To add or subtract fractions with different denominators, we must first make the denominators the same. We do this by finding the Lowest Common Multiple (LCM) of the denominators.

Step 1: Find the LCM of the denominators.

Step 2: Rewrite each fraction as an equivalent fraction with the LCM as the new denominator.

Step 3: Add the numerators (top numbers) while keeping the denominator the same.

Step 4: Simplify the answer if possible.

Worked Example 1

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

Solution

• The denominators are 2 and 4. The LCM of 2 and 4 is 4.
• Rewrite ½ with denominator 4: $\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
• Now add: $\frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4}$

Therefore, $\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$

Worked Example 2

$\frac{2}{5} + \frac{3}{9} = ?$

Solution

• The denominators are 5 and 9. The LCM of 5 and 9 is 45.
• Rewrite each fraction with denominator 45: $\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}$ $\frac{3}{9} = \frac{3 \times 5}{9 \times 5} = \frac{15}{45}$
• Add the numerators: $\frac{18}{45} + \frac{15}{45} = \frac{33}{45}$
• Simplify: Divide both by 3: $\frac{33 \div 3}{45 \div 3} = \frac{11}{15}$

Therefore, $\frac{2}{5} + \frac{3}{9} = \frac{11}{15}$

Step 1: Find the LCM of the denominators.

Step 2: Rewrite each fraction as an equivalent fraction with the LCM as the new denominator.

Step 3: Subtract the numerators while keeping the denominator the same.

Step 4: Simplify the answer if possible.

Worked Example 3

$\frac{3}{5} - \frac{1}{4} = ?$

Solution

• The denominators are 5 and 4. The LCM of 5 and 4 is 20.
• Rewrite each fraction with denominator 20: $\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}$ $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$
• Subtract the numerators: $\frac{12}{20} - \frac{5}{20} = \frac{12-5}{20} = \frac{7}{20}$

Therefore, $\frac{3}{5} - \frac{1}{4} = \frac{7}{20}$

Worked Example 4

$\frac{5}{6} - \frac{4}{7} = ?$

Solution

• The denominators are 6 and 7. The LCM of 6 and 7 is 42.
• Rewrite each fraction with denominator 42: $\frac{5}{6} = \frac{5 \times 7}{6 \times 7} = \frac{35}{42}$ $\frac{4}{7} = \frac{4 \times 6}{7 \times 6} = \frac{24}{42}$
• Subtract the numerators: $\frac{35}{42} - \frac{24}{42} = \frac{35-24}{42} = \frac{11}{42}$

Therefore, $\frac{5}{6} - \frac{4}{7} = \frac{11}{42}$

• Always find the LCM of the denominators first
• When rewriting equivalent fractions, multiply both numerator and denominator by the same number
• Never add or subtract denominators — only add or subtract the numerators
• Always simplify your final answer if possible

In Tanzania, farmers often need to add or subtract fractions when mixing fertilizers or calculating harvest yields. For example, a farmer at the Mwanza market has ½ bag of rice and buys another ¼ bag. To find the total, the farmer adds ½ + ¼ = ¾ bag. Similarly, when a shopkeeper at Kariakoo measures out portions of sugar or flour, they use these skills to ensure accurate quantities when selling in smaller amounts.