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

## Example Questions

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Solve for .

Explanation:

Cross multiply.

Dsitribute.

Solve for .

### Example Question #668 : Algebra

If , what is the value of ?

Explanation:

To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.

45 / -9 = -5

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

The quotient of a fraction is . If the numerator is , what is the value of the denominator?

Explanation:

Step 1: Set up the equation

Step 2: Solve for D

### Example Question #2 : How To Solve For A Variable As Part Of A Fraction

Solve for :

Explanation:

Solve for x:

Step 1: Find the least common denominator, , and adjust the fractions accordingly:

Solve for :

find x

6/x = 9/19

not possible

7/12

9/114

3/38

none of these

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 #3 : How To Solve For A Variable As Part Of A Fraction

Solve the following equation for the given variable:

Explanation:

To solve this equation we have to multiply both sides by the denominator to get rid of the fraction.

Doing this yields

Then to solve the last step is to isolate the variable by dividing both sides by 12.
Thus,

.

### Example Question #4 : How To Solve For A Variable As Part Of A Fraction

For what value of  is the equation   true?

Explanation:

When the equation is cross multiplied, it becomes

.

Hence,

, or

### Example Question #5 : How To Solve For A Variable As Part Of A Fraction

Solve the following equation for :

.