2003 AMC 12B Problem 1

Factor $2$ from the numerator and $3$ from the denominator: $$\frac{2(1 - 2 + 3 - 4 + 5 - 6 + 7)}{3(1 - 2 + 3 - 4 + 5 - 6 + 7)}.$$ The equal parenthesized sums cancel, leaving $\dfrac{2}{3}.$ Thus, the correct answer is C.