1985 AJHSME Problems/Problem 1

Problem

We could go at it by just multiplying it out, dividing, etc, but there is a much more simple method.

Noticing that multiplying and dividing by the same number is the equivalent of multiplying (or dividing) by $1$ , we can rearrange the numbers in the numerator and the denominator (commutative property of multiplication) so that it looks like $\frac{3}{3} \times \frac{5}{5} \times \frac{7}{7} \times \frac{9}{9} \times \frac{11}{11}$

Notice that each number is still there, and nothing has been changed - other than the order.

Finally, since each fraction is equal to one, we have $1\times1\times1\times1\times1$ , which is equal to $1$ .

Thus, $\boxed{\text{A}}$ is the answer.