ACCUPLACER Arithmetic Quiz: Converting Percents

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Converting PercentsQuestion 1 of 20

Which of the following fractions is equivalent to $8\frac{1}{3}\%$ ?

\frac{1}{12}

\frac{1}{8}

\frac{1}{3}

\frac{25}{3}

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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Converting Percents

Practice Converting Percents in ACCUPLACER Arithmetic with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Converting Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Arithmetic.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Which of the following fractions is equivalent to $8\frac{1}{3}\%$ ?

$\frac{1}{12}$ (correct answer)
$\frac{1}{8}$
$\frac{1}{3}$
$\frac{25}{3}$

Explanation: First, convert the mixed number to an improper fraction:

8\frac{1}{3} = \frac{(8 \times 3) + 1}{3} = \frac{25}{3}

. The expression is now

\frac{25}{3}\%

. A percent is a value per 100, so to convert it to a fraction, divide by 100:

\frac{25}{3} \div 100 = \frac{25}{3} \times \frac{1}{100} = \frac{25}{300}

. Finally, simplify the fraction by dividing the numerator and denominator by 25:

\frac{25 \div 25}{300 \div 25} = \frac{1}{12}

Question 2

A recipe calls for $2\frac{3}{4}$ cups of flour. If Maria has already added $0.625$ cups and needs to add $87.5\%$ of the remaining amount, how many more cups should she add?

1.875 cups (correct answer)
2.125 cups
1.312 cups
1.531 cups

Explanation: Convert

2\frac{3}{4}

to decimal:

2.75

cups total needed. Remaining after

0.625

cups:

2.75 - 0.625 = 2.125

cups. Convert

87.5\% = \frac{7}{8} = 0.875

. Amount to add:

0.875 \times 2.125 = 1.859375 \approx 1.875

cups. Choice B is the remaining amount before applying the percentage. Choice C results from applying

87.5\%

to the original recipe amount. Choice D reverses the digits of the correct answer.

Question 3

A basketball player's free throw percentage decreased from $\frac{4}{5}$ to $72\%$ . By what percent did their free throw percentage decrease?

8%
10% (correct answer)
11.1%
12.5%

Explanation: Convert

\frac{4}{5} = 80\%

. The decrease is from

80\%

72\%

, which is

8

percentage points. The percent decrease is

\frac{8}{80} \times 100\% = 10\%

. Choice A gives the absolute decrease in percentage points, not the percent decrease. Choice C results from using

72

as the denominator instead of

80

. Choice D comes from calculation errors in the division.

Question 4

A population increased from 500 to 625. The population increase is what value, expressed as a decimal?

0.2
0.25 (correct answer)
0.8
1.25

Explanation: First, find the amount of the increase:

625 - 500 = 125

. To express this increase as a value relative to the original population, create a fraction with the increase over the original amount:

\frac{125}{500}

. To convert this fraction to a decimal, simplify it first by dividing the numerator and denominator by 125:

\frac{125 \div 125}{500 \div 125} = \frac{1}{4}

. The fraction

\frac{1}{4}

is equal to the decimal 0.25.

Question 5

A student needs a score of at least 70% on a test to pass. The student answered 45 out of 60 questions correctly. Which statement is true?

The student met the passing score exactly.
The student's score was 5% below the passing score.
The student's score was 5% above the passing score. (correct answer)
The student's score was 15% above the passing score.

Explanation: First, calculate the student's score as a percentage. The score is the fraction

\frac{45}{60}

. Simplifying this fraction gives

\frac{3}{4}

. To convert

\frac{3}{4}

to a percentage, convert it to a decimal (0.75) and multiply by 100, which is 75%. The passing score is 70%. The student's score of 75% is 5 percentage points higher than the passing score. Therefore, the student's score was 5% above the passing score.

Question 6

A number, $x$ , is multiplied by 140%. The result is then divided by $\frac{7}{5}$ . Which of the following represents the final value in terms of $x$ ?

$1.96x$
$0.8x$
$1.25x$
$x$ (correct answer)

Explanation: First, convert the percentage and fraction to decimals for easier calculation. 140% is equal to 1.4. The fraction

\frac{7}{5}

is equal to 1.4. The problem states that

x

is multiplied by 140%, which gives

1.4x

. Then, this result is divided by

\frac{7}{5}

, which is

1.4

. The calculation is

\frac{1.4x}{1.4}

. The 1.4 in the numerator and denominator cancel out, leaving just

x

Question 7

What is the result of $\frac{3}{5}$ subtracted from 150%, expressed as a decimal?

-0.9
0.9 (correct answer)
1.44
2.1

Explanation: First, convert both values to decimals.

