SHSAT Math Quiz: Comparing Rational Forms
12 questions · exam conditions
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Comparing Rational FormsQuestion 1 of 12

Three students earned the following scores on a test: Student A earned 2225\frac{22}{25} of the points, Student B earned 87.5%87.5\%, and Student C earned 0.890.89 of the points. Which statement about their relative performance is true?

Student C performed best, followed by Student A, then Student B performed worst
Student A performed best, followed by Student C, then Student B performed worst
Student B performed best, followed by Student C, then Student A performed worst
Student A performed best, followed by Student B, then Student C performed worst
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SHSAT Math Quiz

SHSAT Math Quiz: Comparing Rational Forms

Practice Comparing Rational Forms in SHSAT 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 Comparing Rational Forms, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

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

Three students earned the following scores on a test: Student A earned 2225\frac{22}{25} of the points, Student B earned 87.5%87.5\%, and Student C earned 0.890.89 of the points. Which statement about their relative performance is true?

  1. Student C performed best, followed by Student A, then Student B performed worst (correct answer)
  2. Student A performed best, followed by Student C, then Student B performed worst
  3. Student B performed best, followed by Student C, then Student A performed worst
  4. Student A performed best, followed by Student B, then Student C performed worst
Explanation: Converting to decimals: Student A: 2225=0.88\frac{22}{25} = 0.88, Student B: 87.5%=0.87587.5\% = 0.875, Student C: 0.890.89. Ranking from highest to lowest: 0.89>0.88>0.8750.89 > 0.88 > 0.875, so Student C > Student A > Student B. Choice B incorrectly places Student A first, possibly from converting 2225\frac{22}{25} incorrectly. Choice C incorrectly makes Student B the best performer. Choice D reverses the order of Students B and C.

Question 2

A store advertises a discount of 215\dfrac{2}{15} off an item. Which advertised percent is closest to the same discount?

  1. 11%11\%
  2. 12%12\%
  3. 13%13\% (correct answer)
  4. 15%15\%
Explanation: This question tests your ability to convert fractions to percentages and estimate values—a common skill on standardized math tests. To find what percent 215\frac{2}{15} represents, you need to convert the fraction to a decimal, then to a percentage. Divide the numerator by the denominator: 2÷15=0.1333...2 \div 15 = 0.1333... To convert to a percentage, multiply by 100: 0.1333...×100=13.33...%0.1333... \times 100 = 13.33...\% Since 13.33%13.33\% is closest to 13%13\%, answer choice C is correct. Let's examine why the other choices don't work. Choice A (11%11\%) is too low—it's more than 2 percentage points away from our calculated value of 13.33%13.33\%. Choice B (12%12\%) is closer but still more than a full percentage point off. Choice D (15%15\%) might seem tempting since 15 appears in the denominator, but this represents a common trap. The denominator tells you the total number of parts, not the percentage itself. The key insight here is that 215\frac{2}{15} is slightly more than 216=18=12.5%\frac{2}{16} = \frac{1}{8} = 12.5\%, so you'd expect an answer slightly above 12.5%12.5\%. Strategy tip: When converting fractions to percentages on multiple choice tests, you can often estimate without doing exact division. Compare to familiar benchmark fractions like 18=12.5%\frac{1}{8} = 12.5\% or 110=10%\frac{1}{10} = 10\%. Since 215\frac{2}{15} is close to 216=18\frac{2}{16} = \frac{1}{8}, you know the answer should be close to 12.5%12.5\%.

Question 3

A recipe calls for ingredients in the following proportions: 38\frac{3}{8} flour, 37.5%37.5\% sugar, and 0.3750.375 butter by weight. If these three ingredients must be listed in descending order by weight on the package label, what is the correct order?

  1. Flour, sugar, butter in equal proportions since all values represent the same amount (correct answer)
  2. Sugar, flour, butter because 37.5%>38>0.37537.5\% > \frac{3}{8} > 0.375
  3. Butter, flour, sugar because 0.375>38>37.5%0.375 > \frac{3}{8} > 37.5\%
  4. Flour, butter, sugar because 38>0.375>37.5%\frac{3}{8} > 0.375 > 37.5\%
Explanation: Converting all values: 38=0.375=37.5%\frac{3}{8} = 0.375 = 37.5\%. All three ingredients are in equal proportions, so they represent the same amount by weight. Choice B assumes 37.5%>3837.5\% > \frac{3}{8} which would result from treating the percent as 37.537.5 rather than 0.3750.375. Choice C incorrectly assumes 37.5%=0.37537.5\% = 0.375 means 37.5<37537.5 < 375. Choice D makes a similar error by not recognizing the equivalence.

