Adrians recipe for cranberry relish calls for 1 3/4 cups of sugar. he wants to use 1/2 that amount. how much sugar should he use?

The best way to look at it is to split into 2 numbwrs:
1 + 3/4

So now we can say we really want half of both the numbers since both the numbers make up the original number
1/2 +(3/4)/2

So we know easily that half of 1 is 1/2

to divide any number by another number is the same as multiplying by the numbers reciprocal. So we could change the 2nd part to :
(3/4) * (1/2)

So now we multiply the numerator and denominator and get:
3/8

add in the first part of our number again:
1/2 + 3/8

get common denominator:
4/8 + 3/8

And our answer is 7/8