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?

Question

Mathematics

Dakota Dunlap

27 June, 01:07

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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Answers (1)

Know the Answer?

Castillo · Answer 1

-2

Step-by-step explanation:

Firstly, let's understand that a reciprocal means the inverse of a number so that it multiplies and equals one. So the reciprocal of 2/3 is simply 3/2. This is the key fraction for discovering the mystery number. Secondly, we are given another fraction that will be added and subtracted by the same number. This fraction, 23/12, will experience a change in both its numerical quantities in order to simplify and equalize with our first given fraction of 3/2. Let's pretend X stands for the missing number. The two processes that will occur are 23 + X and 12 - X

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

23 + 1 = 24 12 - 1 = 11 - -> 24/11

23 + 2 = 25 12 - 2 = 10 - -> 25/10

24/11 - -> Can't be simplified 25/10 divided by 5 - -> 5/2 Simplest Form

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!