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Difference between revisions of "1986 AJHSME Problems/Problem 2"
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But which one is it? <math>\frac{1}{3}</math>? or <math>\frac{2}{5}</math>?
 
But which one is it? <math>\frac{1}{3}</math>? or <math>\frac{2}{5}</math>?
−
We see that <math>\frac{1}{3} = \frac{5}{15}</math>, and <math>\frac{2}{5} = \frac{6}{15}</math>, so obviously <math>\frac{2}{5}</math> is larger.
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We see that <math>\frac{1}{3} = \frac{5}{15}</math>, and <math>\frac{2}{5} = \frac{6}{15}</math>, so obviously <math>\frac{1}{3}</math> is smaller.
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 +
<math>\boxed{\text{A}}</math>
  
 
==See Also==
 
==See Also==
  
 
[[1986 AJHSME Problems]]
 
[[1986 AJHSME Problems]]

Revision as of 20:41, 20 January 2009

Problem

Which of the following numbers has the largest reciprocal?

$\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{2}{5} \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 1986$

Solution

For positive numbers, the larger the number, the smaller it's reciprocal. Likewise, smaller numbers have larger reciprocals.

Thus, all we have to do is find the smallest number.

But which one is it? $\frac{1}{3}$? or $\frac{2}{5}$? We see that $\frac{1}{3} = \frac{5}{15}$, and $\frac{2}{5} = \frac{6}{15}$, so obviously $\frac{1}{3}$ is smaller.

$\boxed{\text{A}}$

See Also

1986 AJHSME Problems

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