ISEE Lower Level Mathematics Achievement Quiz: Mixed Number Word Problems

What this quiz covers

This quiz focuses on Mixed Number Word Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

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.

Question 1

1. (4\frac{3}{8}) gallons (correct answer)
2. (4\frac{5}{8}) gallons
3. (5\frac{5}{8}) gallons
4. (9\frac{7}{8}) gallons

Explanation: To find the remaining amount of paint, subtract the amount used from the starting amount: (7\frac{1}{8} - 2\frac{3}{4}). First, find a common denominator, which is 8. The problem becomes (7\frac{1}{8} - 2\frac{6}{8}). Since (\frac{1}{8}) is smaller than (\frac{6}{8}), you need to regroup from the 7. Borrow 1 from 7, making it 6. Add the borrowed 1 (as (\frac{8}{8})) to the fraction: (\frac{1}{8} + \frac{8}{8} = \frac{9}{8}). The problem is now (6\frac{9}{8} - 2\frac{6}{8} = 4\frac{3}{8}) gallons.

Question 2

1. (2\frac{1}{6}) feet (correct answer)
2. (2\frac{3}{5}) feet
3. (3\frac{1}{6}) feet
4. (9\frac{5}{6}) feet

Explanation: First, find the total length of the two pieces cut off: (4\frac{1}{3} + 5\frac{1}{2}). The common denominator is 6. (4\frac{2}{6} + 5\frac{3}{6} = 9\frac{5}{6}) feet. Next, subtract this total from the original length of the plank: (12 - 9\frac{5}{6}). Regroup 12 as (11\frac{6}{6}). Then, (11\frac{6}{6} - 9\frac{5}{6} = 2\frac{1}{6}) feet.

Question 3

1. (2\frac{5}{8}) inches (correct answer)
2. (3\frac{3}{8}) inches
3. (5\frac{5}{8}) inches
4. (13\frac{7}{8}) inches

Explanation: First, find the combined thickness of the math and science books: (2\frac{1}{2} + 3\frac{1}{8}). The common denominator is 8. (2\frac{4}{8} + 3\frac{1}{8} = 5\frac{5}{8}) inches. Next, subtract this combined thickness from the total height of the stack: (8\frac{1}{4} - 5\frac{5}{8}). The common denominator is 8. (8\frac{2}{8} - 5\frac{5}{8}). Regroup from the 8: (7\frac{10}{8} - 5\frac{5}{8} = 2\frac{5}{8}) inches.

Question 4

1. (2\frac{1}{2}) yards
2. (1\frac{1}{4}) yards
3. (\frac{3}{4}) yard (correct answer)
4. (4\frac{1}{4}) yards

Explanation: This is a multi-step word problem involving mixed numbers and subtraction. When you see a problem asking "how much is left over," you need to find the difference between what was bought and what was used. First, calculate how much fabric Sara actually needs by adding the blue and silver fabric requirements: $2\frac{1}{2} + 1\frac{3}{4}$. To add mixed numbers, convert them to improper fractions or find a common denominator. Using common denominators: $2\frac{2}{4} + 1\frac{3}{4} = 3\frac{5}{4} = 4\frac{1}{4}$ yards total needed. Next, subtract the amount needed from the amount bought: $5 - 4\frac{1}{4} = 4\frac{4}{4} - 4\frac{1}{4} = \frac{3}{4}$ yard left over. Looking at the wrong answers: Choice A ($2\frac{1}{2}$ yards) might come from subtracting only one fabric type instead of both. Choice B ($1\frac{1}{4}$ yards) could result from calculation errors when working with the mixed numbers or adding instead of subtracting somewhere in the process. Choice D ($4\frac{1}{4}$ yards) is actually the total amount of fabric Sara needs, not the leftover amount—this represents confusing what the question is asking for. The correct answer is C: $\frac{3}{4}$ yard. Study tip: In word problems involving "left over" or "remaining," always identify what you start with, subtract what you use, and double-check that your answer makes logical sense. Practice converting between mixed numbers and improper fractions to avoid calculation errors.

