# GRE Math : How to find the reciprocal of a fraction

## Example Questions

### Example Question #1 : How To Find The Reciprocal Of A Fraction

Carpenter A takes 45 hours to build a table. Carpenter B takes 30 hours. When they work together, how long will it take them to build a table?

Explanation:

Write their respective rates as fractions:

Carpenter A:

Carpenter B:

Add them together to find their combined rate.  First find a common denominator.  The smallest multiple of both 45 and 30 is 90:

Therefore, they take 18 hours to build a table together.

### Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the sum of the reciprocal of , the reciprocal of , the reciprocal of , and ?

None of the other answers

Explanation:

Begin by finding the reciprocal of , the reciprocal of , and the reciprocal of :

In order to add the four terms together, we will need to find a common denominator. Find the common denominator by multiplying the three different terms in the denominator (x, y, and z). Our common denominator will be . Put each term into terms of this common denominator:

Now, add each term together:

Look for the answer choice that matches this.

### Example Question #3 : How To Find The Reciprocal Of A Fraction

Find the reciprocal of the following expression:

Explanation:

To find the reciprocal of a rational expression--any rational expression--all you need to do is flip the numerator and the denominator.

Therefore, the correct answer is:

You can check this by multiplying the two expressions together and ensuring that your answer is .

### Example Question #4 : How To Find The Reciprocal Of A Fraction

Find the reciprocal of the following expression:

Explanation:

To find the reciprocal of any fraction, you merely need to invert the numerator and denominator.

In this case, first you have to convert the mixed number into a fraction:

Therefore, the answer is: