# GRE Math : Simplifying Fractions

## Example Questions

### Example Question #61 : Fractions

For how many integers, , between 26 and 36 is it true that

and  are all in lowest terms?

Possible Answers:

Correct answer:

Explanation:

If  is even, then  is not in lowest terms, since both  and 4 are divisible by 2. Therefore, the only possibilities are 27,29,31,33, and 35. But , and , so only two integers satisfy the given condition: 29 and 31.

### Example Question #1062 : Gre Quantitative Reasoning

Mrs. Lawrence's class has  students,  of which are girls.  If you were to choose a student at random, what's the probability that the student chosen would be a boy?

Possible Answers:

Correct answer:

Explanation:

In order to find out the probability of choosing a boy, you must first find out how many boys there are. Since there are  girls out of  students,  students should be boys.

Therefore, the probability of choosing a boy is,

.

However, this is not one of the answer choices; therefore, you must reduce the fraction.

In order to reduce a fraction, you have to find their GCM, or greatest common multiple. This is the biggest number that will go into both the numerator  and denominator .  The largest number is . Divide both the top and bottom by , and you will get the answer:

### Example Question #1063 : Gre Quantitative Reasoning

Simplify the fraction:

Possible Answers:

Correct answer:

Explanation:

To simplify the fraction

It may be helpful to write it in terms of scientific notation:

### Example Question #1064 : Gre Quantitative Reasoning

Simply the fraction:

Possible Answers:

Correct answer:

Explanation:

To simplify the fraction

Begin by factoring out common terms in the numerator and denominator:

Now notice that the coefficients for the polynomials in the numerator and denominator match the form of Pascal's Triangle:

The fraction can be rewritten as:

And finally reduced to

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