# 2009 AMC 10B Problems/Problem 2

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

## Problem

Which of the following is equal to $\dfrac{\frac{1}{3}-\frac{1}{4}}{\frac{1}{2}-\frac{1}{3}}$?

$\text{(A) } \frac 14 \qquad \text{(B) } \frac 13 \qquad \text{(C) } \frac 12 \qquad \text{(D) } \frac 23 \qquad \text{(E) } \frac 34$

## Solution

Multiplying the numerator and the denumerator by the same value does not change the value of the fraction. We can multiply both by $12$, getting $\dfrac{4-3}{6-4} = \boxed{\dfrac 12}$.

Alternately, we can directly compute that the numerator is $\dfrac 1{12}$, the denumerator is $\dfrac 16$, and hence their ratio is $\dfrac 12$.