Please answer this math problem:
I am a fraction that is greater than 1 but less than 2. The sum of my numerator and denominator is 11. My denominator subtracted from my numerator is 1. What fraction am I?



Hi Anthony,

Here are two ways to approach this problem.

method 1 - algebaric

let n = numerator and d=denominator
The sum of my numerator and denominator is 11: n+d=11 (equation 1)
My denominator subtracted from my numerator is 1: n-d=1 (equation 2)
Add equation 1 and 2 together: 2n=12, or n=6
sub into equation 1: d=5
therefore, the fraction is 6/5
check: 6+5=11 and 6-5=1 and the fraction is between 1 and 2

(notice that the first line of the problem is not actually needed to solve the problem)

method 2 - numerical

possible combinations to get 11 are:
2 and 9, 3 and 8, 4 and 7, 5 and 6

since greater than 1 (less than 2 is not actually needed), the bigger is the numerator checking for subtraction to get 1: 9-2, 8-3, 7-4 don't work

6-5=1 does work therefore the fraction is 6/5

Paul
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