Subtracting Fractions with Unlike Denominators Math Example 2

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Example 2

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A runner completed 78\frac{7}{8} of a race, then stopped. If the race is 11 km long, what fraction of the race is left? If another runner has already finished 25\frac{2}{5} of the remaining distance, how much of the total race has that runner covered?

Solution

  1. 1
    Find the remaining fraction of the race after the first runner: 1−78=88−78=181 - \frac{7}{8} = \frac{8}{8} - \frac{7}{8} = \frac{1}{8}
  2. 2
    The second runner covers 25\frac{2}{5} of the remaining 18\frac{1}{8}. Multiply: 25×18=240\frac{2}{5} \times \frac{1}{8} = \frac{2}{40}
  3. 3
    Simplify the result: 240=120 of the total race\frac{2}{40} = \frac{1}{20} \text{ of the total race}

Answer

120 of the total race\frac{1}{20} \text{ of the total race}
This two-step problem combines unlike-denominator subtraction (to find the remainder) with fraction multiplication (to find a fraction of the remainder). Reading multi-step word problems carefully is essential.

About Subtracting Fractions with Unlike Denominators

Subtracting fractions with different denominators by first rewriting them with a common denominator, then subtracting numerators.

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More Subtracting Fractions with Unlike Denominators Examples

Example 1 easy

Subtract [formula].

Example 3 easy

Compute [formula].

Example 4 hard

Compute [formula].

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