Question 4

Three investment options show the following annual returns: Option 1 gained 720\frac{7}{20} of its value, Option 2 gained 34%34\% of its value, and Option 3 gained 0.360.36 of its value. If you could only choose one investment for the past year, which option would have provided the highest return?

  1. Option 1 provided the highest return at 35%35\%
  2. Option 2 provided the highest return at 34%34\%
  3. Option 3 provided the highest return at 36%36\% (correct answer)
  4. Options 1 and 3 tied for the highest return at 36%36\% each
Explanation: Converting all returns to percentages: Option 1: 720=0.35=35%\frac{7}{20} = 0.35 = 35\%, Option 2: 34%34\%, Option 3: 0.36=36%0.36 = 36\%. Option 3 has the highest return at 36%36\%. Choice A correctly converts Option 1 but incorrectly claims it's highest. Choice B correctly identifies Option 2's return but incorrectly claims it's highest. Choice D incorrectly states that Options 1 and 3 both equal 36%36\%.

Question 5

A chemistry student measured three different concentrations of a solution: Sample A has a concentration of 316\frac{3}{16}, Sample B has 18.75%18.75\% concentration, and Sample C has 0.18750.1875 concentration. Which statement correctly describes the relationship between these concentrations?

  1. Sample A has the lowest concentration, and Samples B and C have equal concentrations
  2. Sample B has the lowest concentration, and Samples A and C have equal concentrations
  3. Sample C has the lowest concentration, and Samples A and B have equal concentrations
  4. All three samples have exactly the same concentration (correct answer)
Explanation: Converting all concentrations to decimals: Sample A: 316=0.1875\frac{3}{16} = 0.1875, Sample B: 18.75%=0.187518.75\% = 0.1875, Sample C: 0.18750.1875. All three samples have identical concentrations of 0.18750.1875. Choices A, B, and C all incorrectly assume that different representations must mean different values, failing to recognize that 316=18.75%=0.1875\frac{3}{16} = 18.75\% = 0.1875.

Question 6

A store offers three different discounts: Discount X removes 25\frac{2}{5} of the original price, Discount Y removes 42%42\% of the original price, and Discount Z removes 0.380.38 of the original price. Which discount saves the customer the most money?

  1. Discount X saves the most because 25>42%>0.38\frac{2}{5} > 42\% > 0.38
  2. Discount Y saves the most because 42%>25>0.3842\% > \frac{2}{5} > 0.38 (correct answer)
  3. Discount Z saves the most because 0.38>25>42%0.38 > \frac{2}{5} > 42\%
  4. All discounts save the same amount because they are equivalent values
Explanation: Converting to decimals: Discount X: 25=0.4=40%\frac{2}{5} = 0.4 = 40\%, Discount Y: 42%=0.4242\% = 0.42, Discount Z: 0.38=38%0.38 = 38\%. Since 0.42>0.4>0.380.42 > 0.4 > 0.38, Discount Y saves the most money. Choice A incorrectly assumes 25>42%\frac{2}{5} > 42\%, possibly from comparing 22 to 4242 without proper conversion. Choice C incorrectly makes 0.380.38 the largest value. Choice D incorrectly assumes all values are equal.

Question 7

A basketball player's free throw percentage can be expressed as 1725\frac{17}{25}, 0.680.68, or 68%68\%. If another player has a free throw percentage of 1320\frac{13}{20} and a third player shoots 66.5%66.5\% from the free throw line, what is the correct ordering of these three players from lowest to highest free throw percentage?

  1. 1320\frac{13}{20}, 66.5%66.5\%, 1725\frac{17}{25}
  2. 66.5%66.5\%, 1320\frac{13}{20}, 1725\frac{17}{25} (correct answer)
  3. 1320\frac{13}{20}, 1725\frac{17}{25}, 66.5%66.5\%
  4. 66.5%66.5\%, 1725\frac{17}{25}, 1320\frac{13}{20}
Explanation: Converting all values to decimals: 1725=0.68=68%\frac{17}{25} = 0.68 = 68\%, 1320=0.65=65%\frac{13}{20} = 0.65 = 65\%, and 66.5%=0.66566.5\% = 0.665. Ordering from lowest to highest: 0.65<0.665<0.680.65 < 0.665 < 0.68, which corresponds to 1320<66.5%<1725\frac{13}{20} < 66.5\% < \frac{17}{25}. Choice A incorrectly places 66.5%66.5\% before 1725\frac{17}{25} but after 1320\frac{13}{20}, which would be correct if students confused 66.5%66.5\% with 66%66\%. Choice C reverses the order of 66.5%66.5\% and 1725\frac{17}{25}. Choice D completely reverses the correct order.

