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 15 is missing three factors of 2 (i.e., 8), and the denominator 24 is missing the factor 5. 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 39 and 120 share the factor 3. Dividing each by 3 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 2026-06-21

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