Elementary School Math Quiz: Compare Fractions With Unlike Parts

20 questions · exam conditions

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Compare Fractions With Unlike PartsQuestion 1 of 20

Jamal poured $\frac{4}{9}$ liter of water. Sofia poured $\frac{3}{7}$ liter of water into the same-sized bottle. Who poured more water?

You cannot compare because the denominators are different.

Sofia

Jamal

They poured the same amount.

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Elementary School Math Quiz

Elementary School Math Quiz: Compare Fractions With Unlike Parts

Practice Compare Fractions With Unlike Parts in Elementary School 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 Compare Fractions With Unlike Parts, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School 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

Jamal poured $\frac{4}{9}$ liter of water. Sofia poured $\frac{3}{7}$ liter of water into the same-sized bottle. Who poured more water?

You cannot compare because the denominators are different.
Sofia
Jamal (correct answer)
They poured the same amount.

Explanation: This question tests 4th grade ability to compare two fractions with different numerators and different denominators, using strategies like creating common denominators, common numerators, or comparing to benchmark fraction 1/2, recognizing comparisons are valid only when fractions refer to same whole (CCSS.4.NF.2). To compare fractions with different numerators and denominators, we can use several strategies. Common denominators: convert both fractions to the same denominator, then compare numerators (larger numerator = greater fraction). Common numerators: if numerators are the same, the fraction with the SMALLER denominator is GREATER (fewer parts means bigger pieces). Benchmark 1/2: compare each fraction to 1/2—if one is less than 1/2 and the other is greater than 1/2, you immediately know which is bigger. To compare 4/9 and 3/7, we can find common denominator 63, converting to 28/63 and 27/63, allowing direct comparison. Choice A is correct because using common denominators: 4/9 = 28/63 and 3/7 = 27/63, comparing numerators shows 28 > 27, so Jamal poured more. This demonstrates correct fraction comparison. Choice D represents assuming you cannot compare because denominators are different, which happens when students don't know conversion strategies. To help students: Practice all three strategies. For common denominators, find LCM or multiply denominators, convert both fractions, compare numerators. For common numerators (2/3 vs 2/5), emphasize: same numerator means same NUMBER of pieces, so smaller denominator = BIGGER pieces = greater fraction (thirds are bigger than fifths). For benchmark 1/2, teach how to identify: if numerator × 2 = denominator (or close), fraction is about 1/2. Use visual models with SAME-SIZED wholes to show why comparisons must use same whole. Number lines help visualize: farther right = greater. Watch for: reversing > and < symbols, comparing only numerators or only denominators without strategy, thinking larger denominator always means larger fraction, and not recognizing fractions must refer to same whole to compare.

Question 2

Maya ate $\frac{3}{8}$ of a pizza. Carlos ate $\frac{2}{5}$ of the same-sized pizza. Who ate more?

Maya
Carlos (correct answer)
They ate the same amount
Cannot be determined without knowing how many slices each pizza was cut into

Explanation: The correct answer is B, Carlos, because

\frac{2}{5} = 0.4

and

\frac{3}{8} = 0.375

, so Carlos ate the larger share. Choice A picks Maya, who actually ate less. Choice C is incorrect since the two amounts are not equal. Choice D is unnecessary because the fractions themselves, not the number of slices, tell us how much of the whole pizza each person ate.

Question 3

Which symbol correctly compares $\frac{2}{3}$ and $\frac{3}{5}$ ?

#ERROR!
≈
(correct answer)
<

Explanation: Rewriting both fractions with a common denominator of 15 gives

\frac{10}{15}

and

\frac{9}{15}

, so

\frac{2}{3}

is greater than

\frac{3}{5}

. Choice A is incorrect because the two fractions do not have equal value once compared with a common denominator. Choice B is incorrect because an exact comparison is possible here; the fractions are not merely close in value. Choice D reverses the true relationship between the two fractions. Choice C correctly shows that

\frac{2}{3}

is the greater fraction.

Question 4

Use the benchmark $\frac{1}{2}$ to compare. Which symbol makes the comparison true: $\frac{4}{11}$ $\underline{\hspace{2em}}$ $\frac{3}{5}$ ?

Cannot compare because 11 is larger than 5.
#ERROR!
< (correct answer)

Explanation: Choice C is correct because 4/11 is less than 1/2 while 3/5 is greater than 1/2, so 4/11 is less than 3/5. Choice A is incorrect because the two fractions can be compared using the benchmark of 1/2 even though their denominators differ. Choice B is incorrect because the two fractions are not equal. Choice D is incorrect because it reverses the correct direction of the comparison.

Question 5

Tommy ran $\frac{3}{4}$ of a mile on Monday and $\frac{4}{5}$ of a mile on Tuesday. On which day did he run farther?

Monday
They ran equal distances
Tuesday (correct answer)
Cannot be determined without a common denominator

Explanation: Tuesday is correct because

\frac{4}{5} = \frac{16}{20}

and

\frac{3}{4} = \frac{15}{20}

, and

\frac{16}{20} > \frac{15}{20}

. Monday is incorrect because it reverses the true comparison. They ran equal distances is incorrect because the two fractions are not equal. Cannot be determined is incorrect because both fractions can be compared directly using a common denominator.

Question 6

Ben's mom gave him two identical granola bars. He ate $\frac{7}{10}$ of the first bar before recess and $\frac{2}{3}$ of the second bar after recess. Compare the amounts Ben ate using the correct inequality symbol.

$\frac{7}{10} > \frac{2}{3}$ because $\frac{21}{30} > \frac{20}{30}$ with a common denominator of 30 (correct answer)
$\frac{2}{3} > \frac{7}{10}$ because $\frac{20}{30} > \frac{21}{30}$ with a common denominator of 30
$\frac{7}{10} = \frac{2}{3}$ because both fractions are less than 1 whole
$\frac{7}{10} > \frac{2}{3}$ because $7 + 10 = 17$ is greater than $2 + 3 = 5$

Explanation: Using a common denominator of 30,

\frac{7}{10} = \frac{21}{30}

and

\frac{2}{3} = \frac{20}{30}

. Since

21 > 20

\frac{7}{10} > \frac{2}{3}

. Choice B reverses the comparison. Choice C is incorrect because being less than one whole does not mean two fractions are equal. Choice D adds numerators and denominators together, which is not a valid way to compare fractions.

Question 7

Which comparison is true?

$\frac{1}{3} > \frac{3}{10}$ (correct answer)
$\frac{1}{3} < \frac{3}{10}$
$\frac{1}{3} = \frac{3}{10}$
$\frac{1}{3}$ and $\frac{3}{10}$ cannot be compared because their denominators are different.

Explanation: Rewriting with a common denominator of 30 gives

\frac{10}{30}

and

\frac{9}{30}

. Since

10 > 9

\frac{1}{3} > \frac{3}{10}

. Choice B reverses the comparison. Choice C is incorrect since the fractions are not equal. Choice D is incorrect because fractions with different denominators can always be compared once rewritten with a common denominator.

Question 8

Maria ate $\frac{3}{8}$ of her pizza and Jake ate $\frac{2}{5}$ of his pizza. Both pizzas were the same size. Who ate more pizza?

Maria ate more pizza
Jake ate more pizza (correct answer)
They ate the same amount
It cannot be determined

Explanation: Jake ate more pizza because

\frac{2}{5} > \frac{3}{8}

when written with a common denominator. Maria ate more pizza is incorrect because her fraction is smaller. They ate the same amount is incorrect because the two fractions are not equal. It cannot be determined is incorrect because both pizzas are the same size, so the fractions can be compared directly.

Question 9

Lisa's water bottle holds 1 liter. She drank $\frac{4}{7}$ of the water during math class and $\frac{3}{5}$ of the water during science class from two identical bottles. In which class did she drink more water?

Math class, because $\frac{4}{7} > \frac{3}{5}$ when converted to thirty-fifths: $\frac{20}{35} > \frac{21}{35}$
They are equal amounts because $\frac{4}{7}$ and $\frac{3}{5}$ both equal $\frac{12}{21}$ when simplified
Math class, because 4 is greater than 3 in the numerators of the fractions
Science class, because $\frac{3}{5} > \frac{4}{7}$ when converted to thirty-fifths: $\frac{21}{35} > \frac{20}{35}$ (correct answer)

Explanation: Converting both fractions to thirty-fifths shows that 4/7 equals 20/35 and 3/5 equals 21/35, and since 21/35 is greater than 20/35, Lisa drank more water during science class, making Choice D correct. Choice A reverses the comparison, since 20/35 is actually less than 21/35, not greater. Choice B is incorrect because 4/7 and 3/5 are not equal amounts once converted to a common denominator. Choice C compares only the numerators, which ignores the different denominators and does not correctly compare the two fractions.

Question 10

Compare the fractions $\frac{3}{5}$ and $\frac{7}{12}$ . Which comparison is correct?

$\frac{3}{5} < \frac{7}{12}$
$\frac{3}{5} > \frac{7}{12}$ (correct answer)
$\frac{3}{5} = \frac{7}{12}$
Cannot be compared

Explanation: Rewriting both fractions with a common denominator of 60 gives

\frac{36}{60}

and

\frac{35}{60}

, so

\frac{3}{5}

is greater than

\frac{7}{12}

. Choice A reverses the true relationship between the two fractions. Choice C is incorrect because the two fractions convert to different values once given a common denominator. Choice D is incorrect because any two fractions can always be compared using a common denominator. Choice B correctly shows that

\frac{3}{5}

is the greater fraction.

Question 11

Look at the fraction models below. Rectangle A is divided into 6 equal parts with 4 parts shaded. Rectangle B is divided into 8 equal parts with 5 parts shaded. Both rectangles are the same size. Which comparison is correct?

$\frac{4}{6} > \frac{5}{8}$ because $\frac{16}{24} > \frac{15}{24}$ when using equivalent fractions (correct answer)
$\frac{5}{8} > \frac{4}{6}$ because $\frac{15}{24} > \frac{16}{24}$ when using equivalent fractions
$\frac{4}{6} = \frac{5}{8}$ because both fractions are greater than $\frac{1}{2}$ of their wholes
$\frac{5}{8} > \frac{4}{6}$ because 5 parts is more than 4 parts in any rectangle

Explanation: To compare

\frac{4}{6}

and

\frac{5}{8}

, find a common denominator. The LCD of 6 and 8 is 24.

\frac{4}{6} = \frac{16}{24}

and

\frac{5}{8} = \frac{15}{24}

. Since

\frac{16}{24} > \frac{15}{24}

, Rectangle A has more shaded area. Choice B incorrectly calculates the comparison of equivalent fractions. Choice C incorrectly concludes the fractions are equal. Choice D makes the error of comparing numerators without considering the different denominators.

Question 12

At the school carnival, Alex ate $\frac{2}{3}$ of a chocolate bar and $\frac{5}{9}$ of a candy apple. The chocolate bar and candy apple were the same size originally. Which symbol makes this comparison statement true? $\frac{2}{3}$ $\underline{\hspace{2em}}$ $\frac{5}{9}$

$>$ , because $\frac{2}{3} = \frac{6}{9}$ and $\frac{6}{9} > \frac{5}{9}$ (correct answer)
$<$ , because $\frac{2}{3} = \frac{6}{9}$ and $\frac{6}{9} < \frac{5}{9}$
$=$ , because $\frac{2}{3}$ and $\frac{5}{9}$ simplify to the same fraction
$<$ , because comparing only the numerators, $2 < 5$

Explanation: The correct answer is A because rewriting

\frac{2}{3}

\frac{6}{9}

gives a common denominator, and

\frac{6}{9} > \frac{5}{9}

. Choice B applies the same conversion but flips the inequality the wrong way. Choice C is incorrect since

\frac{6}{9}

and

\frac{5}{9}

are not the same value. Choice D compares numerators alone without matching denominators first, which is not a valid way to compare fractions.

Question 13

Jamal poured $\frac{4}{7}$ of a pitcher of lemonade. Sofia poured $\frac{3}{5}$ of the same-sized pitcher. Which symbol makes the comparison true: $\frac{4}{7}$ $\underline{\hspace{2em}}$ $\frac{3}{5}$ ?

< (correct answer)
#ERROR!
≥

Explanation: 4/7 < 3/5 because 4/7 ≈ 0.57 and 3/5 = 0.6, and 0.57 is less than 0.6. Choice B reverses the comparison. Choice C is wrong because the two fractions are not equal. Choice D combines "greater than" with "equal to," neither of which fits here.

Question 14

Sara completed $\frac{5}{12}$ of her homework before dinner and $\frac{3}{8}$ of her homework after dinner. Which statement correctly compares these amounts using the benchmark fraction $\frac{1}{2}$ ?

$\frac{3}{8} > \frac{5}{12}$
$\frac{5}{12} = \frac{3}{8}$
$\frac{5}{12} > \frac{3}{8}$ (correct answer)
It cannot be determined without more information

Explanation:

\frac{5}{12} > \frac{3}{8}

is correct because both fractions are less than

\frac{1}{2}

, but

\frac{5}{12}

is closer to

\frac{1}{2}

\frac{3}{8} > \frac{5}{12}

is incorrect because it reverses the true relationship. The equals statement is incorrect because the two fractions are not equal. It cannot be determined is incorrect because both fractions can be compared directly using the benchmark.

Question 15

In art class, two students painted identical canvases. Maya painted $\frac{5}{8}$ of her canvas blue, and Carlos painted $\frac{3}{4}$ of his canvas blue. Who painted a larger blue area?