Question 8

Which of the following is the smallest value?

  1. −0.08-0.08
  2. −111-\dfrac{1}{11}
  3. −9%-9\%
  4. −0.1-0.1 (correct answer)
Explanation: When comparing negative numbers, remember that the number furthest from zero (with the largest absolute value) is actually the smallest. To solve this systematically, convert all values to the same format - decimals work best here. Let's convert each option to decimal form. Choice A is already −0.08-0.08. For choice B, divide: −111=−0.090909...-\frac{1}{11} = -0.090909... or approximately −0.091-0.091. Choice C converts from percentage: −9%=−9100=−0.09-9\% = -\frac{9}{100} = -0.09. Choice D is already −0.1-0.1. Now compare: −0.08-0.08, −0.091-0.091, −0.09-0.09, and −0.1-0.1. Since these are all negative, the number with the greatest distance from zero is smallest. Think of a number line: −0.1-0.1 is furthest left, making it the smallest value. Choice A (−0.08-0.08) is incorrect because 0.08<0.10.08 < 0.1, so −0.08>−0.1-0.08 > -0.1. Choice B (−111≈−0.091-\frac{1}{11} \approx -0.091) is wrong because 0.091<0.10.091 < 0.1, so this value is greater than −0.1-0.1. Choice C (−0.09-0.09) is incorrect for the same reason - since 0.09<0.10.09 < 0.1, we have −0.09>−0.1-0.09 > -0.1. Study tip: When comparing negative numbers, convert everything to decimals first, then remember that "more negative" means smaller. The trap here is thinking like positive numbers - always double-check your inequality direction when working with negatives.

Question 9

Which statement correctly compares 1125\dfrac{11}{25} and 43%43\%?

  1. 1125<43%\dfrac{11}{25} < 43\%
  2. 1125=43%\dfrac{11}{25} = 43\%
  3. 1125>43%\dfrac{11}{25} > 43\% (correct answer)
  4. 1125\dfrac{11}{25} is approximately 43%43\% but slightly smaller.
Explanation: When comparing fractions and percentages, you need to convert them to the same form. The most straightforward approach is to convert the fraction to a percentage. To convert 1125\dfrac{11}{25} to a percentage, divide the numerator by the denominator: 11÷25=0.4411 ÷ 25 = 0.44. Then multiply by 100 to get the percentage: 0.44×100=44%0.44 × 100 = 44\%. Now you can directly compare: 44%>43%44\% > 43\%, which means 1125>43%\dfrac{11}{25} > 43\%. This confirms that answer choice C is correct. Let's examine why the other options are wrong. Choice A states 1125<43%\dfrac{11}{25} < 43\%, but since 1125=44%\dfrac{11}{25} = 44\%, this is clearly false. Choice B claims 1125=43%\dfrac{11}{25} = 43\%, which would require the fraction to equal exactly 0.430.43, but our calculation shows it equals 0.440.44. Choice D suggests the fraction is "approximately 43%43\% but slightly smaller," which is incorrect in two ways: the fraction is larger than 43%43\%, not smaller, and the difference of 1%1\% isn't really "approximate" when dealing with such precise values. Study tip: When comparing fractions to percentages on the SHSAT, always convert to the same form first. Converting fractions to percentages is usually easier than the reverse. Remember that dividing by 25 is the same as multiplying by 4 and moving the decimal point, so 1125=11×4=44%\dfrac{11}{25} = 11 × 4 = 44\%.

Question 10

Arrange the following numbers from least to greatest: −58,  −0.62,  −64%,  −0.6-\dfrac{5}{8},\; -0.62,\; -64\%,\; -0.6. Which order is correct?

