ACCUPLACER Arithmetic Quiz: Converting Improper Fractions And Mixed Numbers
20 questions · exam conditions
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Converting Improper Fractions And Mixed NumbersQuestion 1 of 20

A student incorrectly converts 5295\frac{2}{9} to the improper fraction 279\frac{27}{9} by adding the whole number to the numerator. What should the correct improper fraction be?

459\frac{45}{9}
529\frac{52}{9}
479\frac{47}{9}
439\frac{43}{9}
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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Converting Improper Fractions And Mixed Numbers

Practice Converting Improper Fractions And Mixed Numbers 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 Improper Fractions And Mixed Numbers, 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

A student incorrectly converts 5295\frac{2}{9} to the improper fraction 279\frac{27}{9} by adding the whole number to the numerator. What should the correct improper fraction be?

  1. 459\frac{45}{9}
  2. 529\frac{52}{9}
  3. 479\frac{47}{9} (correct answer)
  4. 439\frac{43}{9}
Explanation: Converting mixed numbers to improper fractions is a fundamental skill that requires multiplying the whole number by the denominator, then adding the numerator. The student's error of simply adding the whole number to the numerator is a common mistake that ignores the denominator's role. To correctly convert 5295\frac{2}{9}, you multiply the whole number (5) by the denominator (9): 5×9=455 \times 9 = 45. Then add the original numerator (2): 45+2=4745 + 2 = 47. The denominator stays the same, giving you 479\frac{47}{9}. Looking at the wrong answers: Choice A (459\frac{45}{9}) represents only the whole number part converted—you'd get this if you forgot to add the numerator entirely. Choice B (529\frac{52}{9}) appears to reverse the process by adding the denominator to something, which isn't part of any standard conversion method. Choice D (439\frac{43}{9}) might result from subtracting instead of adding the numerator, giving 45−2=4345 - 2 = 43. The correct answer is C (479\frac{47}{9}) because it follows the proper formula: multiply whole number by denominator, then add the original numerator. Study tip: Remember the conversion formula as "multiply and add"—always multiply the whole number by the denominator first, then add the existing numerator. The denominator never changes. You can check your work by converting back: 47÷9=547 \div 9 = 5 remainder 22, which gives you 5295\frac{2}{9}.

Question 2

A mixed number is written as 7587\frac{5}{8}. When this number is converted to an improper fraction, what is its numerator?

  1. 35
  2. 56
  3. 61 (correct answer)
  4. 91
Explanation: To convert the mixed number 7587\frac{5}{8} to an improper fraction, multiply the whole number (7) by the denominator (8) and then add the numerator (5). Calculation: (7×8)+5=56+5=61(7 \times 8) + 5 = 56 + 5 = 61. This result, 61, is the numerator of the improper fraction 618\frac{61}{8}.

Question 3

A recipe requires 2342\frac{3}{4} cups of flour. If the recipe is measured out using only a 14\frac{1}{4} cup scoop, how many scoops of flour are needed?

  1. 8
  2. 9
  3. 10
  4. 11 (correct answer)
Explanation: To solve this, first convert the mixed number 2342\frac{3}{4} into an improper fraction. Multiply the whole number by the denominator (2×4=82 \times 4 = 8) and add the numerator (8+3=118 + 3 = 11). The improper fraction is 114\frac{11}{4}. This fraction represents eleven parts, where each part is 14\frac{1}{4}. Therefore, 11 scoops of 14\frac{1}{4} cup are needed.

Question 4

A point on a number line is located at 173\frac{17}{3}. Between which two consecutive whole numbers does this point lie?

  1. 4 and 5
  2. 5 and 6 (correct answer)
  3. 6 and 7
  4. 16 and 17
Explanation: To find the location on the number line, convert the improper fraction 173\frac{17}{3} to a mixed number. Divide the numerator (17) by the denominator (3). 17÷3=517 \div 3 = 5 with a remainder of 2. This means 173=523\frac{17}{3} = 5\frac{2}{3}. The value 5235\frac{2}{3} is greater than 5 but less than 6, so it lies between the whole numbers 5 and 6.

