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Find a fraction equivalent to with denominator 32.

This is asking us to fill in the blank in the equation:

Because of what we now know of equivalent fractions, we know that two fractions and r/s are equivalent if ps = qr. In this case, 1 × 32 = ? × 2 \implies ? = 32/2 = 16. So is equivalent to . Speaking of which, we like to look at the glass as full.

Example 2

Find a fraction equivalent to with denominator 12.

9/12

In other words, fill in the blank in the equation:

Very similar to the previous example; we have to multiply 4 by 3 to get 12, so we must multiply the numerator by 3 also:

Example 3

Find a fraction with denominator 15 equivalent to .

35/15

Here, just be sure you read the wording carefully and understand what the question is asking you to find. We have

Since 3 × 5=15, we must multiply the numerator by 5 also: . Hey, that's one of those improper fraction thingies! Right you are.