GRE Math : How to find the reciprocal of a fraction

Study concepts, example questions & explanations for GRE Math

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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?

Possible Answers:

Correct answer:

Explanation:

Write their respective rates as fractions:

Carpenter A: \dpi{100} \small \frac{1\ table}{45\ hours}

Carpenter B: \dpi{100} \small \frac{1\ table}{30\ hours}

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

\dpi{100} \small \frac{2}{90}+\frac{3}{90}=\frac{5}{90}=\frac{1\ table}{18\ hours}

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 ?

Possible Answers:

None of the other answers

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

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