### Brain Teasers

# Fractional Operations

A fraction becomes 2/3 when 1 is added to both its numerator and denominator and it becomes 1/2 when 1 is subtracted from both the numerator and denominator.

Find the fraction.

Find the fraction.

### Answer

The original fraction = 3/5.You can solve this fairly quickly by trial-and-error, or you can set up two equations using the information given:

1) (x+1)/(y+1) = 2/3

2) (x-1)/(y-1) = 1/2

where x is the original numerator and y is the original denominator.

First isolate x in equation 1:

x+1 = 2/3*(y+1)

x = 2/3*y-1/3

Plug this value for x into equation 2:

2/3*y - 4/3 = 1/2*(y-1)

Solve this for y to get y = 5.

Plug this value for y into equation 2 to get x = 3.

Therefore the original fraction is 3/5.

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