Answer: [tex]\frac{12}{30}[/tex]
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 [tex]\frac{d-18}{d}[/tex] where d cannot be zero. This fraction is equivalent to [tex]\frac{2}{5}[/tex] so we'll set the two fractions equal to one another and solve for d.
[tex]\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\\\\[/tex]
The denominator is d = 30 and the numerator is d-18 = 30-18 = 12.
The unreduced fraction Eric is thinking of is [tex]\Large \frac{12}{30}[/tex].
To verify the answer, notice that:
[tex]\frac{12}{30} = \frac{6*2}{6*5} = \frac{2}{5}[/tex]
