SOLUTION: Fractions in the form a/b are created such that a and b are positive whole numbers and a + b = 333. How many such fractions are less than one and cannot be simplified? (Cannot be

Question 1133316: Fractions in the form a/b are created such that a and b are positive whole numbers and a + b =
333. How many such fractions are less than one and cannot be simplified?
(Cannot be simplified means that the numerator and denominator have no common factor)
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

(1) For the fraction to be less than 1, the numerator a has to be less than the denominator b. Since a+b=333, that means the maximum value for a is 166.

(2) 333 = 3*3*37. If 3 and/or 37 are factors of a, then they will be factors of b also, which means the fraction a/b can be simplified.

So to find the answer to the problem, take the 166 possible values for a, throw out the multiples of 3 and the multiples of 37; then, if there are any, bring back in the numbers that are multiples of both 3 and 37 (because you will have thrown them out twice).
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