Adding Fractions with unlike denominators exercise - Free Printable

Let's solve each of these fraction addition problems step by step, following the instructions provided:

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Step-by-step Guide:

To add fractions with unlike denominators:
1. Find the Least Common Multiple (LCM) of the denominators.
2. Convert each fraction to an equivalent fraction with the LCM as the denominator.
3. Add the numerators and keep the common denominator.
4. Simplify the result if needed.

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Problem 1:

$$
\frac{1}{2} + \frac{2}{3}
$$

- Multiples of 2: 2, 4, 6, 8, ...
- Multiples of 3: 3, 6, 9, ...
- LCM = 6

Convert:
- $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
- $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Add:
$$
\frac{3}{6} + \frac{4}{6} = \frac{7}{6}
$$

Simplify: $\frac{7}{6} = 1\frac{1}{6}$

✔ Answer: $1\frac{1}{6}$

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Problem 2:

$$
\frac{3}{4} + \frac{1}{8}
$$

- Multiples of 4: 4, 8, 12, ...
- Multiples of 8: 8, 16, ...
- LCM = 8

Convert:
- $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$
- $\frac{1}{8} = \frac{1}{8}$

Add:
$$
\frac{6}{8} + \frac{1}{8} = \frac{7}{8}
$$

✔ Answer: $\frac{7}{8}$

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Problem 3:

$$
\frac{4}{9} + \frac{1}{3}
$$

- Multiples of 9: 9, 18, 27, ...
- Multiples of 3: 3, 6, 9, 12, ...
- LCM = 9

Convert:
- $\frac{4}{9} = \frac{4}{9}$
- $\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}$

Add:
$$
\frac{4}{9} + \frac{3}{9} = \frac{7}{9}
$$

✔ Answer: $\frac{7}{9}$

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Problem 4:

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

- Multiples of 5: 5, 10, 15, ...
- Multiples of 2: 2, 4, 6, 8, 10, ...
- LCM = 10

Convert:
- $\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
- $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$

Add:
$$
\frac{6}{10} + \frac{5}{10} = \frac{11}{10}
$$

Simplify: $\frac{11}{10} = 1\frac{1}{10}$

✔ Answer: $1\frac{1}{10}$

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Problem 5:

$$
\frac{1}{6} + \frac{2}{3}
$$

- Multiples of 6: 6, 12, ...
- Multiples of 3: 3, 6, 9, ...
- LCM = 6

Convert:
- $\frac{1}{6} = \frac{1}{6}$
- $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Add:
$$
\frac{1}{6} + \frac{4}{6} = \frac{5}{6}
$$

✔ Answer: $\frac{5}{6}$

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Problem 6:

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

- Multiples of 4: 4, 8, 12, ...
- Multiples of 6: 6, 12, 18, ...
- LCM = 12

Convert:
- $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
- $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$

Add:
$$
\frac{3}{12} + \frac{2}{12} = \frac{5}{12}
$$

✔ Answer: $\frac{5}{12}$

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Problem 7:

$$
\frac{1}{4} + \frac{1}{2}
$$

- Multiples of 4: 4, 8, ...
- Multiples of 2: 2, 4, 6, ...
- LCM = 4

Convert:
- $\frac{1}{4} = \frac{1}{4}$
- $\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$

Add:
$$
\frac{1}{4} + \frac{2}{4} = \frac{3}{4}
$$

✔ Answer: $\frac{3}{4}$

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Problem 8:

$$
\frac{3}{12} + \frac{1}{4}
$$

First simplify $\frac{3}{12} = \frac{1}{4}$

So:
$$
\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}
$$

Alternatively, use LCM method:
- Denominators: 12 and 4 → LCM = 12
- $\frac{3}{12} = \frac{3}{12}$
- $\frac{1}{4} = \frac{3}{12}$

Add:
$$
\frac{3}{12} + \frac{3}{12} = \frac{6}{12} = \frac{1}{2}
$$

✔ Answer: $\frac{1}{2}$

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✔ Final Answers:

1. $\frac{1}{2} + \frac{2}{3} = 1\frac{1}{6}$
2. $\frac{3}{4} + \frac{1}{8} = \frac{7}{8}$
3. $\frac{4}{9} + \frac{1}{3} = \frac{7}{9}$
4. $\frac{3}{5} + \frac{1}{2} = 1\frac{1}{10}$
5. $\frac{1}{6} + \frac{2}{3} = \frac{5}{6}$
6. $\frac{1}{4} + \frac{1}{6} = \frac{5}{12}$
7. $\frac{1}{4} + \frac{1}{2} = \frac{3}{4}$
8. $\frac{3}{12} + \frac{1}{4} = \frac{1}{2}$

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