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

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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

find x

6/x = 9/19

Possible Answers:

9/114

3/38

none of these

not possible

7/12

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 \frac{8}{25}

None

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

\dpi{100} \small 0.25

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

Solve for :

Possible Answers:

Correct answer:

Explanation:

Solve for :

Step 1: Cross-multiply to eliminate the fraction

Step 2: Solve for :

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