Question

Eric has a riddle: "I am thinking of a fraction that is equivalent to

Answer 1

Answer:  $\frac{12}{30}$

This is the same as writing 12/30

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Explanation:

d = value of the denominator

d-18 = value of the numerator, since it's 18 less than the denominator

The fraction Eric is thinking of is $\frac{d-18}{d}$ where d cannot be zero. This fraction is equivalent to $\frac{2}{5}$ so we'll set the two fractions equal to one another and solve for d.

$\frac{d-18}{d} = \frac{2}{5}\\\\5(d-18) = 2d \ \ \text{ ... cross multiply}\\\\5d-90 = 2d\\\\5d-2d = 90\\\\3d = 90\\\\d = \frac{90}{3}\\\\d = 30$

The denominator is d = 30 and the numerator is d-18 = 30-18 = 12.

The unreduced fraction Eric is thinking of is $\Large \frac{12}{30}$.

To verify the answer, notice that:

$\frac{12}{30} = \frac{6*2}{6*5} = \frac{2}{5}$