Fraction Denominator Numerator Difference
A fraction is equivalent to $ \frac{5}{8}.$ Its denominator and numerator add up to $ 91.$ What is the difference between the denominator and numerator of this fraction?
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- $\frac{a}{b}$
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- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
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Solution
We obtain fractions equivalent to $ \frac{5}{8} $ by multiplying the numerator and denominator by the same number.
The sum of the numerator and denominator of $ \frac{5}{8} $ is $ 13, $ so when we multiply the numerator and denominator by the same number, the sum of the numerator and denominator is also multiplied by this same number.
Since $ 91 = 13 \times 7, $ then we should multiply the numerator and denominator both by $ 7 $ to get a fraction $$\frac{5\times 7}{8 \times 7} = \frac{35}{56}$$equivalent to $ \frac{5}{8} $ whose numerator and denominator add up to $ 91.$
The difference between the denominator and numerator in this fraction is $ 56-35=\boxed{21}.$
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