How to find the reciprocal of a fraction - GRE Quantitative Reasoning

Card 0 of 4

Question

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?

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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 . 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.

Compare your answer with the correct one above

Question

Find the reciprocal of the following expression:

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

Answer

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 .

Compare your answer with the correct one above

Question

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Answer

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:

$\frac{2}{45}$

Compare your answer with the correct one above

Tap the card to reveal the answer