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Step by step please-example-1
User Ezaoutis
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5 votes

Answer:

17/25

Explanation:

You want to know which of 5/16 or 17/25 is closer to 1/2.

Comparison

For the sake of argument, let's assume that 17/25 is closer to 1/2. This means the difference from 1/2 is smaller than for 5/16:

(17/25 -1/2) < (1/2 -5/16)

We can add (5/16 + 1/2) to both sides and we get ...

17/25 + 5/16 < 1

The sum on the left is easily computed:

(17·16 +25·5)/(25·16) < 1

(272 +125)/400 < 1

397/400 < 1 . . . . . . true

Our original premise is true: 17/25 is closer to 1/2.

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Additional comment

A straightforward solution involves finding the positive difference of each number from 1/2, then comparing those differences. The attached calculator screen does that. It shows the difference of 17/25 from 1/2 is smaller than for 5/16, in agreement with the above.

Effectively, we're comparing the midpoint between the two numbers to 1/2. If it is below 1/2 (which it is), then the upper number doesn't have as great a distance from 1/2 as the lower number does.

This sort of comparison only works if the numbers are on either side of 1/2. If they are on the same side, the sign of their difference tells the tale.

Step by step please-example-1
User Michael Hillman
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