  1. −64%,  −0.62,  −58,  −0.6-64\%,\; -0.62,\; -\dfrac{5}{8},\; -0.6 (correct answer)
  2. −0.6,  −64%,  −58,  −0.62-0.6,\; -64\%,\; -\dfrac{5}{8},\; -0.62
  3. −58,  −0.62,  −64%,  −0.6-\dfrac{5}{8},\; -0.62,\; -64\%,\; -0.6
  4. −0.62,  −64%,  −0.6,  −58-0.62,\; -64\%,\; -0.6,\; -\dfrac{5}{8}
Explanation: When comparing negative numbers in different formats, you need to convert everything to the same form first. Remember that with negative numbers, the number closest to zero is actually the greatest, while the number farthest from zero is the least. Let's convert all values to decimals: −58=−0.625-\frac{5}{8} = -0.625, −64%=−0.64-64\% = -0.64, and we already have −0.62-0.62 and −0.6-0.6. Now we can compare: −0.64-0.64, −0.625-0.625, −0.62-0.62, and −0.6-0.6. Since these are all negative, the number with the largest absolute value is actually the smallest. Looking at absolute values: 0.64>0.625>0.62>0.60.64 > 0.625 > 0.62 > 0.6. Therefore, from least to greatest: −0.64<−0.625<−0.62<−0.6-0.64 < -0.625 < -0.62 < -0.6, which translates to −64%<−58<−0.62<−0.6-64\% < -\frac{5}{8} < -0.62 < -0.6. Choice A correctly shows this order. Choice B reverses the entire sequence, treating the negatives as if they were positive. Choice C places −58-\frac{5}{8} first, but −64%-64\% is actually smaller since −0.64<−0.625-0.64 < -0.625. Choice D scrambles the order completely and puts −58-\frac{5}{8} last when it should be second. Strategy tip: When ordering negative decimals, convert everything to the same decimal form first, then remember that "more negative" means "smaller." The negative number closest to zero is the greatest in the set.

Question 11

Which pair of numbers are equal in value?

  1. 940\dfrac{9}{40} and 22%22\%
  2. 0.450.45 and 920\dfrac{9}{20} (correct answer)
  3. 0.180.18 and 15\dfrac{1}{5}
  4. 725\dfrac{7}{25} and 0.270.27
Explanation: When comparing numbers in different forms—fractions, decimals, and percentages—you need to convert them all to the same format to determine which pairs are equal. Let's check each pair by converting to decimals. For choice B, 0.450.45 is already a decimal. To convert 920\dfrac{9}{20} to a decimal, divide: 9÷20=0.459 \div 20 = 0.45. Since both equal 0.450.45, this pair is equal in value. Now let's verify why the other choices are incorrect. For choice A, convert 940\dfrac{9}{40} to a decimal: 9÷40=0.2259 \div 40 = 0.225. Convert 22%22\% to a decimal by dividing by 100: 22%=0.2222\% = 0.22. Since 0.225≠0.220.225 \neq 0.22, these aren't equal. For choice C, 0.180.18 is given as a decimal. Convert 15\dfrac{1}{5}: 1÷5=0.201 \div 5 = 0.20. Since 0.18≠0.200.18 \neq 0.20, these aren't equal. For choice D, convert 725\dfrac{7}{25}: 7÷25=0.287 \div 25 = 0.28. Since 0.28≠0.270.28 \neq 0.27, these aren't equal. The key strategy for these problems is to convert everything to the same format—decimals are usually easiest. When converting fractions to decimals, simply divide the numerator by the denominator. For percentages, divide by 100. Always double-check your division, especially with fractions that might not result in terminating decimals. This systematic approach prevents careless errors and ensures you catch equivalent values that might not be obvious at first glance.

Question 12

Marcus claims that 712\frac{7}{12} is greater than 0.5830.583. Sarah argues that 58.4%58.4\% is the largest of the three numbers. Who is correct?

  1. Marcus is correct, and Sarah is incorrect because 712>0.583>58.4%\frac{7}{12} > 0.583 > 58.4\%
  2. Sarah is correct, and Marcus is incorrect because 58.4%>0.583>71258.4\% > 0.583 > \frac{7}{12}
  3. Both are correct because 58.4%>712>0.58358.4\% > \frac{7}{12} > 0.583 (correct answer)
  4. Neither is correct because 0.583>58.4%>7120.583 > 58.4\% > \frac{7}{12}
Explanation: Converting to decimals: 712=0.583‾≈0.5833\frac{7}{12} = 0.58\overline{3} \approx 0.5833, 0.5830.583, and 58.4%=0.58458.4\% = 0.584. Since 0.584>0.583‾>0.5830.584 > 0.58\overline{3} > 0.583, we have 58.4%>712>0.58358.4\% > \frac{7}{12} > 0.583. Marcus is correct that 712>0.583\frac{7}{12} > 0.583, and Sarah is correct that 58.4%58.4\% is the largest. Choice A incorrectly orders 0.5830.583 and 58.4%58.4\%. Choice B incorrectly claims Marcus is wrong. Choice D incorrectly makes 0.5830.583 the largest value.