Question 5

1. (\frac{1}{24}) of a tank
2. (\frac{5}{12}) of a tank (correct answer)
3. (\frac{5}{8}) of a tank
4. (\frac{11}{12}) of a tank

Explanation: This problem requires subtracting the final amount of gas from the amount present before refueling. First, find the amount of gas in the tank before adding more, which was (\frac{1}{4}) full. The owner filled it to (\frac{2}{3}) full. The amount added is the difference: (\frac{2}{3} - \frac{1}{4}). The common denominator is 12. (\frac{8}{12} - \frac{3}{12} = \frac{5}{12}). The starting amount of (\frac{7}{8}) full is extra information not needed to solve for the amount added.

Question 6

1. (4\frac{1}{4}) pounds (correct answer)
2. (4\frac{3}{4}) pounds
3. (5\frac{3}{4}) pounds
4. (6\frac{1}{2}) pounds

Explanation: First, find the total amount of flour used by adding the two amounts: (3\frac{1}{2} + 2\frac{1}{4}). Find a common denominator for 2 and 4, which is 4. (3\frac{2}{4} + 2\frac{1}{4} = 5\frac{3}{4}) pounds. Next, subtract the total amount used from the initial amount: (10 - 5\frac{3}{4}). To subtract, regroup 10 as (9\frac{4}{4}). So, (9\frac{4}{4} - 5\frac{3}{4} = 4\frac{1}{4}) pounds.

Question 7

1. (1\frac{1}{2}) liters
2. (1\frac{7}{12}) liters (correct answer)
3. (2\frac{5}{12}) liters
4. (6\frac{11}{12}) liters

Explanation: Subtract the amount of water remaining from the initial amount: (4\frac{1}{4} - 2\frac{2}{3}). The least common denominator for 4 and 3 is 12. The problem becomes (4\frac{3}{12} - 2\frac{8}{12}). You need to regroup because (\frac{3}{12}) is less than (\frac{8}{12}). Borrow 1 from 4, which is (\frac{12}{12}). The problem becomes (3\frac{3+12}{12} - 2\frac{8}{12} = 3\frac{15}{12} - 2\frac{8}{12} = 1\frac{7}{12}) liters.

Question 8

1. (5\frac{11}{12}) cups
2. (7\frac{1}{6}) cups
3. (8\frac{5}{12}) cups (correct answer)
4. (15\frac{1}{12}) cups

Explanation: This is a two-step problem. First, subtract the amount poured out: (10\frac{1}{2} - 3\frac{1}{3}). The common denominator is 6. (10\frac{3}{6} - 3\frac{2}{6} = 7\frac{1}{6}) cups. Next, add the amount that was put back in: (7\frac{1}{6} + 1\frac{1}{4}). The common denominator is 12. (7\frac{2}{12} + 1\frac{3}{12} = 8\frac{5}{12}) cups.

Question 9

1. (1\frac{1}{6}) hours
2. (3\frac{2}{3}) hours (correct answer)
3. (3\frac{5}{6}) hours
4. (4\frac{1}{6}) hours

Explanation: First, find the time spent on math homework: (2\frac{1}{2} - 1\frac{1}{3}). The common denominator is 6. (2\frac{3}{6} - 1\frac{2}{6} = 1\frac{1}{6}) hours. Then, add the time spent on both tasks: (2\frac{1}{2} + 1\frac{1}{6}). The common denominator is 6. (2\frac{3}{6} + 1\frac{1}{6} = 3\frac{4}{6}), which simplifies to (3\frac{2}{3}) hours.

Question 10

1. (24) miles
2. (6\frac{3}{4}) miles
3. (20\frac{1}{4}) miles
4. (5\frac{1}{4}) miles (correct answer)

Explanation: When you encounter a problem about combining parts to make a whole, you need to identify what information you have and what you're looking for. Here, you know the total distance and two of the three parts, so you need to find the missing third part. To find the running distance, subtract the swimming and biking distances from the total distance: $25\frac{1}{2} - 1\frac{1}{2} - 18\frac{3}{4}$ First, subtract the swimming portion: $25\frac{1}{2} - 1\frac{1}{2} = 24$ miles remaining for biking and running. Next, subtract the biking portion from what's left: $24 - 18\frac{3}{4}$. Convert 24 to a mixed number with fourths: $24 = 23\frac{4}{4}$. Now subtract: $23\frac{4}{4} - 18\frac{3}{4} = 5\frac{1}{4}$ miles for running. Looking at the wrong answers: Choice A (24 miles) is what you get if you only subtract the swimming portion but forget about the biking. Choice B ($6\frac{3}{4}$ miles) likely results from an error in fraction subtraction, possibly adding fractions instead of subtracting. Choice C ($20\frac{1}{4}$ miles) is what you'd get if you only subtracted the swimming portion and made an arithmetic error. The correct answer is D: $5\frac{1}{4}$ miles. Study tip: In multi-step subtraction problems with mixed numbers, work systematically—subtract one portion at a time and double-check your fraction arithmetic. Convert whole numbers to equivalent fractions when needed to make subtraction easier.

Question 11

1. (10\frac{1}{2}) pounds
2. (7\frac{1}{4}) pounds
3. (8\frac{1}{4}) pounds
4. (6\frac{3}{4}) pounds (correct answer)

Explanation: This problem tests your ability to work with mixed numbers and solve multi-step word problems involving subtraction. When you see a question asking "how much is left," you need to subtract all the amounts used from the original total. Start with the full bag of 15 pounds and subtract what the dog ate each week. First, add up the total food consumed: $4\frac{1}{2} + 3\frac{3}{4}$. To add these mixed numbers, convert to common denominators: $4\frac{2}{4} + 3\frac{3}{4} = 7\frac{5}{4} = 8\frac{1}{4}$ pounds total eaten. Now subtract the total eaten from the original amount: $15 - 8\frac{1}{4} = 14\frac{4}{4} - 8\frac{1}{4} = 6\frac{3}{4}$ pounds remaining. Looking at the wrong answers: Choice A ($10\frac{1}{2}$ pounds) likely comes from subtracting only the first week's consumption ($15 - 4\frac{1}{2} = 10\frac{1}{2}$) and forgetting about the second week. Choice B ($7\frac{1}{4}$ pounds) results from subtracting the weeks separately but making an error in the final calculation. Choice C ($8\frac{1}{4}$ pounds) is actually the total amount the dog ate, not what's left—this happens when you correctly calculate the sum of what was eaten but forget to subtract it from 15. Remember: in "how much is left" problems, always subtract the total amount used from the original amount. Double-check that your final answer makes sense—it should be less than what you started with.

Question 12

1. (8\frac{5}{8}) feet
2. (4\frac{1}{8}) feet
3. (8\frac{1}{4}) feet
4. (3\frac{7}{8}) feet (correct answer)

Explanation: When you see a word problem involving subtracting mixed numbers, you need to carefully track what's being removed from the original amount and find the remainder. Daniel starts with $12\frac{1}{8}$ feet of rope and cuts off two pieces: $3\frac{1}{2}$ feet and $4\frac{3}{4}$ feet. To find what's left, subtract both pieces from the original length. First, convert all fractions to the same denominator (eighths): $3\frac{1}{2} = 3\frac{4}{8}$ and $4\frac{3}{4} = 4\frac{6}{8}$. Now calculate: $12\frac{1}{8} - 3\frac{4}{8} - 4\frac{6}{8}$ You can combine the pieces he cut off first: $3\frac{4}{8} + 4\frac{6}{8} = 7\frac{10}{8} = 8\frac{2}{8} = 8\frac{1}{4}$ Then subtract from the original: $12\frac{1}{8} - 8\frac{1}{4} = 12\frac{1}{8} - 8\frac{2}{8} = 3\frac{7}{8}$ feet. Choice A ($8\frac{5}{8}$) likely comes from only subtracting one of the two pieces. Choice B ($4\frac{1}{8}$) might result from calculation errors when converting fractions or borrowing incorrectly. Choice C ($8\frac{1}{4}$) is actually the total amount Daniel cut off, not what remained—a common trap where students find the wrong quantity. Remember: in multi-step subtraction problems with mixed numbers, convert everything to common denominators first, then double-check that you're finding what the question actually asks for (remainder vs. amount removed).

