Praxis Math Quiz: Convert Fractions And Percents
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Convert Fractions And PercentsQuestion 1 of 20

A solution contains 30% alcohol. If you have 200 mL of this solution and you add 50 mL of pure alcohol, what fraction of the new solution is alcohol?

1125\frac{11}{25}
310\frac{3}{10}
45\frac{4}{5}
1120\frac{11}{20}
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Praxis Math Quiz

Praxis Math Quiz: Convert Fractions And Percents

Practice Convert Fractions And Percents in Praxis Math 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 Convert Fractions And Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis Math.

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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.

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Question 1

A solution contains 30% alcohol. If you have 200 mL of this solution and you add 50 mL of pure alcohol, what fraction of the new solution is alcohol?

  1. 1125\frac{11}{25} (correct answer)
  2. 310\frac{3}{10}
  3. 45\frac{4}{5}
  4. 1120\frac{11}{20}
Explanation: First, calculate the initial amount of alcohol. Convert 30% to a decimal: 0.30. Initial alcohol = 0.30×2000.30 \times 200 mL = 60 mL. Next, 50 mL of pure alcohol is added. The new total amount of alcohol is 60+50=11060 + 50 = 110 mL. The new total volume of the solution is 200+50=250200 + 50 = 250 mL. The fraction of alcohol in the new solution is 110250\frac{110}{250}. Simplifying this fraction by dividing the numerator and denominator by 10 gives 1125\frac{11}{25}.

Question 2

A map scale is 1 inch = 25 miles. The distance between two cities on the map is 3253\frac{2}{5} inches. This distance represents what percentage of 850 miles?

  1. 1%
  2. 10% (correct answer)
  3. 8.5%
  4. 12%
Explanation: First, find the actual distance between the cities. Convert 3253\frac{2}{5} to a decimal: 3.4 inches. The actual distance is 3.4 inches×25milesinch=853.4 \text{ inches} \times 25 \frac{\text{miles}}{\text{inch}} = 85 miles. Next, find what percentage of 850 miles this distance is. The ratio is 85850=110\frac{85}{850} = \frac{1}{10}. To convert 110\frac{1}{10} to a percentage, multiply by 100: 110×100%=10%\frac{1}{10} \times 100\% = 10\%.

Question 3

A company has 120 employees. Of these, 23\frac{2}{3} are full-time. Of the full-time employees, 37.5% have been with the company for over 10 years. What percentage of ALL employees are full-time and have been with the company for over 10 years?

  1. 25% (correct answer)
  2. 30%
  3. 37.5%
  4. 40%
Explanation: First, find the number of full-time employees: 23×120=2×40=80\frac{2}{3} \times 120 = 2 \times 40 = 80 full-time employees. Next, find the number of these employees who have been with the company for over 10 years. Convert 37.5% to a fraction, which is 38\frac{3}{8}. Now, calculate 38\frac{3}{8} of 80: 38×80=3×10=30\frac{3}{8} \times 80 = 3 \times 10 = 30 employees. Finally, express this number as a percentage of the total number of employees (120): 30120=14\frac{30}{120} = \frac{1}{4}. Convert the fraction 14\frac{1}{4} to a percentage: 14=25%\frac{1}{4} = 25\%.

Question 4

In a school election, Candidate A received 0.350.35 of the votes, Candidate B received 42% of the votes, and Candidate C received the remaining 69 votes. How many more votes did Candidate B receive than Candidate A?

  1. 21 (correct answer)
  2. 23
  3. 25
  4. 27
Explanation: First, find the total percentage of votes for Candidates A and B. Convert 0.35 to a percentage: 35%. Total percentage for A and B = 35%+42%=77%35\% + 42\% = 77\%. The remaining percentage for Candidate C is 100%−77%=23%100\% - 77\% = 23\%. We know that these 23% of the votes correspond to 69 votes. Let T be the total number of votes. Then 0.23×T=690.23 \times T = 69, so T=690.23=300T = \frac{69}{0.23} = 300. Now find the number of votes for A and B. A: 0.35×300=1050.35 \times 300 = 105 votes. B: 0.42×300=1260.42 \times 300 = 126 votes. The difference is 126−105=21126 - 105 = 21 votes. Alternatively, the difference in percentage is 42%−35%=7%42\% - 35\% = 7\%. The difference in votes is 0.07×T=0.07×300=210.07 \times T = 0.07 \times 300 = 21.

