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# The denominator of a fraction is 1 less than 3 times the numerator. If the numerator and the denominator are both increased by 2, the fraction becomes 1 over 2. how can I find the original fraction?

You can formulate this with algebra. If the original numerator is x, then the denominator will be 3x-1. Next add two to both these, leaving us with x+2 as numerator and 3x+1 as denominator. Now rewrite these as a fraction and equate to 1/2. Now solve (x+2)/(3x+1)=1/2 2x+4 = 3x+1 x=3 You can now resubstitute into original equations for numerator and denominator, giving a fraction of 3/8.

Alexander Stronach
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