GRE Math : How to add fractions

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Operations

What is the result of adding  of  to ?

Possible Answers:

Correct answer:


Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140)  = 43/140, which cannot be reduced.

Example Question #1 : How To Add Fractions

Reduce to simplest form:  

Possible Answers:






Correct answer:



Simplify expressions inside parentheses first: \dpi{100} \small \left (\frac{4}{3} \times \frac{3}{8} \right ) = \frac{12}{24} = \frac{1}{2}  and \dpi{100} \small \left (\frac{1}{4} \div \frac{3}{8} \right ) = \left (\frac{1}{4} \times \frac{8}{3} \right ) = \frac{8}{12} = \frac{2}{3}


Now we have: \frac{1}{4} + \frac{1}{2} - \frac{2}{3}

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

\dpi{100} \small \frac{1\times 3}{4\times 3} + \frac{1\times 6}{2\times 6} - \frac{2\times 4}{3\times 4} =\frac{3}{12} + \frac{6}{12} - \frac{8}{12} = \frac{1}{12}

Example Question #2 : How To Add Fractions

Quantity A: 

Quantity B: 

Which of the following is true?

Possible Answers:

Quantity A is larger.

The two quantities are equal.

Quantity B is larger.

The relationship between the two quantities cannot be determined.

Correct answer:

The two quantities are equal.


Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

This is the same as:

, or 

This is the same as Quantity B. They are equal!

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