Question 5

A pie is cut into 8 equal slices. A group eats 11 slices, which is one whole pie and 3 slices from a second pie. Which improper fraction represents the total amount of pie eaten?

  1. 1381\frac{3}{8}
  2. 811\frac{8}{11}
  3. 118\frac{11}{8} (correct answer)
  4. 1116\frac{11}{16}
Explanation: The amount eaten is 1381\frac{3}{8} pies. To convert this mixed number to an improper fraction, multiply the whole number (1) by the denominator (8) and add the numerator (3): 1×8+3=111 \times 8 + 3 = 11. The denominator stays 8. Therefore, the improper fraction is 118\frac{11}{8}. Choice A is the mixed number, not the improper fraction. Choice B incorrectly inverts the fraction. Choice D incorrectly adds the denominators of two pies.

Question 6

Two lengths of fabric measure 2162\frac{1}{6} yards and 3563\frac{5}{6} yards. What is the total length of the fabric, expressed as an improper fraction?

  1. 306\frac{30}{6}
  2. 356\frac{35}{6}
  3. 366\frac{36}{6} (correct answer)
  4. 3612\frac{36}{12}
Explanation: First, add the two mixed numbers: 216+3562\frac{1}{6} + 3\frac{5}{6}. Add the whole numbers: 2+3=52+3=5. Add the fractions: 16+56=66=1\frac{1}{6} + \frac{5}{6} = \frac{6}{6} = 1. The total is 5+1=65 + 1 = 6. To express 6 as an improper fraction with a denominator of 6, multiply the whole number by the denominator: 6×6=366 \times 6 = 36. So the answer is 366\frac{36}{6}. Alternatively, convert 216=1362\frac{1}{6} = \frac{13}{6} and 356=2363\frac{5}{6} = \frac{23}{6}, then add 136+236=366\frac{13}{6} + \frac{23}{6} = \frac{36}{6}.

Question 7

Which of the following fractions has the greatest value?

  1. 195\frac{19}{5} (correct answer)
  2. 3343\frac{3}{4}
  3. 278\frac{27}{8}
  4. 3123\frac{1}{2}
Explanation: To compare the values, convert all options to the same format, such as mixed numbers. A) 195=345\frac{19}{5} = 3\frac{4}{5}. B) 3343\frac{3}{4}. C) 278=338\frac{27}{8} = 3\frac{3}{8}. D) 3123\frac{1}{2}. Now compare the fractional parts: 45\frac{4}{5}, 34\frac{3}{4}, 38\frac{3}{8}, and 12\frac{1}{2}. In decimal form, these are 0.8, 0.75, 0.375, and 0.5. The largest fractional part is 45\frac{4}{5}, so 195\frac{19}{5} is the greatest value.

Question 8

What is the difference between 315\frac{31}{5} and 4254\frac{2}{5}?

  1. 1351\frac{3}{5}
  2. 1451\frac{4}{5} (correct answer)
  3. 2152\frac{1}{5}
  4. 2452\frac{4}{5}
Explanation: First, convert both numbers to the same format. Let's use improper fractions. Convert 4254\frac{2}{5} to an improper fraction: (4×5)+2=22(4 \times 5) + 2 = 22, so it is 225\frac{22}{5}. Now subtract the smaller fraction from the larger one: 315−225=95\frac{31}{5} - \frac{22}{5} = \frac{9}{5}. Finally, convert the result 95\frac{9}{5} to a mixed number. 9÷5=19 \div 5 = 1 with a remainder of 4. The difference is 1451\frac{4}{5}.

