ISEE Middle Level Quiz: Fractions Decimals And Percents
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Fractions Decimals And PercentsQuestion 1 of 20

To earn a B in her science class, Maya needs a four-test average of at least 80%. Her scores on the first three tests were 0.76, 7/10, and 85%. What is the lowest score she can get on her fourth test, expressed as a percentage, to earn a B?

89%
85%
92%
80%
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ISEE Middle Level Quiz

ISEE Middle Level Quiz: Fractions Decimals And Percents

Practice Fractions Decimals And Percents in ISEE Middle Level 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 Fractions Decimals And Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level.

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

To earn a B in her science class, Maya needs a four-test average of at least 80%. Her scores on the first three tests were 0.76, 7/10, and 85%. What is the lowest score she can get on her fourth test, expressed as a percentage, to earn a B?

  1. 89% (correct answer)
  2. 85%
  3. 92%
  4. 80%
Explanation: First, convert all scores to percentages: 0.76=76%0.76 = 76\%; 7/10=0.7=70%7/10 = 0.7 = 70\%; 85%85\% is already a percentage. To have an average of 80% on four tests, the sum of the scores must be at least 4×80%=320%4 \times 80\% = 320\%. The sum of her first three scores is 76%+70%+85%=231%76\% + 70\% + 85\% = 231\%. Let the fourth score be x. Then 231%+x≥320%231\% + x \ge 320\%. Subtracting 231% from both sides gives x≥89%x \ge 89\%. The lowest score she can get is 89%.

Question 2

For this question, compare the quantity in Column A to the quantity in Column B.

Column A: 0.2% of 1,000

Column B: 1,000% of 0.2

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The two quantities are equal. (correct answer)
  4. The relationship cannot be determined from the information given.
Explanation: Evaluate Column A: Convert 0.2% to a decimal by dividing by 100, which gives 0.002. Then, 0.002×1,000=20.002 \times 1,000 = 2. Evaluate Column B: Convert 1,000% to a decimal by dividing by 100, which gives 10. Then, 10×0.2=210 \times 0.2 = 2. Since both columns evaluate to 2, the quantities are equal.

Question 3

For this question, compare the quantity in Column A to the quantity in Column B. Let P represent a positive number.

Column A: The value of P after it is increased by 1/5 of its value.

Column B: The value of P after it is increased by 25%.

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater. (correct answer)
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.
Explanation: Let's express the increase in Column A as a percentage. The fraction 1/51/5 is equal to 1÷5=0.201 \div 5 = 0.20, which is 20%20\%. So, Column A represents P increased by 20%. Column B represents P increased by 25%. Since P is a positive number, an increase of 25% will result in a larger value than an increase of 20%. Therefore, the quantity in Column B is greater.

Question 4

A store offers two discount plans for a $200 bicycle. Plan X is a single discount of 25%. Plan Y is a 15% discount, followed by an additional discount of 1/10 off the sale price. How much more money is saved by choosing the better plan?

  1. $0
  2. $1.50
  3. $3.00 (correct answer)
  4. $5.00
Explanation: Calculate the savings for Plan X: The discount is 25% of $200, which is (0.25 \times 200 = 50\). Now, calculate the savings for Plan Y. The first discount is 15% of $200, which is \(0.15 \times 200 = 30). The sale price is (200−200 - 30 = 170\). The second discount is 1/10of this sale price, which is \((1/10) \times 170 =17). The total savings for Plan Y is (30+30 + 17 = 47\). Plan X offers a saving of $50, and Plan Y offers a saving of 47. Plan X is the better plan. The difference in savings is ($50 - $47 = $3.00).

Question 5

For this question, compare the quantity in Column A to the quantity in Column B.

Column A: The value of the number 0.545454...