\frac{3}{5} = 0.6

. 150% = 1.5. The question asks for

\frac{3}{5}

to be subtracted from 150%, so the calculation is

1.5 - 0.6

. The result is 0.9.

Question 8

Calculate $(50\% \times \frac{1}{5}) + 0.15$ and express the answer as a simplified fraction.

$\frac{1}{4}$ (correct answer)
$\frac{13}{50}$
$\frac{3}{10}$
$\frac{13}{2}$

Explanation: First, convert all numbers to a common format. Using decimals: 50% = 0.5,

\frac{1}{5} = 0.2

, and 0.15 is already a decimal. Following the order of operations, perform the multiplication first:

0.5 \times 0.2 = 0.10

. Then, perform the addition:

0.10 + 0.15 = 0.25

. Finally, convert the decimal result back to a simplified fraction.

0.25 = \frac{25}{100} = \frac{1}{4}

Question 9

A parking lot has 250 spaces. 30% of the spaces are reserved. Of the non-reserved spaces, $\frac{1}{5}$ are for compact cars. What simplified fraction represents the portion of the total parking lot that is for non-reserved compact cars?

$\frac{3}{50}$
$\frac{7}{50}$ (correct answer)
$\frac{1}{5}$
$\frac{7}{10}$

Explanation: First, find the percentage of non-reserved spaces: 100% - 30% = 70%. Next, find the portion of these that are for compact cars:

\frac{1}{5}

of 70%. To calculate this, convert 70% to a fraction (

\frac{70}{100}

\frac{7}{10}

) and multiply:

\frac{1}{5} \times \frac{7}{10} = \frac{7}{50}

. This fraction is already in its simplest form.

Question 10

What is 40% of $\frac{5}{8}$ ? Express the answer as a decimal.

0.25 (correct answer)
0.45
0.625
1.025

Explanation: To solve this, first convert the values to a common format, like decimals. 40% is equivalent to 0.40, and the fraction

\frac{5}{8}

is equivalent to 0.625. The problem asks for '40% of

\frac{5}{8}

', which means you multiply the two values:

0.40 \times 0.625 = 0.25

Question 11

What is 0.035 expressed as a percentage?

0.035%
0.35%
3.5% (correct answer)
35%

Explanation: To convert a decimal to a percentage, multiply the decimal by 100. This is equivalent to moving the decimal point two places to the right. For 0.035, moving the decimal point two places to the right gives 3.5. Therefore, 0.035 is equal to 3.5%.

Question 12

A salesperson earns a commission of $\frac{1}{20}$ of their total sales. What is this commission rate expressed as a percentage?

0.5%
1.2%
5% (correct answer)
20%

Explanation: To convert a fraction to a percentage, you can first convert the fraction to a decimal and then multiply by 100. To convert

\frac{1}{20}

to a decimal, divide 1 by 20, which is 0.05. To convert the decimal 0.05 to a percentage, multiply by 100, which gives 5%. Alternatively, you can find an equivalent fraction with a denominator of 100:

\frac{1}{20} = \frac{1 \times 5}{20 \times 5} = \frac{5}{100}

, which is 5%.

Question 13

A store marks up an item by $25\%$ from its wholesale cost. During a sale, the store offers a $20\%$ discount off the marked price. If the final sale price is $30, what was the original wholesale cost?

$25.00
$30.00 (correct answer)
$37.50
$31.25

Explanation: Let the wholesale cost be

x

. After a 25% markup, the marked price is

1.25x

. After a 20% discount, the sale price is

0.80 \times 1.25x = x

. Since the sale price is $30, the wholesale cost is $30. Choice A results from incorrectly calculating

30 ÷ 1.25 = 24

, then rounding. Choice C assumes the $30 is before the discount. Choice D results from applying only the markup without the discount.

Question 14

A solution contains $37.5\%$ alcohol by volume. If this percentage is first converted to a decimal, then that decimal is converted to a fraction and reduced to lowest terms, what is the sum of the numerator and denominator?

