Algebraic Fractions worksheet with practice questions and a video tutorial link.

Let’s solve each part step by step. We’re adding or subtracting algebraic fractions — just like regular fractions, but with letters (variables). The key is to find a common denominator, then combine the numerators.

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(a)
$\frac{x}{3} + \frac{x}{5}$

Common denominator of 3 and 5 is 15.

Convert:
- $\frac{x}{3} = \frac{5x}{15}$
- $\frac{x}{5} = \frac{3x}{15}$

Add:
$\frac{5x}{15} + \frac{3x}{15} = \frac{8x}{15}$

✔ Final: $\frac{8x}{15}$

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(b)
$\frac{c}{2} + \frac{c}{7}$

Common denominator of 2 and 7 is 14.

Convert:
- $\frac{c}{2} = \frac{7c}{14}$
- $\frac{c}{7} = \frac{2c}{14}$

Add:
$\frac{7c}{14} + \frac{2c}{14} = \frac{9c}{14}$

✔ Final: $\frac{9c}{14}$

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(c)
$\frac{w}{3} + \frac{w}{9}$

Common denominator of 3 and 9 is 9.

Convert:
- $\frac{w}{3} = \frac{3w}{9}$
- $\frac{w}{9}$ stays same

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

✔ Final: $\frac{4w}{9}$

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(d)
$\frac{x}{2} - \frac{x}{3}$

Common denominator of 2 and 3 is 6.

Convert:
- $\frac{x}{2} = \frac{3x}{6}$
- $\frac{x}{3} = \frac{2x}{6}$

Subtract:
$\frac{3x}{6} - \frac{2x}{6} = \frac{x}{6}$

✔ Final: $\frac{x}{6}$

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(e)
$\frac{a}{5} - \frac{a}{9}$

Common denominator of 5 and 9 is 45.

Convert:
- $\frac{a}{5} = \frac{9a}{45}$
- $\frac{a}{9} = \frac{5a}{45}$

Subtract:
$\frac{9a}{45} - \frac{5a}{45} = \frac{4a}{45}$

✔ Final: $\frac{4a}{45}$

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(f)
$\frac{m}{2} - \frac{m}{8}$

Common denominator of 2 and 8 is 8.

Convert:
- $\frac{m}{2} = \frac{4m}{8}$
- $\frac{m}{8}$ stays same

Subtract:
$\frac{4m}{8} - \frac{m}{8} = \frac{3m}{8}$

✔ Final: $\frac{3m}{8}$

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(g)
$\frac{m}{3} + \frac{2m}{7}$

Common denominator of 3 and 7 is 21.

Convert:
- $\frac{m}{3} = \frac{7m}{21}$
- $\frac{2m}{7} = \frac{6m}{21}$

Add:
$\frac{7m}{21} + \frac{6m}{21} = \frac{13m}{21}$

✔ Final: $\frac{13m}{21}$

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(h)
$\frac{3x}{5} + \frac{x}{2}$

Common denominator of 5 and 2 is 10.

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

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

✔ Final: $\frac{11x}{10}$

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(i)
$\frac{3c}{4} + \frac{5c}{9}$

Common denominator of 4 and 9 is 36.

Convert:
- $\frac{3c}{4} = \frac{27c}{36}$
- $\frac{5c}{9} = \frac{20c}{36}$

Add:
$\frac{27c}{36} + \frac{20c}{36} = \frac{47c}{36}$

✔ Final: $\frac{47c}{36}$

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(j)
$\frac{m}{2} - \frac{2m}{5}$

Common denominator of 2 and 5 is 10.

Convert:
- $\frac{m}{2} = \frac{5m}{10}$
- $\frac{2m}{5} = \frac{4m}{10}$

Subtract:
$\frac{5m}{10} - \frac{4m}{10} = \frac{m}{10}$

✔ Final: $\frac{m}{10}$

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(k)
$\frac{3n}{4} - \frac{5n}{9}$

Common denominator of 4 and 9 is 36.

Convert:
- $\frac{3n}{4} = \frac{27n}{36}$
- $\frac{5n}{9} = \frac{20n}{36}$

Subtract:
$\frac{27n}{36} - \frac{20n}{36} = \frac{7n}{36}$

✔ Final: $\frac{7n}{36}$

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(l)
$\frac{7h}{8} - \frac{5h}{12}$

Common denominator of 8 and 12 is 24.

Convert:
- $\frac{7h}{8} = \frac{21h}{24}$
- $\frac{5h}{12} = \frac{10h}{24}$

Subtract:
$\frac{21h}{24} - \frac{10h}{24} = \frac{11h}{24}$

✔ Final: $\frac{11h}{24}$

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Final Answer:

(a) $\frac{8x}{15}$
(b) $\frac{9c}{14}$
(c) $\frac{4w}{9}$
(d) $\frac{x}{6}$
(e) $\frac{4a}{45}$
(f) $\frac{3m}{8}$
(g) $\frac{13m}{21}$
(h) $\frac{11x}{10}$
(i) $\frac{47c}{36}$
(j) $\frac{m}{10}$
(k) $\frac{7n}{36}$
(l) $\frac{11h}{24}$