Compare Fractions With Unlike Parts - 4th Grade Math

Maya ate $\frac{3}{8}$ of a pizza. Carlos ate $\frac{2}{5}$ of the same-sized pizza. Who ate more?
Answer: Carlos 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.
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: $\frac{4}{7}$ $\underline{\hspace{2em}}$ $\frac{3}{5}$ ?
Answer: < 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.
Use a common denominator to compare. Which fraction is greater: $\frac{2}{9}$ or $\frac{1}{4}$ ?
Answer: $\frac{1}{4}$ 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 2/9 and 1/4, we can find common denominator 36, converting to 8/36 and 9/36. Choice B is correct because using common denominators: 2/9 = 8/36 and 1/4 = 9/36, comparing numerators shows 8 < 9 so 2/9 < 1/4, meaning 1/4 is greater. Choice A represents reversed comparison, which happens when students compare numerators only. 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.
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? $\frac{2}{3}$ $\underline{\hspace{2em}}$ $\frac{5}{9}$
Answer: $>$ , because $\frac{2}{3} = \frac{6}{9}$ and $\frac{6}{9} > \frac{5}{9}$ The correct answer is A because rewriting $\frac{2}{3}$ as $\frac{6}{9}$ 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.
Which comparison is true?
Answer: $\frac{1}{3} > \frac{3}{10}$ 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.
Use common denominators to compare the fractions. Which symbol makes the comparison true: $\frac{2}{3}$ $\underline{\hspace{2em}}$ $\frac{3}{4}$ ?
Answer: < 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.
Maya ate $\frac{3}{8}$ of a pizza. Carlos ate $\frac{2}{5}$ of the same-sized pizza. Who ate more?
Answer: Carlos 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.
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?
Answer: Jake ate more pizza 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.
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.
Answer: $\frac{7}{10} > \frac{2}{3}$ because $\frac{21}{30} > \frac{20}{30}$ with a common denominator of 30 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.
Sofia walked $\frac{3}{10}$ of a mile. Chen walked $\frac{4}{9}$ of a mile. Who walked farther?
Answer: Chen 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.
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 $\frac{1}{2}$ ?
Answer: $\frac{5}{12} > \frac{3}{8}$ $\frac{5}{12} > \frac{3}{8}$ 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.
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?
Answer: Carlos painted more because $\frac{3}{4} > \frac{5}{8}$ when both are converted to eighths 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!
Which symbol correctly compares $\frac{2}{3}$ and $\frac{3}{5}$ ?
Answer: > 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.
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?
Answer: Jamal 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.
Which symbol makes this comparison true: $\frac{1}{4}$ $\underline{\hspace{2em}}$ $\frac{3}{10}$ ?
Answer: < 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.
Which fraction is greater: $\frac{5}{12}$ or $\frac{3}{7}$ ?
Answer: $\frac{3}{7}$ 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.
Use the benchmark $\frac{1}{2}$ to compare $\frac{3}{7}$ and $\frac{5}{11}$ . Which statement is true?
Answer: $\frac{3}{7} < \frac{5}{11}$ $\frac{3}{7} < \frac{5}{11}$ is correct because $\frac{3}{7} \approx 0.43$ and $\frac{5}{11} \approx 0.45$ . The greater-than statement 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 $\frac{1}{2}$ .
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?
Answer: $\frac{4}{6} > \frac{5}{8}$ because $\frac{16}{24} > \frac{15}{24}$ when using equivalent fractions 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.
A recipe calls for 5/6 cup of flour, but Emma only has 7/9 cup available. Does she have enough flour for the recipe?
Answer: No, because 5/6 is greater than 7/9 Rewriting both fractions with a common denominator shows 5/6 is greater than 7/9, so Emma's 7/9 cup is not enough for the recipe. Choices A and C incorrectly conclude Emma has enough. Choice D compares the numerators alone without considering the denominators, which doesn't actually tell us which fraction is larger.
On the same number line from 0 to 1, which fraction is farther to the right (greater): $\frac{7}{10}$ or $\frac{2}{3}$ ?
Answer: $\frac{7}{10}$ 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 7/10 and 2/3, we can find common denominator 30, converting to 21/30 and 20/30. Choice A is correct because using common denominators: 7/10 = 21/30 and 2/3 = 20/30, comparing numerators shows 21 > 20 so 7/10 is greater and farther right on the number line. This demonstrates correct fraction comparison. Choice B represents thinking 2/3 is greater, which happens when students compare numerators only without accounting for denominators. 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.

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