Column B: 6/11

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The two quantities are equal. (correct answer)
  4. The relationship cannot be determined from the information given.
Explanation: To convert the repeating decimal in Column A to a fraction, let x=0.545454...x = 0.545454.... Then 100x=54.545454...100x = 54.545454.... Subtracting the first equation from the second gives 99x=5499x = 54, so x=54/99x = 54/99. Simplifying this fraction by dividing the numerator and denominator by their greatest common divisor, 9, gives x=6/11x = 6/11. Thus, the quantity in Column A is equal to the quantity in Column B.

Question 6

For this question, compare the quantity in Column A to the quantity in Column B. Assume k > 0.

Column A: 37.5% of 8k

Column B: 3/4 of 4k

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The two quantities are equal. (correct answer)
  4. The relationship cannot be determined from the information given.
Explanation: First, evaluate Column A. Convert 37.5% to a fraction. 37.5%=37.5/100=375/1000=3/837.5\% = 37.5/100 = 375/1000 = 3/8. Now, calculate (3/8)×8k=3k(3/8) \times 8k = 3k. Next, evaluate Column B. Calculate (3/4)×4k=3k(3/4) \times 4k = 3k. Since both columns equal 3k, the two quantities are equal.

Question 7

Which of the following lists the numbers in order from least to greatest?

  1. 4/5, 0.8, 83%, 5/6 (correct answer)
  2. 4/5, 0.8, 5/6, 83%
  3. 0.8, 83%, 4/5, 5/6
  4. 4/5, 5/6, 0.8, 83%
Explanation: When comparing numbers in different formats (fractions, decimals, and percentages), you need to convert them all to the same format to accurately determine their order. Let's convert everything to decimals to make comparison easier:
  • 45=0.8\frac{4}{5} = 0.8
  • 0.8=0.80.8 = 0.8 (already a decimal)
  • 83%=0.8383\% = 0.83
  • 56=0.833...\frac{5}{6} = 0.833... (approximately 0.833)
Now we can clearly see the order from least to greatest: 0.8,0.8,0.83,0.8330.8, 0.8, 0.83, 0.833. Since 45\frac{4}{5} and 0.80.8 are equal, the correct order is 45\frac{4}{5}, 0.80.8, 83%83\%, 56\frac{5}{6}. Choice A correctly lists this order. Choice B incorrectly places 56\frac{5}{6} before 83%83\%, but 56=0.833\frac{5}{6} = 0.833 is greater than 83%=0.8383\% = 0.83. Choice C starts with 0.80.8 instead of recognizing that 45\frac{4}{5} equals 0.80.8, and also misorders the larger values. Choice D places 56\frac{5}{6} second, which would make it smaller than 0.80.8, but 56\frac{5}{6} is actually the largest number in the group. Study tip: When comparing mixed number formats, convert everything to decimals first. For fractions, divide the numerator by the denominator. For percentages, move the decimal point two places left. This eliminates confusion and makes ordering straightforward.

Question 8

For this question, compare the quantity in Column A to the quantity in Column B.

Column A: 1/8 of 40%

Column B: 20% of 1/4

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The relationship cannot be determined from the information given.
  4. The two quantities are equal. (correct answer)
Explanation: When you encounter comparison problems involving fractions and percentages, the key is to convert everything to the same format so you can make an accurate comparison. Let's calculate each quantity step by step. For Column A, you need 18\frac{1}{8} of 40%. First, convert 40% to a decimal: 40% = 0.40. Then multiply: 18×0.40=0.408=0.05\frac{1}{8} \times 0.40 = \frac{0.40}{8} = 0.05. Converting back to a percentage, this equals 5%. For Column B, you need 20% of 14\frac{1}{4}. Convert 14\frac{1}{4} to a decimal: 14=0.25\frac{1}{4} = 0.25. Then calculate 20% of 0.25: 0.20×0.25=0.050.20 \times 0.25 = 0.05, which also equals 5%. Since both quantities equal 0.05 (or 5%), they are equal. Choice A is incorrect because Column A (5%) is not greater than Column B (5%). Choice B is wrong because Column B (5%) is not greater than Column A (5%). Choice C is incorrect because we have all the information needed to determine the relationship—both calculations can be completed with the given values. Choice D is correct because both quantities equal exactly 5%. Strategy tip: When comparing fractions and percentages, always convert to the same format (either all decimals or all percentages) before comparing. This eliminates confusion and makes the relationship clear. Also, double-check your arithmetic—these problems often have small numbers that are easy to miscalculate.

