# GRE Math : How to solve for a variable as part of a fraction

## Example Questions

find x

6/x = 9/19

not possible

7/12

none of these

9/114

3/38

none of these

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

Find x.

None

Explanation:

Cross multiply:

### Example Question #1 : How To Solve For A Variable As Part Of A Fraction

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Explanation:

Let numerator = N and denominator = D.

According to the first statement,

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D.

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+[N = (D x 5) + 4]

=

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

### Example Question #1 : How To Solve For A Variable As Part Of A Fraction

If  , what is the value of ?

Explanation:

Start by cross multiplying to get the equation

.

Then simplify by subtracting  from each side to get the solution,

.

### Example Question #1571 : Gre Quantitative Reasoning

If , then what is  equal to?

Explanation:

We start by solving for x in  by multiplying 4 and 15, which gives us .

Then substituting 60 for x in,

gives us

which equals 0.

### Example Question #1 : How To Solve For A Variable As Part Of A Fraction

If  , and , what is the value of ?

Explanation:

Start by cross multiplying which gives us .

Simplify by dividing both sides by  which gives us .

Isolate  by dividing both sides by  and then adding  to both sides, which gives us .

### Example Question #1 : How To Solve For A Variable As Part Of A Fraction

If , and  what is the value of ?