PSAT Math : How to evaluate a fraction

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #11 : How To Evaluate A Fraction

\frac{7^{12}-7^{10}}{7^{11}-7^{9}}=

Possible Answers:

Correct answer:

Explanation:

Factor out 7 from the numerator: \frac{7(7^{11}-7^{9})}{7^{11}-7^{9}}

This simplifies to 7.

Example Question #11 : How To Evaluate A Fraction

If  pizzas cost  dollars and  sodas cost  dollars, what is the cost of  pizzas and  sodas in terms of  and ?

Possible Answers:

5x+\frac{3y}{15}

\frac{3x+5y}{15}

Correct answer:

\frac{3x+5y}{15}

Explanation:

If 10 pizzas cost x dollars, then each pizza costs x/10. Similarly, each soda costs y/6. We can add the pizzas and sodas together by finding a common denominator:

 

Example Question #11 : How To Evaluate A Fraction

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According the pie chart, the degree measure of the sector representing the number of workers spending 5 to 9 years in the same role is how much greater in the construction industry chart than in the financial industry chart?

Possible Answers:

Correct answer:

Explanation:

Since the values in the pie charts are currently in terms of percentages (/100), we must convert them to degrees (/360, since within a circle) to solve the question. The "5 to 9 years" portion for the financial and construction industries are 18 and 25 percent, respectively. As such, we can cross-multiply both:

18/100 = x/360 

x = 65 degrees

25/100 = y/360

y = 90 degrees

Subtract: 90 – 65 = 25 degrees

Alternatively, we could first subtract the percentages (25 – 18 = 7), then convert the 7% to degree form via the same method of cross-multiplication.

Example Question #11 : How To Evaluate A Fraction

6 contestants have an equal chance of winning a game.  One contestant is disqualified, so now the 5 remaining contestants again have an equal chance of winning.  How much more likely is a contestant to win after the disqualification?

Possible Answers:

Correct answer:

Explanation:

When there are 6 people playing, each contestant has a 1/6 chance of winning.  After the disqualification, the remaining contestants have a 1/5 chance of winning.

1/5 – 1/6 = 6/30 – 5/30 = 1/30.

Example Question #11 : How To Evaluate A Fraction

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by simplifying the numerator.

 has a common denominator of .  Therefore, we can rewrite it as:

Now, in our original problem this is really is:

When you divide by a fraction, you really multiply by the reciprocal:

Example Question #261 : Gre Quantitative Reasoning

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by simplifying the numerator and the denominator.

Numerator

 has a common denominator of .  Therefore, we have:

Denominator

 has a common denominator of .  Therefore, we have:

Now, reconstructing our fraction, we have:

To make this division work, you multiply the numerator by the reciprocal of the denominator:

Example Question #261 : Algebra

Simplify:

 

Possible Answers:

 

None of the other answer choices are correct.

Correct answer:

Explanation:

Recall that dividing is equivalent multiplying by the reciprocal.  Therefore, ((x - 4) / (1 / 2)) / (1 / (x + 4)) = ((x - 4) * 2)  *  (x + 4) / 1. 

Let's simplify this further:

(2x – 8) * (x + 4) = 2x2 – 8x + 8x – 32 = 2x2 – 32

Example Question #11 : How To Evaluate A Fraction

Solve for :

Possible Answers:

Correct answer:

Explanation:

Begin by isolating the variables:

Now, the common denominator of the variable terms is . The common denominator of the constant values is . Thus, you can rewrite your equation:

Simplify:

Cross-multiply:

Simplify:

Finally, solve for :

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