1375
8
375
11 (correct answer)

Explanation: This question tests your ability to convert between percentages, decimals, and fractions while simplifying to lowest terms. When you see a problem asking for conversions through multiple forms, work systematically through each step. Start by converting the percentage to a decimal:

37.5\% = 37.5 ÷ 100 = 0.375

. Next, convert this decimal to a fraction. Since

0.375

has three decimal places, write it as

\frac{375}{1000}

. Now you need to reduce this fraction to lowest terms by finding the greatest common factor (GCF) of 375 and 1000. To find the GCF, factor both numbers:

$375 = 3 × 125 = 3 × 5^3$
$1000 = 8 × 125 = 2^3 × 5^3$

The GCF is

125

, so:

\frac{375}{1000} = \frac{375 ÷ 125}{1000 ÷ 125} = \frac{3}{8}

The sum of numerator and denominator is

3 + 8 = 11

, which is answer choice D. Let's examine why the other answers are wrong: Choice A (1375) likely comes from adding the original numbers 375 + 1000 without reducing the fraction. Choice C (375) represents just the original numerator before reduction. Choice B (8) is only the denominator of the reduced fraction, missing the numerator entirely. Remember that "reduced to lowest terms" means you must find the GCF and divide both numerator and denominator by it. Always double-check that your final fraction cannot be simplified further.

Question 15

The price of an item is reduced by $0.\overline{3}\%$ . Which of the following fractions represents this reduction?

$\frac{1}{300}$ (correct answer)
$\frac{1}{30}$
$\frac{1}{3}$
$\frac{10}{3}$

Explanation: First, recognize that the repeating decimal

0.\overline{3}

is equivalent to the fraction

\frac{1}{3}

. So, the reduction is

\frac{1}{3}\%

. To convert a percentage to a fraction, you divide by 100. So, we need to calculate

\frac{1}{3} \div 100

, which is the same as

\frac{1}{3} \times \frac{1}{100} = \frac{1}{300}

Question 16

Arrange the following numbers from least to greatest: $\frac{11}{20}$ , 5.5%, 0.505.

5.5%, 0.505, $\frac{11}{20}$ (correct answer)
0.505, $\frac{11}{20}$ , 5.5%
$\frac{11}{20}$ , 0.505, 5.5%
5.5%, $\frac{11}{20}$ , 0.505

Explanation: To compare the numbers, convert them all to decimals. 5.5% becomes 0.055.

\frac{11}{20}

becomes

\frac{55}{100}

, which is 0.55. The third number is 0.505. Now, compare the decimals: 0.055, 0.55, and 0.505. The smallest is 0.055 (5.5%). The next is 0.505. The largest is 0.55 (

\frac{11}{20}

). The correct order from least to greatest is 5.5%, 0.505,

\frac{11}{20}

Question 17

A shirt is discounted by 30%. The sale price is then taxed at 10%. The total tax paid is what fraction of the original price?

$\frac{77}{100}$
$\frac{1}{10}$
$\frac{3}{10}$
$\frac{7}{100}$ (correct answer)

Explanation: Let the original price be

P

. A 30% discount means the sale price is 100% - 30% = 70% of the original price, or

0.70P

. The tax is 10% of this sale price:

0.10 \times 0.70P = 0.07P

. The tax paid is 0.07 of the original price

P

. To express 0.07 as a fraction, write it as

\frac{7}{100}

Question 18

Which of the following fractions is equivalent to 0.4%?

$\frac{1}{250}$ (correct answer)
$\frac{1}{25}$
$\frac{2}{5}$
$\frac{4}{5}$

Explanation: To convert a percent to a fraction, write it as a number over 100. So, 0.4% is

\frac{0.4}{100}

. To remove the decimal in the numerator, multiply both the numerator and the denominator by 10:

\frac{0.4 \times 10}{100 \times 10} = \frac{4}{1000}

. Finally, simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4:

\frac{4 \div 4}{1000 \div 4} = \frac{1}{250}

Question 19

A company's revenue this year is 165% of its revenue last year. Which of the following mixed numbers represents this year's revenue as a fraction of last year's revenue?

$\frac{13}{20}$
$1\frac{13}{20}$ (correct answer)
$1\frac{2}{3}$
$16\frac{1}{2}$

Explanation: To convert a percentage to a fraction, place it over 100. So, 165% becomes

\frac{165}{100}

. This is an improper fraction. To convert it to a mixed number, divide 165 by 100. It goes in 1 time with a remainder of 65. This gives

1\frac{65}{100}

. The fraction part,

\frac{65}{100}

, can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 5:

\frac{65 \div 5}{100 \div 5} = \frac{13}{20}

. So the final mixed number is

1\frac{13}{20}

Question 20

What is $\frac{7}{16}$ converted to a percentage?

4.375%
7.16%
43.75% (correct answer)
56.25%

Explanation: To convert a fraction to a percentage, first convert the fraction to a decimal by dividing the numerator by the denominator.

7 \div 16 = 0.4375

. Then, to convert the decimal to a percentage, multiply by 100 (or move the decimal point two places to the right).

0.4375 \times 100 = 43.75

. So,

\frac{7}{16}

is equal to 43.75%.