Question 5

A student's grade is based on three tests, weighted 20%, 30%, and 50% respectively. The student scored 45\frac{4}{5} on the first test and 70% on the second test. What score, as a percentage, must the student get on the third test to have an overall grade of 80%?

  1. 86% (correct answer)
  2. 88%
  3. 92%
  4. 94%
Explanation: First, convert all scores and weights to decimals. The first test score is 45=0.80\frac{4}{5} = 0.80. The second test score is 70% = 0.70. The weights are 0.20, 0.30, and 0.50. Let T be the score on the third test. The overall grade must be 80% or 0.80. The equation for the weighted average is: (0.20×0.80)+(0.30×0.70)+(0.50×T)=0.80(0.20 \times 0.80) + (0.30 \times 0.70) + (0.50 \times T) = 0.80. Calculate the known parts: 0.16+0.21+0.50T=0.800.16 + 0.21 + 0.50T = 0.80. Combine the terms: 0.37+0.50T=0.800.37 + 0.50T = 0.80. Subtract 0.37 from both sides: 0.50T=0.430.50T = 0.43. Solve for T: T=0.430.50=0.86T = \frac{0.43}{0.50} = 0.86. As a percentage, the student must score 86% on the third test.

Question 6

A restaurant bill is $45. A tip of 16\frac{1}{6} of the bill amount is added. To the nearest whole percent, what percentage of the total cost (bill plus tip) is the tip?

  1. 17%
  2. 14% (correct answer)
  3. 15%
  4. 19%
Explanation: First, calculate the tip amount: (\frac{1}{6} \times 45=45 = 7.50). Next, calculate the total cost: (45+45 + 7.50 = 52.50\). The question asks for the percentage of the total cost that is the tip. This is \frac{\text{tip}}{\text{total cost}} = \frac{7.50}{52.50}.Toconvertthistoapercentage,performthedivisionandmultiplyby100:. To convert this to a percentage, perform the division and multiply by 100: (\frac{7.5}{52.5}) \times 100 \approx 0.1428 \times 100 \approx 14.28%.Roundedtothenearestwholepercent,thisis14. Rounded to the nearest whole percent, this is 14%. A common mistake is to simply convert \frac{1}{6}toapercent( to a percent (\approx 17%$), which is the tip as a percentage of the bill, not the total cost.

Question 7

What is 37.5% of the value that is 52\frac{5}{2} of 16?

  1. 15 (correct answer)
  2. 20
  3. 25
  4. 12
Explanation: This is a two-step problem. First, find the value that is 52\frac{5}{2} of 16: 52×16=5×8=40\frac{5}{2} \times 16 = 5 \times 8 = 40. Second, calculate 37.5% of this value. It's helpful to know the fraction equivalent of 37.5%, which is 38\frac{3}{8}. Now, calculate 38\frac{3}{8} of 40: 38×40=3×5=15\frac{3}{8} \times 40 = 3 \times 5 = 15.

Question 8

If 38%\frac{3}{8}\% of a number is 24, what is the number?

  1. 9
  2. 90
  3. 640
  4. 6400 (correct answer)
Explanation: Let the number be xx. The problem states that (38%)×x=24(\frac{3}{8}\% ) \times x = 24. First, convert the percentage to a decimal or fraction. 38%=0.375%\frac{3}{8}\% = 0.375\%. As a decimal, this is 0.003750.00375. So, 0.00375x=240.00375x = 24. Solving for xx gives x=240.00375=6400x = \frac{24}{0.00375} = 6400. Alternatively, convert 38%\frac{3}{8}\% to a fraction: 3/8100=3800\frac{3/8}{100} = \frac{3}{800}. Then 3800x=24\frac{3}{800}x = 24, so x=24×8003=8×800=6400x = 24 \times \frac{800}{3} = 8 \times 800 = 6400.

Question 9

A mixture is 40% acid. If 14\frac{1}{4} of the mixture is removed and replaced with pure water, what is the new concentration of acid, expressed as a simplified fraction?

  1. 310\frac{3}{10} (correct answer)
  2. 14\frac{1}{4}
  3. 25\frac{2}{5}
  4. 38\frac{3}{8}
Explanation: Let the initial volume of the mixture be V. The initial amount of acid is 0.40V0.40V. When 14\frac{1}{4} of the mixture is removed, 34\frac{3}{4} of the mixture remains. The amount of acid remaining is 34×(0.40V)=0.30V\frac{3}{4} \times (0.40V) = 0.30V. The problem states that the removed portion is replaced with pure water, so the total volume is restored to V. The new concentration of acid is the amount of acid divided by the total volume: 0.30VV=0.30\frac{0.30V}{V} = 0.30. As a simplified fraction, 0.30 is 310\frac{3}{10}.

Question 10

The number 18 is 34%\frac{3}{4}\% of which number?

  1. 13.5
  2. 24
  3. 1350
  4. 2400 (correct answer)
Explanation: Let the unknown number be x. The problem can be written as an equation: 18=(34%)×x18 = (\frac{3}{4}\%) \times x. First, convert the percentage to a decimal. 34%=0.75%\frac{3}{4}\% = 0.75\%. To convert a percent to a decimal, divide by 100: 0.75÷100=0.00750.75 \div 100 = 0.0075. So, the equation is 18=0.0075x18 = 0.0075x. To solve for x, divide both sides by 0.0075: x=180.0075=2400x = \frac{18}{0.0075} = 2400. A common error is to use 0.75 instead of 0.0075, which would yield 24.

Question 11

In a bag of marbles, 37.5% are red, 25\frac{2}{5} are blue, and the rest are green. If there are 80 marbles in total, how many are green?

  1. 16
  2. 18 (correct answer)
  3. 24
  4. 32
Explanation: First, find the fraction of green marbles. Convert 37.5% to its fraction equivalent: 37.5% = 37.5/100 = 3/8. The fraction of blue marbles is 2/5. To add these fractions, find a common denominator of 40: 3/8 = 15/40 and 2/5 = 16/40. The combined fraction of red and blue marbles is 15/40 + 16/40 = 31/40. The fraction of green marbles is 1 - 31/40 = 9/40. To find the number of green marbles, multiply this fraction by the total: (9/40) × 80 = 9 × 2 = 18 green marbles.

Question 12

What is the value of the expression (78−0.8)÷0.5(\frac{7}{8} - 0.8) \div 0.5 expressed as a percentage?

  1. 7.5%
  2. 15% (correct answer)
  3. 25%
  4. 50%
Explanation: First, convert the fraction to a decimal to perform the subtraction in the parentheses. 78=0.875\frac{7}{8} = 0.875. So, the expression in the parentheses is 0.875−0.8=0.0750.875 - 0.8 = 0.075. Next, divide this result by 0.5: 0.075÷0.5=0.150.075 \div 0.5 = 0.15. Finally, convert this decimal to a percentage by multiplying by 100: 0.15×100=15%0.15 \times 100 = 15\%.

Question 13

A length of fabric is 4.5 yards long. A piece measuring 6 feet is cut from it. What fraction of the original fabric remains? (1 yard = 3 feet)

  1. 13\frac{1}{3}
  2. 12\frac{1}{2}
  3. 79\frac{7}{9}
  4. 59\frac{5}{9} (correct answer)
Explanation: First, convert all measurements to the same unit. Let's use feet. The original length is 4.5 yards. Since 1 yard = 3 feet, the original length is 4.5×3=13.54.5 \times 3 = 13.5 feet. A piece of 6 feet is cut, so the remaining length is 13.5−6=7.513.5 - 6 = 7.5 feet. The question asks for the fraction of the original fabric that remains. This is remaining lengthoriginal length=7.513.5\frac{\text{remaining length}}{\text{original length}} = \frac{7.5}{13.5}. To simplify this fraction, multiply the numerator and denominator by 10 to remove the decimals: 75135\frac{75}{135}. Both numbers are divisible by 5, giving 1527\frac{15}{27}. Both of these are divisible by 3, giving 59\frac{5}{9}.

Question 14

If 80 is increased by 45%, the result is decreased by 34\frac{3}{4} of the new value. What is the final result?

  1. 29 (correct answer)
  2. 36
  3. 87
  4. 20
Explanation: First, increase 80 by 45%. The increase is 0.45×80=360.45 \times 80 = 36. The new value is 80+36=11680 + 36 = 116. Next, this new value is decreased by 34\frac{3}{4} of itself. The decrease amount is 34×116=3×29=87\frac{3}{4} \times 116 = 3 \times 29 = 87. The final result is the new value minus the decrease: 116−87=29116 - 87 = 29. Alternatively, if a value is decreased by 34\frac{3}{4}, then 14\frac{1}{4} of it remains. So the final result is 14×116=29\frac{1}{4} \times 116 = 29.