Question 13

1. (3\frac{5}{6}) miles
2. (1\frac{1}{5}) miles
3. (3\frac{1}{6}) miles
4. (1\frac{1}{6}) miles (correct answer)

Explanation: When you encounter word problems involving movement in opposite directions along the same path, think about net displacement—how far you end up from where you started, not the total distance traveled. Let's track the hiker's position step by step. Starting at point zero, the hiker walks $2\frac{1}{2}$ miles east (positive direction), reaching a position $2\frac{1}{2}$ miles from the start. Then the hiker walks $1\frac{1}{3}$ miles west (negative direction) along the same path. To find the final position, subtract the westward distance from the eastward distance: $2\frac{1}{2} - 1\frac{1}{3}$. Converting to improper fractions: $\frac{5}{2} - \frac{4}{3}$. Finding a common denominator of 6: $\frac{15}{6} - \frac{8}{6} = \frac{7}{6} = 1\frac{1}{6}$ miles east of the starting point. Choice A ($3\frac{5}{6}$) represents the trap of adding the distances instead of finding net displacement. Choice B ($1\frac{1}{5}$) comes from incorrectly adding the fractions without proper common denominators. Choice C ($3\frac{1}{6}$) results from adding the whole numbers and subtracting only the fractional parts, showing incomplete mixed number arithmetic. The correct answer is D: $1\frac{1}{6}$ miles. Study tip: For movement problems, draw a number line with your starting point at zero. Mark each movement as positive or negative based on direction. The final position tells you the distance from start—don't confuse this with total distance traveled.

Question 14

1. (22\frac{7}{12}) miles
2. (3\frac{1}{12}) miles
3. (2\frac{11}{12}) miles (correct answer)
4. (48\frac{1}{12}) miles

Explanation: This is a multi-step word problem involving mixed numbers, where you need to find how much distance remains after David has already traveled part of the way. To solve this, you need to add up the distances David has already traveled, then subtract that total from his destination distance. First, add the bike and bus distances: $7\frac{1}{4} + 15\frac{1}{3}$. To add mixed numbers, convert to a common denominator. The LCD of 4 and 3 is 12, so: $7\frac{3}{12} + 15\frac{4}{12} = 22\frac{7}{12}$ miles traveled so far. Now subtract this from the total distance: $25\frac{1}{2} - 22\frac{7}{12}$. Convert $25\frac{1}{2}$ to twelfths: $25\frac{6}{12}$. Since $\frac{6}{12} < \frac{7}{12}$, you need to borrow: $24\frac{18}{12} - 22\frac{7}{12} = 2\frac{11}{12}$ miles remaining. Answer A ($22\frac{7}{12}$) represents the total distance David has already traveled, not the remaining distance. Answer B ($3\frac{1}{12}$) likely comes from an error in borrowing when subtracting fractions. Answer D ($48\frac{1}{12}$) results from incorrectly adding all three distances together instead of subtracting. When solving multi-step word problems, always identify what the question is actually asking for. Here, "How much farther does he need to travel?" means you want the remaining distance, not the distance already covered. Set up your equation to match: total distance minus distance traveled equals distance remaining.

Question 15

1. (1\frac{3}{8}) miles (correct answer)
2. (1\frac{5}{8}) miles
3. (2\frac{5}{8}) miles
4. (9\frac{1}{8}) miles

Explanation: To find the difference in distance, subtract Sunday's run from Saturday's run: (5\frac{1}{4} - 3\frac{7}{8}). The common denominator is 8. The problem is (5\frac{2}{8} - 3\frac{7}{8}). Regroup from the 5, making it 4 and adding (\frac{8}{8}) to the fraction: (4\frac{2+8}{8} = 4\frac{10}{8}). Now subtract: (4\frac{10}{8} - 3\frac{7}{8} = 1\frac{3}{8}) miles.

