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

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors amazon store varsity tutors ibooks store

Example Questions

← Previous 1 3 4 5

Example Question #51 : Algebraic Fractions

Solve for .

Possible Answers:

Correct answer:

Explanation:

Cross multiply.

Dsitribute.

Solve for .

Example Question #52 : Algebraic Fractions

If , what is the value of ?

 

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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 :

Possible Answers:

Correct answer:

Explanation:

Solve for x:

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

Solve for :

 

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

find x

6/x = 9/19

Possible Answers:

7/12

3/38

9/114

none of these

not possible

Correct answer:

none of these

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

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

\dpi{100} \small \frac{4 }{x} = \frac{2}{25}

Find x.

Possible Answers:

\dpi{100} \small 50

\dpi{100} \small 0.25

\dpi{100} \small \frac{25}{8}

\dpi{100} \small \frac{8}{25}

None

Correct answer:

\dpi{100} \small 50

Explanation:

Cross multiply:

\dpi{100} \small 4 \times 25 = 2x

\dpi{100} \small 100 = 2x

\dpi{100} \small x = 50

Example Question #2 : 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.

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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 :


.

Reduce any fractions in your final answer.

Possible Answers:

Correct answer:

Explanation:

To solve an equation with a variable in a fraciton, treat the denominator as a constant value and multiply both sides of the equation by the denominator in order to eliminate it.

← Previous 1 3 4 5
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: