ISEE Middle Level Quiz: Fraction And Mixed Number Sums

20 questions · exam conditions

0:00

Fraction And Mixed Number SumsQuestion 1 of 20

A recipe for a batch of muffins requires a total of $4\frac{1}{2}$ cups of dry ingredients. The recipe calls for $1\frac{3}{4}$ cups of flour and $1\frac{1}{3}$ cups of sugar. After adding the flour and sugar, how many cups of other ingredients are needed?

1\frac{5}{12}

1\frac{13}{14}

2\frac{1}{6}

3\frac{1}{12}

← Back to quizzes

ISEE Middle Level Quiz

ISEE Middle Level Quiz: Fraction And Mixed Number Sums

Practice Fraction And Mixed Number Sums 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 Fraction And Mixed Number Sums, 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

$1\frac{5}{12}$ (correct answer)
$1\frac{13}{14}$
$2\frac{1}{6}$
$3\frac{1}{12}$

Explanation: First, find the combined amount of flour and sugar:

1\frac{3}{4} + 1\frac{1}{3}

. The common denominator is 12. The sum is

1\frac{9}{12} + 1\frac{4}{12} = 2\frac{13}{12}

, which simplifies to

3\frac{1}{12}

cups. Next, subtract this amount from the total amount of ingredients:

4\frac{1}{2} - 3\frac{1}{12}

. The common denominator is 12. The difference is

4\frac{6}{12} - 3\frac{1}{12} = 1\frac{5}{12}

cups.

Question 2

A ribbon is $8\frac{1}{4}$ meters long. A piece measuring $3\frac{2}{3}$ meters is cut from it. What is the length of the remaining ribbon?

$4\frac{7}{12}$ meters (correct answer)
$4\frac{5}{12}$ meters
$5\frac{5}{12}$ meters
$11\frac{11}{12}$ meters

Explanation: To find the length of the remaining ribbon, subtract the length of the cut piece from the original length:

8\frac{1}{4} - 3\frac{2}{3}

. The least common denominator for 4 and 3 is 12. Convert the fractions:

8\frac{3}{12} - 3\frac{8}{12}

. Since

\frac{3}{12}

is smaller than

\frac{8}{12}

, you need to borrow from the 8:

7\frac{15}{12} - 3\frac{8}{12} = 4\frac{7}{12}

. The remaining ribbon is

4\frac{7}{12}

meters long.

Question 3

Over three days, a cyclist rode a total of 30 miles. On the first day, she rode $9\frac{1}{2}$ miles. On the second day, she rode $11\frac{3}{5}$ miles. How many miles did she ride on the third day?

$8\frac{9}{10}$ (correct answer)
$9\frac{1}{10}$
$9\frac{3}{7}$
$21\frac{1}{10}$

Explanation: First, find the total distance ridden on the first two days:

9\frac{1}{2} + 11\frac{3}{5}

. The common denominator is 10. The sum is

9\frac{5}{10} + 11\frac{6}{10} = 20\frac{11}{10}

, which is

21\frac{1}{10}

miles. To find the distance for the third day, subtract this from the total:

30 - 21\frac{1}{10}

. Rewrite 30 as

29\frac{10}{10}

. Then,

29\frac{10}{10} - 21\frac{1}{10} = 8\frac{9}{10}

Question 4

What number must be added to $3\frac{2}{5}$ to obtain a sum of $7\frac{1}{3}$ ?

$3\frac{14}{15}$ (correct answer)
$4\frac{1}{15}$
$4\frac{1}{2}$
$10\frac{11}{15}$

Explanation: This problem requires finding the difference between the two numbers:

7\frac{1}{3} - 3\frac{2}{5}

. The least common denominator for 3 and 5 is 15. Convert the fractions:

7\frac{5}{15} - 3\frac{6}{15}

. Since

\frac{5}{15}

is less than

\frac{6}{15}

, you must borrow from the 7:

6\frac{20}{15} - 3\frac{6}{15} = 3\frac{14}{15}

Question 5

A water jug has a capacity of 3 liters. If it already contains $1\frac{1}{4}$ liters of water, how much more water must be added to fill it to exactly $2\frac{1}{2}$ liters?

$3\frac{3}{4}$ liters
$\frac{1}{2}$ liter
$1\frac{3}{4}$ liters
$1\frac{1}{4}$ liters (correct answer)

Explanation: This is a subtraction problem involving mixed numbers. When you see questions asking "how much more is needed," you're finding the difference between what you want and what you currently have. You need to subtract the current amount from the target amount:

2\frac{1}{2} - 1\frac{1}{4}

. To subtract mixed numbers, you can work with the whole numbers and fractions separately, but first make sure the fractions have common denominators. Convert

2\frac{1}{2}

2\frac{2}{4}

so both fractions have denominator 4. Now subtract:

2\frac{2}{4} - 1\frac{1}{4} = (2-1) + (\frac{2}{4} - \frac{1}{4}) = 1 + \frac{1}{4} = 1\frac{1}{4}

liters. Let's examine why the other answers are incorrect. Choice A (

3\frac{3}{4}

liters) likely comes from adding the current amount to the target amount instead of finding their difference. Choice B (

\frac{1}{2}

liter) might result from subtracting whole numbers only (2-1 = 1) then incorrectly handling the fraction part. Choice C (

1\frac{3}{4}

liters) could come from adding the fractions incorrectly (

\frac{1}{2} + \frac{1}{4} = \frac{3}{4}

) while correctly subtracting whole numbers. When solving "how much more" problems, always set up the subtraction as (target amount) - (current amount). Double-check by adding your answer to the current amount—you should get the target amount. Here:

1\frac{1}{4} + 1\frac{1}{4} = 2\frac{2}{4} = 2\frac{1}{2}

✓

Question 6

On Monday, a seedling was $3\frac{1}{4}$ inches tall. By Wednesday, it had grown $1\frac{1}{8}$ inches. By Friday, it had grown another $\frac{3}{4}$ of an inch. What was the total height of the seedling on Friday?

$4\frac{3}{8}$ inches
$5\frac{1}{8}$ inches (correct answer)
$4\frac{5}{16}$ inches
$1\frac{7}{8}$ inches

Explanation: This problem tests your ability to add mixed numbers, which requires finding common denominators and carefully tracking whole numbers and fractions. To find the seedling's final height, you need to add all three measurements: the starting height plus both growth amounts. Start with

3\frac{1}{4} + 1\frac{1}{8} + \frac{3}{4}

. First, convert all fractions to the same denominator. The least common denominator of 4 and 8 is 8, so:

3\frac{2}{8} + 1\frac{1}{8} + \frac{6}{8}

. Now add the whole numbers:

3 + 1 = 4

. Then add the fractions:

\frac{2}{8} + \frac{1}{8} + \frac{6}{8} = \frac{9}{8}

. Since

\frac{9}{8} = 1\frac{1}{8}

, add this to the whole number part:

4 + 1\frac{1}{8} = 5\frac{1}{8}

inches. Answer A (

4\frac{3}{8}

) likely results from incorrectly adding the fractions as

\frac{2+1+6}{8} = \frac{9}{8}

but then converting

\frac{9}{8}

\frac{3}{8}

instead of

1\frac{1}{8}

. Answer C (

4\frac{5}{16}

) comes from using 16 as the common denominator but making calculation errors. Answer D (

1\frac{7}{8}

) represents adding only the fractional parts while ignoring the whole numbers entirely. When adding mixed numbers, always convert to common denominators first, add separately (whole numbers, then fractions), and remember to carry over when your fraction sum exceeds one whole. Double-check by ensuring your final answer is reasonable given the original measurements.

Question 7

For a class party, Sarah brought $2\frac{1}{4}$ cheese pizzas and Leo brought $1\frac{1}{2}$ pepperoni pizzas. If the class ate a total of $3\frac{1}{8}$ pizzas, what fraction of a pizza was left over?

$\frac{5}{24}$
$\frac{5}{8}$ (correct answer)
$3\frac{3}{4}$
$6\frac{7}{8}$

Explanation: This problem tests your ability to work with mixed numbers and fractions in a real-world context. When you see a word problem involving adding and subtracting mixed numbers, organize the information first: what came in, what went out, and what's left. Start by finding the total pizzas brought:

2\frac{1}{4} + 1\frac{1}{2}

. Convert to a common denominator of 4:

2\frac{1}{4} + 1\frac{2}{4} = 3\frac{3}{4}

pizzas total. Since the class ate

3\frac{1}{8}

pizzas, subtract this from the total:

3\frac{3}{4} - 3\frac{1}{8}

. Convert to eighths:

3\frac{6}{8} - 3\frac{1}{8} = \frac{5}{8}

pizza left over. Choice A (

\frac{5}{24}

) likely comes from incorrectly using 24 as a common denominator when converting fractions, then making calculation errors. Choice C (

3\frac{3}{4}

) is the total amount brought, not what's left after eating. This is a common trap - students sometimes identify an intermediate step as the final answer. Choice D (

6\frac{7}{8}

) results from adding all the given numbers together instead of recognizing that you need to subtract what was eaten from what was brought. Remember to always identify what the question is actually asking for. In "how much is left" problems, you're looking for the difference between what you started with and what was used or consumed. Set up the problem as: Total brought - Total eaten = Amount remaining.

Question 8

A carpenter has a wooden plank that is 10 feet long. He cuts off a piece that is $4\frac{1}{3}$ feet long and another piece that is $2\frac{1}{2}$ feet long. What is the length of the remaining plank?

$6\frac{5}{6}$ feet
$3\frac{3}{5}$ feet
$4\frac{1}{6}$ feet
$3\frac{1}{6}$ feet (correct answer)

Explanation: This problem tests your ability to subtract mixed numbers, which requires careful handling of fractions with different denominators. To find the remaining plank length, you need to subtract both cut pieces from the original 10-foot plank:

10 - 4\frac{1}{3} - 2\frac{1}{2}

First, convert the mixed numbers to improper fractions or work with them systematically. Let's combine the pieces being cut off:

4\frac{1}{3} + 2\frac{1}{2}

To add these mixed numbers, find a common denominator for the fractions. The LCD of 3 and 2 is 6:

$4\frac{1}{3} = 4\frac{2}{6}$
$2\frac{1}{2} = 2\frac{3}{6}$

Adding:

4\frac{2}{6} + 2\frac{3}{6} = 6\frac{5}{6}

Now subtract from the original length:

10 - 6\frac{5}{6} = 9\frac{6}{6} - 6\frac{5}{6} = 3\frac{1}{6}

feet. Choice A (

6\frac{5}{6}

) represents the total length cut off, not what remains. Choice B (

3\frac{3}{5}

) results from incorrectly adding the fractional parts without finding a common denominator. Choice C (

4\frac{1}{6}

) comes from a calculation error, likely subtracting only one of the cut pieces or making an arithmetic mistake. When working with mixed number subtraction problems, always double-check that your answer makes logical sense—the remaining piece should be smaller than the original, and your fractions should use the correct common denominator throughout your calculations.

Question 9

If $m - 1\frac{5}{8} = 3\frac{1}{2} + 1\frac{3}{4}$ , what is the value of $m$ ?

$6\frac{7}{8}$ (correct answer)
$3\frac{5}{8}$
$5\frac{1}{4}$
$6\frac{7}{24}$

Explanation: First, evaluate the right side of the equation:

3\frac{1}{2} + 1\frac{3}{4}

. The common denominator is 4. The sum is

3\frac{2}{4} + 1\frac{3}{4} = 4\frac{5}{4}

, which is

5\frac{1}{4}

. The equation is now

m - 1\frac{5}{8} = 5\frac{1}{4}

. To find

m

, add

1\frac{5}{8}

to both sides:

m = 5\frac{1}{4} + 1\frac{5}{8}

. The common denominator is 8. The sum is

m = 5\frac{2}{8} + 1\frac{5}{8} = 6\frac{7}{8}

Question 10

What is the result of subtracting $1\frac{1}{6}$ from the sum of $2\frac{3}{4}$ and $1\frac{1}{2}$ ?

$3\frac{1}{12}$ (correct answer)
$3\frac{1}{4}$
$4\frac{1}{4}$
$5\frac{5}{12}$

Explanation: First, find the sum of

2\frac{3}{4}

and

1\frac{1}{2}

. The common denominator is 4. The sum is

2\frac{3}{4} + 1\frac{2}{4} = 3\frac{5}{4}

, which simplifies to

4\frac{1}{4}

. Next, subtract

1\frac{1}{6}

from this sum:

4\frac{1}{4} - 1\frac{1}{6}

. The common denominator for 4 and 6 is 12. The expression becomes

4\frac{3}{12} - 1\frac{2}{12} = 3\frac{1}{12}

Question 11

A recipe uses $1\ 2/3$ cups sugar, then you add $1/3$ cup more. What is the sum?

$2$ (correct answer)
$1\ 3/6$
$1\ 1/3$
$2/6$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 1 2/3 + 1/3 = 5/3 + 1/3 = 6/3 = 2. Choice B is incorrect due to a common arithmetic error where fractions were not simplified. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 12

On a road trip, you drive $2\ 2/5$ hours, then take a $3/5$ hour detour. After adding, how long?

$3$ (correct answer)
$2\ 1/5$
$2\ 5/10$
$5/10$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 2 2/5 + 3/5 = 12/5 + 3/5 = 15/5 = 3. Choice B is incorrect due to a common arithmetic error where the whole numbers were mishandled. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 13

On a road trip, combine these distances: $1/2$ mile, $1/4$ mile, and $2\ 1/2$ miles. Total?

$3\ 1/4$ (correct answer)
$2\ 3/4$
$3\ 2/4$
$3/6$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 1/2 + 1/4 + 2 1/2 = 2/4 + 1/4 + 10/4 = 13/4 = 3 1/4. Choice B is incorrect due to a common arithmetic error where the numerators were added directly without a common denominator. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 14

In a garden, you plant $1\ 1/4$ rows of carrots and $1/2$ row of lettuce. What is the sum?

$1\ 3/4$ (correct answer)
$1\ 2/4$
$2\ 1/4$
$2/6$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 1 1/4 + 1/2 = 5/4 + 2/4 = 7/4 = 1 3/4. Choice B is incorrect due to a common arithmetic error where the fractions were not properly simplified. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 15

On a trip, you traveled $3\ 1/2$ miles, then drove $1/4$ mile more. After adding, how far?

$3\ 3/4$ (correct answer)
$3\ 2/6$
$4\ 1/4$
$4/6$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 3 1/2 + 1/4 = 14/4 + 1/4 = 15/4 = 3 3/4. Choice B is incorrect due to a common arithmetic error where the fractions were not converted properly. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 16

For a birdhouse roof, you need $1\ 3/5$ feet, but you subtract $4/5$ foot for a notch. Result?

$4/5$ (correct answer)
$1\ 7/5$
$2\ 2/5$
$1/5$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 1 3/5 - 4/5 = 8/5 - 4/5 = 4/5. Choice B is incorrect due to a common arithmetic error where borrowing was mishandled. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 17

Cooking soup, you have $2\ 1/8$ cups broth and add $5/8$ cup. What is the sum?

$2\ 3/4$ (correct answer)
$2\ 6/16$
$3\ 1/4$
$7/16$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 2 1/8 + 5/8 = 17/8 + 5/8 = 22/8 = 2 3/4. Choice B is incorrect due to a common arithmetic error where simplification was not done. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 18

In a garden, you have $3\ 1/6$ bags of soil and use $5/6$ bag. If you subtract, what remains?

$2\ 1/3$ (correct answer)
$3\ 2/3$
$2\ 2/6$
$8/36$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 3 1/6 - 5/6 = 19/6 - 5/6 = 14/6 = 2 1/3. Choice B is incorrect due to a common arithmetic error where subtraction was done incorrectly. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 19

On a road trip, you drove $1\ 7/8$ hours, then drove $1/8$ hour more. After adding, how long?

$2$ (correct answer)
$1\ 8/8$
$1\ 3/4$
$2/16$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 1 7/8 + 1/8 = 15/8 + 1/8 = 16/8 = 2. Choice B is incorrect due to a common arithmetic error where the whole number was not carried over. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.

Question 20

While baking, you use $1\ 1/2$ cups flour, then add $3/4$ cup more. After adding, how much flour?

$2\ 1/4$ (correct answer)
$2\ 1/2$
$1\ 5/8$
$4/6$

Explanation: This question tests the ISEE Middle Level skill of adding or subtracting fractions and mixed numbers. Understanding how to perform operations with fractions and mixed numbers is critical in problem-solving and real-world applications. In the given problem, converting fractions to a common denominator or mixed numbers to improper fractions is necessary to simplify calculations. The correct answer, Choice A, accurately combines the fractions/mixed numbers using proper methods and simplification, as 1 1/2 + 3/4 = 3/2 + 3/4 = 6/4 + 3/4 = 9/4 = 2 1/4. Choice B is incorrect due to a common arithmetic error where the numerators were added directly without a common denominator. To help students master this skill, teach them to always find a common denominator first and check their work by simplifying results. Encourage practice with real-world scenarios to see the relevance of fractions and mixed numbers.