Mary purchased 3 yards of fabric from a roll containing 8 1/2 yards. How many 1/2 yards of fabric remain on the roll?    

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We are given that Mary purchased 3 yards of fabric from a roll that started with 8 1/2 yards, and we are asked to find the number of 1/2 yards remaining on the roll.

There are a couple of good approaches for a problem like this. One idea is to convert every measurement to half-yards. We choose half-yards because the answer is to be given in terms of half-yards.

Thus, Mary's purchase of 3 yards becomes a purchase of 6 half-yards. (Every yard contains 2 half yards. so 3 yards is 6 half yards.) The roll originally had 8 1/2 yards, which is 17 half-yards.

Starting with 17 half-yards and removing 6 half-yards leaves 11 half-yards.

Here's another potential way to approach this problem. Since we are removing 3 yards from the roll, we subtract 3 from 8 1/2. 8 1/2 - 3 = 5 1/2. (Subtract the like terms.) Now we can convert 5 1/2 yards to half-yards. One way to accomplish this is to realize we are adding 5 to 1/2; to add fractions, we need a common denominator, so we rewrite 5 as 10/2. Now 10/2 + 1/2 = 11/2, which is 11*1/2, or 11 half-yards, as before.

We could also write everything as decimals instead of fractions. Now 8.5 - 3 = 5.5, so there are 5.5 yards remaining. We can divide by .5 to get the number of half-yards: `5.5 -: .5=11`, as before.

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