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Example

Subtracting 7151924\frac{7}{15} - \frac{19}{24}

Subtract two fractions with unlike denominators by finding the LCD and converting to equivalent fractions:

7151924\frac{7}{15} - \frac{19}{24}

Step 1 — Find the LCD and rewrite: Factor each denominator: 15=3515 = 3 \cdot 5 and 24=222324 = 2 \cdot 2 \cdot 2 \cdot 3. The LCD is 22235=1202 \cdot 2 \cdot 2 \cdot 3 \cdot 5 = 120. The denominator 1515 is missing three factors of 22 (i.e., 88), and the denominator 2424 is missing the factor 55. Multiply accordingly:

78158195245=5612095120\frac{7 \cdot 8}{15 \cdot 8} - \frac{19 \cdot 5}{24 \cdot 5} = \frac{56}{120} - \frac{95}{120}

Step 2 — Subtract: Combine the numerators: 5695120=39120\frac{56 - 95}{120} = \frac{-39}{120}.

Step 3 — Simplify: Both 3939 and 120120 share the factor 33. Dividing each by 33 gives 1340\frac{-13}{40}, which is written as 1340-\frac{13}{40}.

When the first numerator is smaller than the second after conversion, the result is negative. As with addition, never simplify the equivalent fractions before subtracting — that would destroy the common denominator.

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Updated 2026-04-21

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