Reciprocals - GRE Quantitative Reasoning

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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?

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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.

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Question

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

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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.

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Question

Find the reciprocal of the following expression:

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

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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 .

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Question

Find the reciprocal of the following expression:

$22\frac{1}{2}$

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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:

$\frac{2}{45}$

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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?

Tap to reveal answer

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.

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Question

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

Tap to reveal answer

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.

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Question

Find the reciprocal of the following expression:

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

Tap to reveal answer

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 .

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Question

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Tap to reveal answer

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:

$\frac{2}{45}$

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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?

Tap to reveal answer

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.

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Question

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

Find the reciprocal of the following expression:

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

Tap to reveal answer

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 .

← Didn't Know|Knew It →

Question

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Tap to reveal answer

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:

$\frac{2}{45}$

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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?

Tap to reveal answer

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.

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Question

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

Find the reciprocal of the following expression:

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

Tap to reveal answer

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 .

← Didn't Know|Knew It →

Question

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Tap to reveal answer

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:

$\frac{2}{45}$

← Didn't Know|Knew It →

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?

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

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.

← Didn't Know|Knew It →

Question

Find the reciprocal of the following expression:

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

Tap to reveal answer

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 .

← Didn't Know|Knew It →

Question

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Tap to reveal answer

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:

$\frac{2}{45}$

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Knew It

Reciprocals - GRE Quantitative Reasoning

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?

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.

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

Find the reciprocal of the following expression:

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 .

Find the reciprocal of the following expression:

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:

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?

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.

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

Find the reciprocal of the following expression:

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 .

Find the reciprocal of the following expression:

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:

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?

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.

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

Find the reciprocal of the following expression:

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 .

Find the reciprocal of the following expression:

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:

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?

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.

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

Find the reciprocal of the following expression:

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 .

Find the reciprocal of the following expression:

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:

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?

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.

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

Find the reciprocal of the following expression:

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 .

Find the reciprocal of the following expression:

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:

Find the reciprocal of the following expression:

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

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 .

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Find the reciprocal of the following expression:

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

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 .

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Find the reciprocal of the following expression:

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

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 .

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Find the reciprocal of the following expression:

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

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 .

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Find the reciprocal of the following expression:

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

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 .

Find the reciprocal of the following expression:

$22\frac{1}{2}$