PSAT Math : Fractions and Percentage

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Fractions And Percentage

Write as a fraction: 22%

Possible Answers:

11/50

11/100

4/7

2/3

4/9

Correct answer:

11/50

Explanation:

22% = 22/100

Divide everything by 2:

22/100 = 11/50

11 is a prime number, so this is as reduced as this fraction can get.

Example Question #1 : Percentage

When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?

Possible Answers:

1/3

3

6

1/6

18

Correct answer:

6

Explanation:

The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.

If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90y = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.

Similarly, we can write 15% of x as 0.15x = (15/100)x = (3/20)x.

Now, we set these two expressions equal to one another.

(9/10)y = (3/20)x

Multiply both sides by 20 to eliminate fractions.

18y = 3x

The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.

18y = 3x

Divide both sides by 3.

6y = x

Divide both sides by y.

6 = x/y

Thus, the ratio of x to y is 6.

The answer is 6.

Example Question #2 : Percentage

Write 7.5% as a fraction.

Possible Answers:

Correct answer:

Explanation:

First convert the percentage to a decimal:

7.5% = .075

Then turn this into a fraction:

.075 = 75/1000

Simplify by dividing the numerator and denominator by 25:

75/1000 = 3/40

Example Question #3 : Percentage

25% of 64 is equal to 5% of what number?

Possible Answers:

94

108

112

320

90

Correct answer:

320

Explanation:

25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)

Example Question #1 : Fractions And Percentage

Convert 62% into simplified fraction form.

Possible Answers:

Correct answer:

Explanation:

To convert a percent into a fraction, simply divide by 100 and reduce. In our case, 62 and 100 have the common factor of 2, so solving and simplification are as follows:

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

What is  as a percentage?

Possible Answers:

Correct answer:

Explanation:

Convert the improper fraction  to the mixed numeral  or as the decimal .   as a percentage is

Example Question #2 : How To Find Percentage From A Fraction

A family with 6 children, aged 4, 4, 5, 7, 12, and 13 are moving to a new home. They all want the same bedroom, so the parents have a lottery. Each child places their name in once for every year of age (the four year olds each put their name in 4 times, the seven year old puts his name in 7 times, etc.) What is the probability of the chosen child being 4 years old?

Possible Answers:

8.\overline{8}\%

It is most likely that the chosen child will be the oldest child.

None of the available answers

20\%

17.\overline{7}\%

Correct answer:

17.\overline{7}\%

Explanation:

First, we will determine the total number of ballots:

4+4+5+7+12+13=45\hspace{1 mm}ballots

Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:

\frac{4+4}{45}=\frac{8}{45}=0.1\overline{7}=17.\overline{7}\%

Example Question #3 : How To Find Percentage From A Fraction

Three hens each lay 20 eggs for a farmer. Two-fifths of the first hen's eggs are brown. One-fourth of the second hen's eggs are brown. Seven-tenths of the third hen's eggs are white. What percentage of all the eggs are brown?

Possible Answers:

Correct answer:

Explanation:

The first hen lays 8 brown eggs: 2/5 * 20 = 8

The second lays 5 brown eggs: 1/4 * 20 = 5

The third lays 6 brown eggs: 3/10 * 20 = 6

Add up the brown eggs and divide by 60, the total number of eggs:

19/60 = 0.31666667 = 31.67%, or 32%.

 

Example Question #71 : Percentage

There is a sale in a store and every item is discounted 23%. If a shirt is normally $18.59, what is the price of it after the discount?

Possible Answers:

Correct answer:

Explanation:

We can right 23% as a fraction and set that equal to  over the original price. 

From here we cross multiply and divide.

We round this number to $4.28. This is the amount of discoount we need to apply to the original price. To do this we subtract 4.28 from 18.59.

Example Question #3 : Fractions And Percentage

Louisa and Caroline are trying to save up to start a small business together. Louisa has saved  of their goal money, and Carolina has saved  of their goal money. About how much of their goal money have they saved up together?

Possible Answers:

45%

56%

18%

78%

64%

Correct answer:

78%

Explanation:

The goal of this problem is to solve for how much Louisa and Caroline have saved, together, towards their goal money for starting a small business.  In order to do that, you must add what Louisa has saved to what Caroline has saved, then convert the fraction into a percentage.

Add Louisa and Caroline:

Find the lowest common multiple for the denominator:

Add:

Simplify:

To convert a fraction into a percentage, simply multiply the numerator by 100 and divide by the denominator. There are other methods, but this is the easiest.

Equals

78% is your answer.

Learning Tools by Varsity Tutors