Question 9

A tablet computer originally priced at $480 is on sale for 12 1/2% off. What is the sale price of the tablet?

  1. $60
  2. $420 (correct answer)
  3. $432
  4. $468
Explanation: First, convert the mixed number percentage to a fraction. 121/2%=12.5%=12.5/100=125/1000=1/812 1/2\% = 12.5\% = 12.5/100 = 125/1000 = 1/8. The discount is 1/81/8 of the original price. Calculate the discount amount: ((1/8) \times 480=480 = 60). The sale price is the original price minus the discount: (480−480 - 60 = $420).

Question 10

For this question, compare the quantity in Column A to the quantity in Column B. Let N be a positive number.

Column A: 320% of N

Column B: The value of N increased by 2.2 times its original value.

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The relationship cannot be determined from the information given.
  4. The two quantities are equal. (correct answer)
Explanation: When you encounter percentage and multiplication problems, the key is translating each expression into the same mathematical form so you can compare them directly. Let's convert both columns to algebraic expressions. Column A asks for 320% of N. Remember that 320% means 320100=3.2\frac{320}{100} = 3.2, so Column A equals 3.2N3.2N. For Column B, you need to carefully parse "N increased by 2.2 times its original value." This means you start with N, then add 2.2 times N to it: N+2.2N=3.2NN + 2.2N = 3.2N. Since both columns equal 3.2N3.2N, they're equal regardless of what positive value N takes. Looking at the wrong answers: Choice A claims Column A is greater, but 3.2N3.2N cannot be greater than itself. Choice B claims Column B is greater, which has the same logical flaw. Choice C suggests the relationship depends on the value of N, but since both expressions are identical (3.2N=3.2N3.2N = 3.2N), the relationship is always equality no matter what N equals. The answer is D - the quantities are equal. Watch out for the language trap in Column B. "Increased by 2.2 times its original value" means adding 2.2N2.2N to the original NN, not multiplying N by 2.2. When you see "increased by," always think addition, not replacement. Practice converting percentage and verbal expressions into algebra to avoid these common misinterpretations.

Question 11

For this question, compare the quantity in Column A to the quantity in Column B.

Column A: 0.8 - 1/4

Column B: 55%

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The two quantities are equal. (correct answer)
  4. The relationship cannot be determined from the information given.
Explanation: Convert all values to decimals to compare them. In Column A, 1/4=0.251/4 = 0.25. So, the expression is 0.8−0.25=0.550.8 - 0.25 = 0.55. In Column B, 55%55\% is equivalent to the decimal 0.55. Since both columns evaluate to 0.55, the two quantities are equal.

Question 12

For this question, compare the quantity in Column A to the quantity in Column B. Let x and y be positive numbers, and y is 150% of x.

Column A: x as a fraction of y

Column B: 2/3

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The relationship cannot be determined from the information given.
  4. The two quantities are equal. (correct answer)
Explanation: When you encounter comparison problems involving percentages and fractions, start by translating the percentage relationship into mathematical terms, then work systematically to find what you're comparing. Since y is 150% of x, you can write this as y=1.5xy = 1.5x or y=3x2y = \frac{3x}{2}. Now you need to find "x as a fraction of y," which means xy\frac{x}{y}. Substituting the relationship: xy=x3x2=x⋅23x=2x3x=23\frac{x}{y} = \frac{x}{\frac{3x}{2}} = \frac{x \cdot 2}{3x} = \frac{2x}{3x} = \frac{2}{3} So Column A equals 23\frac{2}{3}, which is exactly what Column B shows. Looking at why the other answers are wrong: Choice A claims Column A is greater, but we've shown both quantities equal 23\frac{2}{3}. Choice B claims Column B is greater, which is also incorrect since they're equal. Choice C suggests the relationship can't be determined, but we have enough information—the percentage relationship between x and y allows us to calculate the exact fraction. The key insight is that when y is 150% of x, then x must be 11.5=23\frac{1}{1.5} = \frac{2}{3} of y. This makes intuitive sense: if something grows by 50% (from 100% to 150%), then the original amount represents 23\frac{2}{3} of the new amount. Study tip: When working with percentage relationships, always convert to fractions or decimals and set up equations. The reciprocal relationship (if A is 150% of B, then B is 23\frac{2}{3} of A) appears frequently on standardized tests.

