + \frac{8}{12} = \frac{9}{12} = \frac{3}{4}$

✔ Answer: $\frac{3}{4}$

Now let’s list all final answers in order:

1. $\frac{7}{12}$
2. $\frac{47}{132}$
3. $\frac{11}{36}$
4. $\frac{1}{2}$
5. $\frac{34}{35}$
6. $\frac{13}{30}$
7. $\frac{19}{48}$
8. $\frac{109}{120}$
9. $\frac{11}{12}$
10. $\frac{7}{6}$
11. $\frac{11}{12}$
12. $\frac{3}{4}$

All checked and verified.

Final Answer:
$\frac{7}{12},\ \frac{47}{132},\ \frac{11}{36},\ \frac{1}{2},\ \frac{34}{35},\ \frac{13}{30},\ \frac{19}{48},\ \frac{109}{120},\ \frac{11}{12},\ \frac{7}{6},\ \frac{11}{12},\ \frac{3}{4}$