Maya painted more because $\frac{5}{8} > \frac{3}{4}$ when both are converted to eighths
Maya painted more because she used 5 parts while Carlos only used 3 parts
They painted equal amounts because $\frac{5}{8} = \frac{3}{4}$ when simplified to lowest terms
Carlos painted more because $\frac{3}{4} > \frac{5}{8}$ when both are converted to eighths (correct answer)

Explanation: When comparing fractions, you need to find a common denominator to see which is actually larger. Since Maya and Carlos painted identical canvases, you're comparing

\frac{5}{8}

and

\frac{3}{4}

of the same size canvas. To compare these fractions, convert them to the same denominator. Since 8 is a multiple of 4, use eighths as your common denominator. Maya already painted

\frac{5}{8}

, so no conversion needed. For Carlos:

\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}

. Now you can compare:

\frac{5}{8}

versus

\frac{6}{8}

. Since

\frac{6}{8} > \frac{5}{8}

, Carlos painted more blue area. This makes choice D correct. Choice A incorrectly states that

\frac{5}{8} > \frac{3}{4}

, but as we saw,

\frac{5}{8} = \frac{5}{8}

while

\frac{3}{4} = \frac{6}{8}

, so this comparison is backwards. Choice B makes the mistake of only looking at the numerators (5 vs. 3) without considering that the denominators are different - you can't compare parts without knowing the size of the whole. Choice C incorrectly claims the fractions are equal, but

\frac{5}{8}

and

\frac{6}{8}

are clearly different amounts. Remember: when comparing fractions, always convert to a common denominator first. Don't just compare numerators when denominators differ - the "pieces" aren't the same size!

Question 16

Sofia walked $\frac{3}{10}$ of a mile. Chen walked $\frac{4}{9}$ of a mile. Who walked farther?

There is not enough information to tell
Sofia
Chen (correct answer)
They walked the same distance

Explanation: Chen walked farther because 4/9 is greater than 3/10. As decimals, 4/9 is about 0.44 and 3/10 is 0.3, so 4/9 is larger. Choice A is wrong because both distances are known and can be compared directly. Choice B reverses which student walked farther. Choice D is incorrect because the two fractions are not equal.

Question 17

Maya ate $\frac{3}{8}$ of a pizza. Carlos ate $\frac{2}{5}$ of the same-sized pizza. Who ate more?

Maya
They ate the same amount.
Carlos (correct answer)
You cannot compare without changing both fractions to decimals.

Explanation: The correct answer is C, Carlos. Rewriting both fractions with a common denominator of 40 shows Maya ate 15/40 of the pizza and Carlos ate 16/40, so Carlos ate slightly more. Choice A reverses which person ate more. Choice B is incorrect because the two fractions are not equal. Choice D is incorrect because fractions can be compared directly by finding a common denominator, without switching to decimals.

Question 18

Which symbol makes this comparison true: $\frac{1}{4}$ $\underline{\hspace{2em}}$ $\frac{3}{10}$ ?

#ERROR!
< (correct answer)
They are both greater than $\frac{1}{2}$

Explanation: Converting to a common denominator of 20:

\frac{1}{4} = \frac{5}{20}

and

\frac{3}{10} = \frac{6}{20}

. Since

5 < 6

\frac{1}{4} < \frac{3}{10}

. Choice A is incorrect because the fractions are not equal. Choice C is incorrect: both fractions are actually less than

\frac{1}{2}

, not greater. Choice D reverses the comparison.

Question 19

Which fraction is greater: $\frac{5}{12}$ or $\frac{3}{7}$ ?

$\frac{5}{12}$
$\frac{3}{7}$ (correct answer)
$\frac{1}{2}$
They are equal

Explanation: Both

\frac{5}{12}

and

\frac{3}{7}

are less than the benchmark

\frac{1}{2}

, so comparing each to

\frac{1}{2}

alone doesn't settle it. Cross-multiplying shows

5 \times 7 = 35

and

3 \times 12 = 36

, and since

36 > 35

\frac{3}{7} > \frac{5}{12}

. Choice A reverses the comparison. Choice C picks the benchmark itself rather than one of the two fractions being compared. Choice D is incorrect because the two fractions are not equal.

Question 20

Use common denominators to compare the fractions. Which symbol makes the comparison true: $\frac{2}{3}$ $\underline{\hspace{2em}}$ $\frac{3}{4}$ ?

< (correct answer)
#ERROR!
Cannot be determined without converting to decimals

Explanation: The correct answer is A because using twelfths as a common denominator,

\frac{2}{3} = \frac{8}{12}

and

\frac{3}{4} = \frac{9}{12}

, and

\frac{8}{12} < \frac{9}{12}

. Choice B is incorrect since the two fractions are not equal. Choice C reverses the true relationship. Choice D is unnecessary since common denominators, as the stem directs, are enough to compare the fractions directly.