# Guess a fraction

Tom was asked to guess a fraction. The sum of 1/2 the numerator and 1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the fraction becomes 1/3. What is the fraction that Tom was asked to guess? (Leave your answer in simplest form)

Result

d =  72
n =  12
f =  0.167

#### Solution:

n/2+d/3=30
n= (d-36)/3

2d+3n = 180
d-3n = 36

d = 72
n = 12

Calculated by our linear equations calculator.
$f=n/d=12/72 \doteq \dfrac{ 1 }{ 6 } \doteq 0.1667 \doteq 0.167$

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