Question 15

The value 13÷1300%\frac{1}{3} \div \frac{1}{300}\% is equivalent to which of the following?

  1. 1
  2. 100
  3. 1000
  4. 10000 (correct answer)
Explanation: First, correctly interpret the term 1300%\frac{1}{300}\%. This means 1/300100\frac{1/300}{100}, which is 130000\frac{1}{30000}. The problem is now to calculate 13÷130000\frac{1}{3} \div \frac{1}{30000}. To divide by a fraction, multiply by its reciprocal: 13×300001=300003=10000\frac{1}{3} \times \frac{30000}{1} = \frac{30000}{3} = 10000. A common mistake is to ignore the percent sign.

Question 16

An item is on sale for 20% off. The sales tax is 8% of the sale price. The total cost of the item is what percentage of the original price?

  1. 86.4% (correct answer)
  2. 88.0%
  3. 92.0%
  4. 85.6%
Explanation: Let the original price be P. After a 20% discount, the sale price is 100100% - 20% = 80% of the original price, or 0.80P0.80P. The sales tax is 8% of this sale price: 0.08×0.80P=0.064P0.08 \times 0.80P = 0.064P. The total cost is the sale price plus the tax: 0.80P+0.064P=0.864P0.80P + 0.064P = 0.864P. As a percentage of the original price, this is 86.4%.

Question 17

Which of the following fractions is equivalent to 1.25%?

  1. 54\frac{5}{4}
  2. 18\frac{1}{8}
  3. 180\frac{1}{80} (correct answer)
  4. 125100\frac{125}{100}
Explanation: To convert a percentage to a fraction, first write it as a fraction over 100: 1.25100\frac{1.25}{100}. To eliminate the decimal in the numerator, multiply both the numerator and the denominator by 100: 1.25×100100×100=12510000\frac{1.25 \times 100}{100 \times 100} = \frac{125}{10000}. Now, simplify the fraction. Both are divisible by 125. 125÷125=1125 \div 125 = 1 and 10000÷125=8010000 \div 125 = 80. So the simplified fraction is 180\frac{1}{80}. Distractor A, 54\frac{5}{4}, is 1.25, not 1.25%.

Question 18

Which of the following values is greater than 45% but less than 35\frac{3}{5}?

  1. 25\frac{2}{5}
  2. 0.58 (correct answer)
  3. 61%
  4. 920\frac{9}{20}
Explanation: To compare the values, convert them to decimals. 45% is 0.45, and 35\frac{3}{5} is 0.60. The question asks for a value between 0.45 and 0.60. A) 25=0.40\frac{2}{5} = 0.40, which is too small. B) 0.58 is between 0.45 and 0.60. C) 61% is 0.61, which is too large. D) 920=0.45\frac{9}{20} = 0.45, which is equal to the lower bound, not greater than it.

Question 19

If x=0.875x = 0.875 and y=87.5y = 87.5%, what is the value of xy+yx\frac{x}{y} + \frac{y}{x} expressed as a mixed number?

  1. 11
  2. 22 (correct answer)
  3. 1121 \frac{1}{2}
  4. 2142 \frac{1}{4}
Explanation: First, convert all values to the same format. 0.8750.875 is the decimal form. 87.587.5% is also 0.8750.875 in decimal form. The fraction form is 78\frac{7}{8}. Since xx and yy represent the same value, xy=1\frac{x}{y} = 1 and yx=1\frac{y}{x} = 1. Therefore, xy+yx=1+1=2\frac{x}{y} + \frac{y}{x} = 1 + 1 = 2.

Question 20

The fraction 211\frac{2}{11} is equivalent to a repeating decimal. What is the digit in the 50th decimal place of this decimal representation?

  1. 1
  2. 2
  3. 8 (correct answer)
  4. 9
Explanation: First, convert 211\frac{2}{11} to a decimal by dividing 2 by 11. This gives 0.181818...0.181818..., which can be written as 0.18‾0.\overline{18}. The repeating block of digits is '18', which has a length of 2. To find the 50th decimal digit, we need to determine if the position is odd or even. Since 50 is an even number, the digit will be the second digit in the repeating block, which is 8.