All questions
Question 1
Jamal poured 94 liter of water. Sofia poured 73 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 83 of a pizza. Carlos ate 52 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 52=0.4 and 83=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 32 and 53?
- #ERROR!
- ≈
(correct answer)- <
Explanation: Rewriting both fractions with a common denominator of 15 gives 1510 and 159, so 32 is greater than 53. 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 32 is the greater fraction. Question 4
Use a common denominator to compare. Which fraction is greater: 92 or 41?
- 41 (correct answer)
- They are equal
- Not enough information
- 92
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 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.
Question 5
Use the benchmark 21 to compare. Which symbol makes the comparison true: 114 53?
- 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 6
Tommy ran 43 of a mile on Monday and 54 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 54=2016 and 43=2015, and 2016>2015. 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 7
Ben's mom gave him two identical granola bars. He ate 107 of the first bar before recess and 32 of the second bar after recess. Compare the amounts Ben ate using the correct inequality symbol.
- 107>32 because 3021>3020 with a common denominator of 30 (correct answer)
- 32>107 because 3020>3021 with a common denominator of 30
- 107=32 because both fractions are less than 1 whole
- 107>32 because 7+10=17 is greater than 2+3=5
Explanation: Using a common denominator of 30, 107=3021 and 32=3020. Since 21>20, 107>32. 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 8
Which comparison is true?
- 31>103 (correct answer)
- 31<103
- 31=103
- 31 and 103 cannot be compared because their denominators are different.
Explanation: Rewriting with a common denominator of 30 gives 3010 and 309. Since 10>9, 31>103. 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 9
Maria ate 83 of her pizza and Jake ate 52 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 52>83 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 10
Lisa's water bottle holds 1 liter. She drank 74 of the water during math class and 53 of the water during science class from two identical bottles. In which class did she drink more water?
- Math class, because 74>53 when converted to thirty-fifths: 3520>3521
- They are equal amounts because 74 and 53 both equal 2112 when simplified
- Math class, because 4 is greater than 3 in the numerators of the fractions
- Science class, because 53>74 when converted to thirty-fifths: 3521>3520 (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 11
Compare the fractions 53 and 127. Which comparison is correct?
- 53<127
- 53>127 (correct answer)
- 53=127
- Cannot be compared
Explanation: Rewriting both fractions with a common denominator of 60 gives 6036 and 6035, so 53 is greater than 127. 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 53 is the greater fraction. Question 12
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?
- 64>85 because 2416>2415 when using equivalent fractions (correct answer)
- 85>64 because 2415>2416 when using equivalent fractions
- 64=85 because both fractions are greater than 21 of their wholes
- 85>64 because 5 parts is more than 4 parts in any rectangle
Explanation: To compare 64 and 85, find a common denominator. The LCD of 6 and 8 is 24. 64=2416 and 85=2415. Since 2416>2415, 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 13
At the school carnival, Alex ate 32 of a chocolate bar and 95 of a candy apple. The chocolate bar and candy apple were the same size originally. Which symbol makes this comparison statement true? 32 95
- >, because 32=96 and 96>95 (correct answer)
- <, because 32=96 and 96<95
- =, because 32 and 95 simplify to the same fraction
- <, because comparing only the numerators, 2<5
Explanation: The correct answer is A because rewriting 32 as 96 gives a common denominator, and 96>95. Choice B applies the same conversion but flips the inequality the wrong way. Choice C is incorrect since 96 and 95 are not the same value. Choice D compares numerators alone without matching denominators first, which is not a valid way to compare fractions. Question 14
Jamal poured 74 of a pitcher of lemonade. Sofia poured 53 of the same-sized pitcher. Which symbol makes the comparison true: 74 53?
- < (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 15
Sara completed 125 of her homework before dinner and 83 of her homework after dinner. Which statement correctly compares these amounts using the benchmark fraction 21?
- 83>125
- 125=83
- 125>83 (correct answer)
- It cannot be determined without more information
Explanation: 125>83 is correct because both fractions are less than 21, but 125 is closer to 21. 83>125 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 16
In art class, two students painted identical canvases. Maya painted 85 of her canvas blue, and Carlos painted 43 of his canvas blue. Who painted a larger blue area?
- Maya painted more because 85>43 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 85=43 when simplified to lowest terms
- Carlos painted more because 43>85 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 85 and 43 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 85, so no conversion needed. For Carlos: 43=4×23×2=86.
Now you can compare: 85 versus 86. Since 86>85, Carlos painted more blue area. This makes choice D correct.
Choice A incorrectly states that 85>43, but as we saw, 85=85 while 43=86, 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 85 and 86 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 17
Sofia walked 103 of a mile. Chen walked 94 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 18
Maya ate 83 of a pizza. Carlos ate 52 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 19
Which symbol makes this comparison true: 41 103?
- #ERROR!
- < (correct answer)
- They are both greater than 21
Explanation: Converting to a common denominator of 20: 41=205 and 103=206. Since 5<6, 41<103. Choice A is incorrect because the fractions are not equal. Choice C is incorrect: both fractions are actually less than 21, not greater. Choice D reverses the comparison. Question 20
Which fraction is greater: 125 or 73?
- 125
- 73 (correct answer)
- 21
- They are equal
Explanation: Both 125 and 73 are less than the benchmark 21, so comparing each to 21 alone doesn't settle it. Cross-multiplying shows 5×7=35 and 3×12=36, and since 36>35, 73>125. 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.