Question

1. 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

The number is -2

Explanation:

step 1

Find the reciprocal of 2/3

Remember that when multiply a number by its reciprocal, the result is 1

so

The reciprocal of 2/3 is 3/2

step 2

Let

x-----> the number added to the numerator and denominator

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

Solve for x

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

step 3

verify

`(23+x)/(12-x)`

substitute x=-2

`(23-2)/(12+2)`

`(21)/(14)`

Simplify

`(3)/(2)` ----> is ok

therefore

The number is -2