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PSAT Math : Fractions

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

If Ben is taller than Jaime, Mary is taller than Ben, and Chris is taller than Mary. Who is the second tallest?

Possible Answers:

Chris

Jaime

Mary

Ben

Not possible to tell

Correct answer:

Mary

Explanation:

Using math symbols to dictate height we find that Ben>Jaime, Mary>Ben, Chris>Mary. Putting these in order we have Chris>Mary, Mary>Ben, Ben>Jaime. This shows that Mary is the second tallest.

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Example Question #1 : Fractions

Order the following fractions in descending order.

¹/₂, ²/₃, ²/₅, ³/₄, ⁴/₇

Possible Answers:

¹/₂, ²/₃, ²/₅, ³/₄, ⁴/₇

²/₅, ¹/₂, ³/₄, ⁴/₇, ²/₃

³/₄, ²/₃, ⁴/₇, ¹/₂, ²/₅

²/₃, ⁴/₇, ³/₄, ¹/₂, ²/₅

²/₅, ¹/₂, ⁴/₇, ²/₃, ³/₄

Correct answer:

³/₄, ²/₃, ⁴/₇, ¹/₂, ²/₅

Explanation:

Method 1:

Find the common denominator (420) and convert each fraction to this denominator:

¹/₂ = 210/420

²/₃ = 280/420

²/₅ = 168/420

³/₄ = 315/420

⁴/₇ = 240/420

Now sort by numerator, largest to smallest.

Method 2:

Divide each fraction to obtain a decimal. Sort the decimals, largest to smallest.

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Example Question #1 : Fractions

Increasing_n1

Possible Answers:

I and III only

I and II only

II and III only

II only

I only

Correct answer:

I and III only

Explanation:

Increasing_n2

Increasing_n4

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Example Question #161 : Fractions

Which of the following fractions is between 0.2 and 0.3?

Possible Answers:

$\dpi{100} \small \frac{2}{3}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small \frac{1}{6}$

$\dpi{100} \small \frac{1}{4}$

$\dpi{100} \small \frac{1}{3}$

Correct answer:

$\dpi{100} \small \frac{1}{4}$

Explanation:

$\dpi{100} \small \frac{1}{4}=0.25$

$\dpi{100} \small 0.2<0.25<0.3$

$\dpi{100} \small \frac{1}{6}\approx 0.167<0.2$

The other three choices are larger than 0.3.

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Example Question #2 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Which of the following fractions is the greatest?

Possible Answers:

$\frac{7}{10}$

$\frac{20}{23}$

$\frac{3}{4}$

$\frac{25}{28}$

$\frac{2}{3}$

Correct answer:

$\frac{25}{28}$

Explanation:

The trick to this problem is to see that three of the choices have the numerator and denominator 3 units apart. The other two choices can be made three units apart as well- multiply both $\frac{3}{4}$ and $\frac{2}{3}$ by $\frac{3}{3}$ to get them to be $\frac{9}{12}$ and $\frac{6}{9}$ , respectively.

The trick is that once all fractions are the same units apart in denominator and numerator, the biggest number is the largest fraction.

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Example Question #3 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Order the following from least to greatest: three-fifths, seven-eighths, 0.5, sixteen-eighteenths, 97%, 17-fifths.

Possible Answers:

0.5 , three-fifths, seven-eighths, sixteen-eighteenths, -fifths, $97\%$

0.5 , three-fifths, seven-eighths, sixteen-eighteenths, $97\%$ , -fifths

0.5 , $97\%$ , three-fifths, seven-eighths, sixteen-eighteenths, -fifths

three-fifths, 0.5 , $97\%$ , seven-eighths, sixteen-eighteenths, -fifths

0.5 , three-fifths, sixteen-eighteenths, seven-eighths, $97\%$ , -fifths

Correct answer:

0.5 , three-fifths, seven-eighths, sixteen-eighteenths, $97\%$ , -fifths

Explanation:

We need to order: three fifths, seven eights, 0.5, sixteen eighteenths, 97%, seventeen fifths.

Let us re-write each as a fraction: $\frac{3}{5}$ , $\frac{7}{8}$ , $\frac{1}{2}$ , $\frac{16}{18}=\frac{8}{9}$ , $\frac{97}{100}$ , and $\frac{17}{5}$ . We can now easily order these:

$\frac{1}{2},\frac{3}{5},\frac{7}{8},\frac{8}{9},\frac{97}{100},\frac{17}{5}$

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Example Question #1 : Decimals

Which of the following numbers is between 1/5 and 1/6?

Possible Answers:

0.13

0.22

0.25

0.19

0.16

Correct answer:

0.19

Explanation:

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

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Example Question #4 : Decimals

Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?

Possible Answers:

1/10

9/15

2/7

8/9

3/5

Correct answer:

2/7

Explanation:

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

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Example Question #1 : Fractions And Percentage

If there are 3 boys in a class and 7 girls. What percent of the class is made up of boys?

Possible Answers:

30%

25%

70%

Correct answer:

30%

Explanation:

To solve this problem we set up a ratio of part of total. The part is the number of boys in the class and the total is the number of boys and girls in the class.

$\frac{3}{10}$

now to find the percent we can multiply this fraction by 10/10

$\frac{3}{10}*\frac{10}{10}=\frac{30}{100}$

From here we can see that it is 30%

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Example Question #1 : How To Find Percentage From A Fraction

Marker Colors	Students
Blue	13
Pink	10
Orange	5
Brown	5
Green	7

The above chart shows the number of students in a class who chose each of the five marker colors available.

What percentage of the class chose a green marker?

Possible Answers:

$40\%$

$17.5\%$

$7\%$

$20\%$

$13.5\%$

Correct answer:

$17.5\%$

Explanation:

To figure out what percentage of the class chose green markers, you must first figure out what fraction of the class chose green markers. Then, you must convert that fraction into a percentage.

Figure out the fraction:

7 students chose green markers

40 students total

Fraction of students who chose green: $\frac{7}{40}$

To convert this fraction to a percentage, you must multiply the fraction times 100, then divide the numerator by the denominator. You multiply the fraction times 100 because in order to figure out the percent, you must figure out what the fraction means "for (per) every hundred (cent)".

$\frac{7}{40}$

Multiply times 100

$\frac{7}{40} \times 100 = \frac{700}{40}$

$700\div40 = 17.5$

Therefore, the answer is $17.5\%$ .

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PSAT Math : Fractions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 : Fractions

Example Question #1 : Fractions

Example Question #161 : Fractions

Example Question #2 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #3 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 : Decimals

Example Question #4 : Decimals

Example Question #1 : Fractions And Percentage

Example Question #1 : How To Find Percentage From A Fraction

All PSAT Math Resources

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