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?

-2

Step-by-step explanation:

After trying possible numbers, such as 1 or 2, this happens.

However, these answers are not suitable to equal the fraction 3/2.

Now let's try a different route. Search for possible GCF's of 3 and 2, then create fractions with them.

Example:

6/4, 9/6, 12/8, 15/10, 18/12, etc.

The number I found that matched the requirements was 21/14.

Here's how we find and solve this problem.

Let's replace X with -2.

23 + (-2) = 21 12 – (-2) = 14 --> 21/14

21/14 can be divided by 7 to equal 3/2.

This is also the same fraction as the original reciprocal. The fraction was created by adding and subtracting the same number from the numerator and the denominator. Therefore, we can claim that the number is in fact negative two!

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4