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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?

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TaeKwonDoIsDead

Answer:

-2

Step-by-step 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:

[tex]\frac{23+x}{12-x}=\frac{3}{2}[/tex]

Now we cross multiply and solve for x:

[tex]\frac{23+x}{12-x}=\frac{3}{2}\\2(23+x)=3(12-x)\\46+2x=36-3x\\5x=-10\\x=\frac{-10}{5}\\x=-2[/tex]

So the number is -2

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