1985 AJHSME Problems/Problem 1

Question

$\frac{3\times5}{9\times11} \times \frac{7\times9\times11}{3\times5\times7}$

$(A) 1 (B) 0 (C) 49 (D) \frac{1}{49} (E) 50$

Solution

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.

Page

Toolbox

Search

1985 AJHSME Problems/Problem 1

Question

Solution