Question 16

1. (2\frac{1}{3}) bushels (correct answer)
2. (3\frac{1}{3}) bushels
3. (27\frac{2}{3}) bushels
4. (57\frac{2}{3}) bushels

Explanation: First, find the total amount of corn harvested so far: (15\frac{1}{6} + 12\frac{1}{2}). The common denominator is 6. (15\frac{1}{6} + 12\frac{3}{6} = 27\frac{4}{6}), which simplifies to (27\frac{2}{3}) bushels. Next, subtract the harvested amount from the goal: (30 - 27\frac{2}{3}). Regroup 30 as (29\frac{3}{3}). Then, (29\frac{3}{3} - 27\frac{2}{3} = 2\frac{1}{3}) bushels.

Question 17

1. (3\frac{1}{10}) miles
2. (6\frac{1}{10}) miles
3. (7\frac{7}{10}) miles (correct answer)
4. (10\frac{7}{10}) miles

Explanation: This is a two-step problem. First, find the distance Maria walked on the second day by subtracting: (4\frac{3}{5} - 1\frac{1}{2}). The common denominator is 10. (4\frac{6}{10} - 1\frac{5}{10} = 3\frac{1}{10}) miles. Second, find the total distance by adding the distances from both days: (4\frac{3}{5} + 3\frac{1}{10}). Convert to a common denominator: (4\frac{6}{10} + 3\frac{1}{10} = 7\frac{7}{10}) miles.

Question 18

1. (1\frac{1}{6}) cups (correct answer)
2. (1\frac{3}{5}) cups
3. (2\frac{1}{6}) cups
4. (4\frac{5}{6}) cups

Explanation: First, calculate the total amount of broth added to the pot: (3\frac{1}{3} + 1\frac{1}{2}). The common denominator is 6. (3\frac{2}{6} + 1\frac{3}{6} = 4\frac{5}{6}) cups. Next, subtract this total from the pot's capacity to find the remaining room: (6 - 4\frac{5}{6}). Regroup 6 as (5\frac{6}{6}). Then, (5\frac{6}{6} - 4\frac{5}{6} = 1\frac{1}{6}) cups.

Question 19

1. (1\frac{5}{8}) pounds (correct answer)
2. (1\frac{7}{8}) pounds
3. (2\frac{3}{8}) pounds
4. (18\frac{5}{8}) pounds

Explanation: To find the weight gain, subtract last week's weight from this week's weight: (10\frac{1}{8} - 8\frac{1}{2}). The common denominator is 8. The problem becomes (10\frac{1}{8} - 8\frac{4}{8}). Since (\frac{1}{8}) is smaller than (\frac{4}{8}), you need to regroup. Borrow 1 from 10, making it 9, and add (\frac{8}{8}) to the fraction: (9\frac{1+8}{8} = 9\frac{9}{8}). Now subtract: (9\frac{9}{8} - 8\frac{4}{8} = 1\frac{5}{8}) pounds.

Question 20

1. $3\ \tfrac{1}{3}$ pounds
2. $4$ pounds (correct answer)
3. $3\ \tfrac{2}{3}$ pounds
4. $4\ \tfrac{1}{3}$ pounds

Explanation: This question tests the ability to add mixed numbers in a real-world context, specifically for ISEE lower-level students. Mixed numbers combine whole numbers and fractions, requiring careful alignment of like parts for operations. In this word problem, the shopper's fruit weights of 2⅔ pounds and 1⅓ pounds must be added to find the total weight. The correct answer is choice B (4 pounds) because when we add the whole numbers (2 + 1 = 3) and the fractions (⅔ + ⅓ = ³/₃ = 1), we get 3 + 1 = 4 pounds. Choice C (3⅔ pounds) is incorrect because it fails to recognize that the fractions add up to a whole number, keeping the fractional part instead of converting it. To improve, students should always simplify fractions and recognize when fractional parts combine to make whole numbers, converting improper fractions accordingly.