Final answer:
To find the fraction equivalent to 2/5 where the numerator is 18 less than the denominator, set up an equation and solve for the value of the denominator. The fraction is (denominator - 18) / denominator, which simplifies to 12/30.
Step-by-step explanation:
To find the fraction equivalent to 2/5 where the numerator is 18 less than the denominator, we can set up an equation. Let the denominator be x, then the numerator is x - 18.
We can write the fraction as (x - 18) / x.
We know that this fraction is equivalent to 2/5, so we can set up the equation (x - 18) / x = 2/5.
To solve this equation, we can cross multiply: 5(x - 18) = 2x.
Distributing, we get 5x - 90 = 2x. Subtracting 2x from both sides, we have 3x - 90 = 0.
Adding 90 to both sides, we get 3x = 90. Dividing both sides by 3, we find that x = 30.
Therefore, the fraction that is equivalent to 2/5 and has a numerator 18 less than the denominator is (30 - 18) / 30 = 12/30.