Question 13

In a jar of marbles, the probability of selecting a green marble is 1/4 and the probability of selecting a yellow marble is 0.4. The rest of the marbles are purple. What percentage of the marbles in the jar are purple?

  1. 35% (correct answer)
  2. 45%
  3. 65%
  4. 75%
Explanation: The sum of all probabilities must be 1 (or 100%). First, convert the probabilities to a common format, such as decimals. The probability of selecting a green marble is 1/4=0.251/4 = 0.25. The probability of selecting a yellow marble is 0.4. The combined probability of selecting a green or yellow marble is 0.25+0.4=0.650.25 + 0.4 = 0.65. The remaining marbles are purple, so their probability is 1−0.65=0.351 - 0.65 = 0.35. To express this as a percentage, multiply by 100: 0.35×100=35%0.35 \times 100 = 35\%.

Question 14

For this question, compare the quantity in Column A to the quantity in Column B.

Column A: The reciprocal of 0.125

Column B: 800%

  1. The quantity in Column A is greater.
  2. The quantity in Column B is greater.
  3. The relationship cannot be determined from the information given.
  4. The two quantities are equal. (correct answer)
Explanation: This question tests your ability to work with reciprocals, decimals, and percentages - all fundamental number concepts that often appear together on quantitative reasoning exams. To find the reciprocal of 0.125, you need to calculate 10.125\frac{1}{0.125}. The easiest approach is to convert the decimal to a fraction first. Since 0.125=180.125 = \frac{1}{8}, the reciprocal becomes 118=8\frac{1}{\frac{1}{8}} = 8. Alternatively, you could divide directly: 1÷0.125=81 ÷ 0.125 = 8. For Column B, convert 800% to a decimal by dividing by 100: 800%=800100=8800\% = \frac{800}{100} = 8. Both columns equal 8, so the quantities are equal. Choice A is incorrect because Column A (8) is not greater than Column B (8). Choice B is wrong because Column B (8) is not greater than Column A (8). Choice C is incorrect because we have all the information needed to determine the relationship - both quantities can be calculated precisely. Choice D correctly identifies that the two quantities are equal. Study tip: When you see decimals like 0.125, 0.25, or 0.5, memorize their fraction equivalents (1/8, 1/4, 1/2). This makes reciprocal calculations much faster. Also, remember that finding a reciprocal means "flipping" the fraction, and percentages convert to decimals by moving the decimal point two places left.

Question 15

The population of a city was 15,000. In one year, the population increased by 1/3. The following year, it decreased by 25%. What was the population of the city after the two years?

  1. 14,500
  2. 15,000 (correct answer)
  3. 16,250
  4. 20,000
Explanation: First, calculate the population increase. An increase of 1/3 of 15,000 is (1/3)×15,000=5,000(1/3) \times 15,000 = 5,000. The new population is 15,000+5,000=20,00015,000 + 5,000 = 20,000. The next year, this new population decreased by 25%. A 25% decrease is equivalent to a multiplier of 1−0.25=0.751 - 0.25 = 0.75, or 3/4. The final population is 20,000×0.75=15,00020,000 \times 0.75 = 15,000. The population returned to its original size.

Question 16

A clearance tag shows 0.125 off; what fraction is equivalent to the decimal 0.125?