Question 9

How many of the following fractions are greater than the whole number 4? 174,235,113,359\frac{17}{4}, \frac{23}{5}, \frac{11}{3}, \frac{35}{9}

  1. 1
  2. 2 (correct answer)
  3. 3
  4. 4
Explanation: Convert each improper fraction to a mixed number to compare it to 4. 174=414\frac{17}{4} = 4\frac{1}{4}, which is greater than 4. 235=435\frac{23}{5} = 4\frac{3}{5}, which is greater than 4. 113=323\frac{11}{3} = 3\frac{2}{3}, which is less than 4. 359=389\frac{35}{9} = 3\frac{8}{9}, which is less than 4. Only two of the fractions, 174\frac{17}{4} and 235\frac{23}{5}, are greater than 4.

Question 10

The number 5785\frac{7}{8} is written as an improper fraction. What is that fraction?

  1. 408\frac{40}{8}
  2. 478\frac{47}{8} (correct answer)
  3. 477\frac{47}{7}
  4. 578\frac{57}{8}
Explanation: To convert the mixed number 5785\frac{7}{8} to an improper fraction, multiply the whole number (5) by the denominator (8) and add the numerator (7). Calculation: (5×8)+7=40+7=47(5 \times 8) + 7 = 40 + 7 = 47. The denominator remains 8. The improper fraction is 478\frac{47}{8}.

Question 11

The improper fraction 536\frac{53}{6} is equivalent to the mixed number X56X\frac{5}{6}. What is the value of X?

  1. 7
  2. 8 (correct answer)
  3. 9
  4. 48
Explanation: To find the whole number part (X) of the mixed number, divide the numerator of the improper fraction (53) by its denominator (6). 53÷6=853 \div 6 = 8 with a remainder of 5. The quotient, 8, is the whole number X. The mixed number is 8568\frac{5}{6}.

Question 12

A carpenter cuts a board into three pieces with lengths 23162\frac{3}{16} inches, 4116\frac{41}{16} inches, and 115161\frac{15}{16} inches. What was the total length of the original board expressed as an improper fraction?

  1. 9516\frac{95}{16}
  2. 9916\frac{99}{16}
  3. 10316\frac{103}{16}
  4. 10716\frac{107}{16} (correct answer)
Explanation: First, convert all measurements to improper fractions: 2316=32+316=35162\frac{3}{16} = \frac{32 + 3}{16} = \frac{35}{16}; 4116\frac{41}{16} is already improper; 11516=16+1516=31161\frac{15}{16} = \frac{16 + 15}{16} = \frac{31}{16}. Now add: 3516+4116+3116=35+41+3116=10716\frac{35}{16} + \frac{41}{16} + \frac{31}{16} = \frac{35 + 41 + 31}{16} = \frac{107}{16}.

Question 13

Which of the following improper fractions is equivalent to 87128\frac{7}{12}?

  1. 8712\frac{87}{12}
  2. 9612\frac{96}{12}
  3. 10312\frac{103}{12} (correct answer)
  4. 11212\frac{112}{12}
Explanation: To convert the mixed number 87128\frac{7}{12} to an improper fraction, multiply the whole number (8) by the denominator (12), and then add the numerator (7). The calculation is (8×12)+7=96+7=103(8 \times 12) + 7 = 96 + 7 = 103. The denominator remains 12. So the improper fraction is 10312\frac{103}{12}.

Question 14

A plank of wood is 5145\frac{1}{4} feet long. A section measuring 114\frac{11}{4} feet is cut off. What is the length of the remaining piece of wood?

  1. 2142\frac{1}{4} feet
  2. 2122\frac{1}{2} feet (correct answer)
  3. 33 feet
  4. 3143\frac{1}{4} feet
Explanation: First, convert the mixed number 5145\frac{1}{4} to an improper fraction: 5×4+1=215 \times 4 + 1 = 21, so it's 214\frac{21}{4}. Now subtract the length of the cut section: 214−114=104\frac{21}{4} - \frac{11}{4} = \frac{10}{4}. To express this as a mixed number, divide 10 by 4, which is 2 with a remainder of 2. The result is 2242\frac{2}{4}, which simplifies to 2122\frac{1}{2}.

Question 15

A movie is 135 minutes long. How long is the movie in hours, expressed as a mixed number in simplest form? (There are 60 minutes in 1 hour.)

