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

Answer:

The number is -2

Step-by-step 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

$\frac{23+x}{12-x}=\frac{3}{2}$

Solve for x

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

step 3

verify

$\frac{23+x}{12-x}$

substitute x=-2

$\frac{23-2}{12+2}$

$\frac{21}{14}$

Simplify

$\frac{3}{2}$ ----> is ok

therefore

The number is -2