  1. 12510\dfrac{125}{10}
  2. 18\dfrac{1}{8} (correct answer)
  3. 81\dfrac{8}{1}
  4. 125\dfrac{12}{5}
Explanation: This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through place value understanding. To convert 0.125 to a fraction, we recognize that 0.125 = 125/1000, which simplifies by dividing both numerator and denominator by 125, giving us 1/8. The correct answer choice B (1/8) is correct because 0.125 = 125/1000 = 1/8 when fully simplified. A common mistake would be selecting 125/10 (choice A) by misunderstanding decimal place value, or 8/1 (choice C) by inverting the correct answer. To help students master this skill, teaching strategies should emphasize understanding decimal place values (0.125 has three decimal places, so the denominator is 1000). Recognizing that 0.125 is half of 0.25, which is 1/4, can help students see that 0.125 must be 1/8.

Question 17

A store advertises 0.20 off a price; what percent discount is that amount?

  1. 2%
  2. 20% (correct answer)
  3. 200%
  4. 0.20%
Explanation: This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through multiplication or division by 100. To convert the decimal 0.20 to a percent, we multiply by 100, which gives us 0.20 × 100 = 20%. The correct answer choice B (20%) is correct because it accurately follows the conversion method of multiplying a decimal by 100 to get a percent. A common mistake would be selecting 2% (choice A) by incorrectly moving the decimal point only one place, or 200% (choice C) by confusing the conversion direction. To help students master this skill, teaching strategies should emphasize that moving the decimal point two places to the right when converting to percent is the same as multiplying by 100. Practice with real-world shopping scenarios helps students understand that 0.20 off means a 20% discount.

Question 18

While shopping, a jacket is 25% off; what fraction of the original price is discounted?

  1. 14\dfrac{1}{4} (correct answer)
  2. 34\dfrac{3}{4}
  3. 125\dfrac{1}{25}
  4. 254\dfrac{25}{4}
Explanation: This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through multiplication or division by 100. To convert 25% to a fraction, we write it as 25/100 and then simplify by dividing both numerator and denominator by their greatest common factor, which is 25, giving us 1/4. The correct answer choice A (1/4) is correct because 25% = 25/100 = 1/4 when simplified. A common mistake would be selecting 3/4 (choice B), which represents the amount still to be paid rather than the discount amount. To help students master this skill, teaching strategies should focus on understanding that percent means 'per hundred' and practicing simplification of fractions. Visual representations like pie charts showing 25% as one quarter of a circle can reinforce this concept.

Question 19

A discount is 18\dfrac{1}{8} of the price; what percent discount is 18\dfrac{1}{8}?

  1. 8%
  2. 12.5% (correct answer)
  3. 1.8%
  4. 125%
Explanation: This question tests the ISEE middle level quantitative reasoning skill of converting between fractions, decimals, and percents. Understanding this concept involves knowing that fractions, decimals, and percents are different representations of the same value and can be converted through multiplication or division by 100. To convert 1/8 to a percent, we first convert to a decimal by dividing: 1 ÷ 8 = 0.125, then multiply by 100 to get 12.5%. The correct answer choice B (12.5%) is correct because 1/8 = 0.125 = 12.5%. A common mistake would be selecting 8% (choice A) by confusing the denominator with the percent value, or 125% (choice D) by forgetting the decimal point. To help students master this skill, teaching strategies should include recognizing common fraction-percent equivalents like 1/8 = 12.5%. Using visual models of dividing a whole into 8 parts and calculating what percent one part represents reinforces this conversion.

Question 20

After a 20% price increase, the cost of a concert ticket is $54.00. What was the original price of the ticket?

  1. $43.20
  2. $45.00 (correct answer)
  3. $50.00
  4. $64.80
Explanation: Let the original price be P. A 20% increase means the new price is P+0.20P=1.20PP + 0.20P = 1.20P. We are given that this new price is $54.00. So, 1.20P=541.20P = 54. To find the original price P, divide 54 by 1.2: P=54/1.2=540/12=45P = 54 / 1.2 = 540 / 12 = 45. The original price was $45.00.