GRE Math : Reciprocals

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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:

$10\ hrs$

$25\ hrs$

$20\ hrs$

$18\ hrs$

$15\ hrs$

Correct answer:

$18\ hrs$

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.

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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 xyz ?

Possible Answers:

$\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

$\frac{x^2+y^2+z^2+xyz}{xyz}$

$\frac{xy+xz+yz+xyz+x^2y^2z^2}{xyz}$

None of the other answers

$\frac{x+y+z+xyz}{xyz}$

Correct answer:

$\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

Explanation:

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

$\frac{1}{x}$ , $\frac{1}{y}$ , $\frac{1}{z}$

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 xyz . Put each term into terms of this common denominator:

$\frac{1}{x}*\frac{yz}{yz}=\frac{yz}{xyz}$

$\frac{1}{y}*\frac{xz}{xz}=\frac{xz}{xyz}$

$\frac{1}{z}*\frac{xy}{xy}=\frac{xy}{xyz}$

$xyz*\frac{xyz}{xyz}=\frac{x^2y^2z^2}{xyz}$

Now, add each term together:

$\frac{xy}{xyz}+\frac{xz}{xyz}+\frac{yz}{xyz}+\frac{x^2y^2z^2}{xyz}=\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

Look for the answer choice that matches this.

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Example Question #1 : Reciprocals

Find the reciprocal of the following expression:

$\frac{2x^2 + 3x + 4}{3b}$

Possible Answers:

$\frac{2x^2 + 3x + 4}{3b}$

$\frac{3b}{3b}$

$\frac{2x^2 + 3x + 4}{2x^2 + 3x + 4}$

$\frac{3b}{2x^2 +3x + 4}$

$\frac{3b}{2x^2 + 2x + 2}$

Correct answer:

$\frac{3b}{2x^2 +3x + 4}$

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:

$\frac{3b}{2x^2 +3x + 4}$

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

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

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Possible Answers:

$\frac{33}{22}$

$\frac{1}{22}$

$\frac{22}{33}$

$\frac{45}{2}$

$\frac{2}{45}$

Correct answer:

$\frac{2}{45}$

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:

$22\frac{1}{2} = \frac{2\cdot 22}{2}+\frac{1}{2}=\frac{44}{2} + \frac{1}{2} = \frac{45}{2}$

Therefore, the answer is:

$\frac{2}{45}$

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GRE Math : Reciprocals

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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

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

Example Question #1 : Reciprocals

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

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