  1. 2142\frac{1}{4} hours (correct answer)
  2. 2151002\frac{15}{100} hours
  3. 2132\frac{1}{3} hours
  4. 2122\frac{1}{2} hours
Explanation: To convert minutes to hours, divide the total minutes by 60. This gives the fraction 13560\frac{135}{60}. To convert this improper fraction to a mixed number, divide 135 by 60. 135÷60=2135 \div 60 = 2 with a remainder of 15. This gives the mixed number 215602\frac{15}{60}. To simplify the fractional part, divide both the numerator and denominator by their greatest common divisor, which is 15. 15÷1560÷15=14\frac{15 \div 15}{60 \div 15} = \frac{1}{4}. The final answer is 2142\frac{1}{4} hours.

Question 16

Which mixed number is equivalent to 1139\frac{113}{9}?

  1. 114911\frac{4}{9}
  2. 124912\frac{4}{9}
  3. 125912\frac{5}{9} (correct answer)
  4. 132913\frac{2}{9}
Explanation: To convert 1139\frac{113}{9} to a mixed number, divide 113 by 9. 113÷9=12113 \div 9 = 12 with a remainder of 5. The quotient (12) is the whole number, the remainder (5) is the numerator, and the denominator (9) stays the same. The equivalent mixed number is 125912\frac{5}{9}.

Question 17

A jug contains 3123\frac{1}{2} liters of water. This amount is poured into glasses that each hold 12\frac{1}{2} of a liter. How many glasses can be completely filled?

  1. 3
  2. 4
  3. 6
  4. 7 (correct answer)
Explanation: The problem asks how many 12\frac{1}{2}-liter portions are in 3123\frac{1}{2} liters. First, convert the mixed number 3123\frac{1}{2} to an improper fraction. Multiply the whole number by the denominator (3×2=63 \times 2 = 6) and add the numerator (6+1=76 + 1 = 7). The improper fraction is 72\frac{7}{2}. This fraction means there are 7 portions of 12\frac{1}{2} liter. Therefore, 7 glasses can be filled.

Question 18

Which of the following is equivalent to 253\frac{25}{3}?

  1. 7137\frac{1}{3}
  2. 8138\frac{1}{3} (correct answer)
  3. 8238\frac{2}{3}
  4. 9139\frac{1}{3}
Explanation: To convert the improper fraction 253\frac{25}{3} to a mixed number, divide the numerator (25) by the denominator (3). 25÷3=825 \div 3 = 8 with a remainder of 1. The quotient (8) becomes the whole number, the remainder (1) becomes the numerator, and the denominator (3) remains the same. The result is 8138\frac{1}{3}.

Question 19

What is the sum of 2352\frac{3}{5} and 95\frac{9}{5}, expressed as a mixed number?

  1. 3253\frac{2}{5}
  2. 37103\frac{7}{10}
  3. 4154\frac{1}{5}
  4. 4254\frac{2}{5} (correct answer)
Explanation: First, convert the mixed number 2352\frac{3}{5} to an improper fraction: 2×5+3=132 \times 5 + 3 = 13, so it is 135\frac{13}{5}. Now add the two fractions: 135+95=225\frac{13}{5} + \frac{9}{5} = \frac{22}{5}. Finally, convert 225\frac{22}{5} back to a mixed number. 22÷5=422 \div 5 = 4 with a remainder of 2. So the answer is 4254\frac{2}{5}.

Question 20

A sack of flour weighs 374\frac{37}{4} kilograms. How can this weight be expressed as a mixed number?

  1. 9149\frac{1}{4} (correct answer)
  2. 9129\frac{1}{2}
  3. 101410\frac{1}{4}
  4. 371437\frac{1}{4}
Explanation: To convert the improper fraction 374\frac{37}{4} to a mixed number, divide the numerator (37) by the denominator (4). 37÷4=937 \div 4 = 9 with a remainder of 1. The quotient (9) becomes the whole number, the remainder (1) becomes the new numerator, and the denominator (4) stays the same. Thus, the mixed number is 9149\frac{1}{4}.