Question

If the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting fraction is equivalent to the reciprocal of 2/3 . What is the number?

Answer 1

-2

Explanation:

The reciprocal of 2/3 is just the "flipped" fraction. Hence, it is

3/2

Now, in 23/12,

23 is the numerator

12 is the denominator

Let the number to add/subtract be "x", so we can say:

23 + x [for numerator]

12 - x [for denominator]

This should be equal to 3/2

THus we have:

`(23+x)/(12-x)=(3)/(2)`

Now we cross multiply and solve for x:

`(23+x)/(12-x)=(3)/(2)\\2(23+x)=3(12-x)\\46+2x=36-3x\\5x=-10\\x=(-10)/(5)\\x=-2`

So the number is -2