Difference between revisions of "1985 AJHSME Problems/Problem 1"
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| − | == | + | ==Problem== |
| − | <math>\frac{3\ | + | |
| − | <math>(A) 1 (B) 0 (C) 49 (D) \frac{1}{49} (E) 50</math> | + | <math>\frac{3\times 5}{9\times 11}\times \frac{7\times 9\times 11}{3\times 5\times 7}=</math> |
| + | |||
| + | <math>\text{(A)}\ 1 \qquad \text{(B)}\ 0 \qquad \text{(C)}\ 49 \qquad \text{(D)}\ \frac{1}{49} \qquad \text{(E)}\ 50</math> | ||
==Solution== | ==Solution== | ||
Revision as of 17:04, 12 January 2009
Problem
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 
, we can rearrange the numbers in the numerator and the denominator (commutative property of multiplication) so that it looks like ![\[\frac{3}{3} \times \frac{5}{5} \times \frac{7}{7} \times \frac{9}{9} \times \frac{11}{11}\]](http://latex.artofproblemsolving.com/1/9/2/1924081e229a5fced26d3b0d923dea3636de92d5.png)
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 
, which is equal to .
Thus, 
is the answer.
