1985 AJHSME Problems/Problem 1
Problem
Solutions
Solution 1
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
Notice that each number is still there, and nothing has been changed - other than the order.
Finally, since all of the fractions are equal to one, we have , which is equal to .
Thus, is the answer.
Solution 2 (Brute force)
If you want to multiply it out, then it would be
That would be which is 1. Therefore, the answer is .
See Also
1985 AJHSME (Problems • Answer Key • Resources) | ||
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Followed by Problem 2 | |
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