All questions
Question 1
A school district has 54,006 students. 28,947 students ride the bus. How many students do not ride the bus?
- 25,059 (correct answer)
- 25,159
- 26,059
- 35,059
Explanation: 25,059 is correct because 54,006−28,947=25,059. 25,159 is incorrect because it results from a small subtraction slip in the tens place. 26,059 is incorrect because it results from a slip in the thousands place. 35,059 is incorrect because it results from a slip of ten thousand in the subtraction. Question 2
Find the sum: 3,895+7,468
- 11,363 (correct answer)
- 11,253
- 10,363
- 11,364
Explanation: This question tests 4th grade fluency with adding and subtracting multi-digit whole numbers using the standard algorithm (CCSS.4.NBT.4). The standard algorithm for addition involves aligning numbers by place value, adding each place starting from the ones, and regrouping (carrying) when the sum in a place is 10 or more. The standard algorithm for subtraction involves aligning numbers by place value, subtracting each place starting from the ones, and regrouping (borrowing) when the top digit is less than the bottom digit. Regrouping means taking 10 from the next left place and adding it to the current place. To add 3,895 and 7,468, align the places and add ones (carries if ≥10), tens (including any carried value), hundreds, and so on, requiring proper regrouping to get the correct sum. Choice A is correct because following the standard algorithm with proper regrouping: ones 5+8=13 (write 3, carry 1), tens 9+6+1=16 (write 6, carry 1), hundreds 8+4+1=13 (write 3, carry 1), thousands 3+7+1=11, giving 11,363. Choice B represents forgetting to carry in the tens place, which happens when students add without including the carried value. To help students: Use graph paper or place value columns to align digits correctly. For addition, emphasize checking each column—if sum is 10 or more, write the ones digit and carry the tens digit to the next column. Practice borrowing across zeros (like 5,003 - 2,456) by borrowing from the next non-zero place. Have students estimate first (round to nearest thousand) to check if answer is reasonable. Watch for: forgetting to add carried values, subtracting smaller from larger in each column without borrowing, not reducing the borrowed-from digit, and misaligning place values.
Question 3
A school has 54,006 students. 28,947 students ride the bus. How many students do not ride the bus?
- 25,159
- 35,059
- 25,059 (correct answer)
- 26,059
Explanation: Subtracting 28,947 from 54,006 gives 25,059, making Choice C correct. Choice A, 25,159, comes from a regrouping slip in the tens place during subtraction. Choice B, 35,059, comes from a borrowing error in the ten-thousands place. Choice D, 26,059, comes from a small error in the thousands place during regrouping.
Question 4
- 16,675
- 16,665
- 15,665
- 16,765 (correct answer)
Explanation: Adding 6,807 and 9,958 using place value gives 16,765. Choices A (16,675) and B (16,665) come from small regrouping errors in the tens and hundreds places. Choice C (15,665) is off by a thousand, as if a digit was misplaced during carrying.
Question 5
What is 5,406+3,895?
- 8,301
- 9,311
- 9,301 (correct answer)
- 9,201
Explanation: This question tests 4th grade fluency with adding and subtracting multi-digit whole numbers using the standard algorithm (CCSS.4.NBT.4). The standard algorithm for addition involves aligning numbers by place value, adding each place starting from the ones, and regrouping (carrying) when the sum in a place is 10 or more. The standard algorithm for subtraction involves aligning numbers by place value, subtracting each place starting from the ones, and regrouping (borrowing) when the top digit is less than the bottom digit. Regrouping means taking 10 from the next left place and adding it to the current place. To add 5,406 and 3,895, align the places and add ones (carries if ≥10), tens (including any carried value), hundreds, and so on, requiring proper regrouping to get the correct sum. Choice C is correct because following the standard algorithm with proper regrouping: ones 6+5=11 (write 1, carry 1), tens 0+9+1=10 (write 0, carry 1), hundreds 4+8+1=13 (write 3, carry 1), thousands 5+3+1=9, giving 9,301. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice A represents forgetting to carry over in the hundreds place, which happens when students add 4+8=12 without adding the carried 1. To help students: Use graph paper or place value columns to align digits correctly. For addition, emphasize checking each column—if sum is 10 or more, write the ones digit and carry the tens digit to the next column. For subtraction, check each column—if top digit is less than bottom digit, borrow 10 from the next left column (reducing that column's top digit by 1). Practice borrowing across zeros (like 5,003 - 2,456) by borrowing from the next non-zero place. Have students estimate first (round to nearest thousand) to check if answer is reasonable. Watch for: forgetting to add carried values, subtracting smaller from larger in each column without borrowing, not reducing the borrowed-from digit, and misaligning place values.
Question 6
What is 39,784+6,509?
- 45,293
- 46,393
- 46,293 (correct answer)
- 46,283
Explanation: This question tests 4th grade fluency with adding and subtracting multi-digit whole numbers using the standard algorithm (CCSS.4.NBT.4). The standard algorithm for addition involves aligning numbers by place value, adding each place starting from the ones, and regrouping (carrying) when the sum in a place is 10 or more. The standard algorithm for subtraction involves aligning numbers by place value, subtracting each place starting from the ones, and regrouping (borrowing) when the top digit is less than the bottom digit. Regrouping means taking 10 from the next left place and adding it to the current place. To add 39,784 and 6,509, align the places and add ones (carries if ≥10), tens (including any carried value), hundreds, and so on, requiring proper regrouping to get the correct sum. Choice A is correct because following the standard algorithm with proper regrouping: ones 4+9=13 (write 3, carry 1), tens 8+0+1=9, hundreds 7+5=12 (write 2, carry 1), thousands 9+6+1=16 (write 6, carry 1), ten thousands 3+0+1=4, giving 46,293. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice B represents forgetting to carry over in the thousands place, which happens when students add 9+6=15 without adding the carried 1. To help students: Use graph paper or place value columns to align digits correctly. For addition, emphasize checking each column—if sum is 10 or more, write the ones digit and carry the tens digit to the next column. For subtraction, check each column—if top digit is less than bottom digit, borrow 10 from the next left column (reducing that column's top digit by 1). Practice borrowing across zeros (like 5,003 - 2,456) by borrowing from the next non-zero place. Have students estimate first (round to nearest thousand) to check if answer is reasonable. Watch for: forgetting to add carried values, subtracting smaller from larger in each column without borrowing, not reducing the borrowed-from digit, and misaligning place values.
Question 7
A theater printed 70,008 tickets. It sold 46,579 tickets. How many tickets are left?
- 23,529 tickets (correct answer)
- 23,429 tickets
- 33,529 tickets
- 24,429 tickets
Explanation: This question tests 4th grade fluency with adding and subtracting multi-digit whole numbers using the standard algorithm (CCSS.4.NBT.4). The standard algorithm for subtraction involves aligning numbers by place value, subtracting each place starting from the ones, and regrouping (borrowing) when the top digit is less than the bottom digit. Regrouping means taking 10 from the next left place and adding it to the current place. To subtract 46,579 from 70,008, align places and subtract ones (8-9 requires borrow across multiple zeros, resulting in 18-9=9 after adjusting), tens (9-7=2), hundreds (9-5=4), thousands (9-6=3), and ten thousands (6-4=2), requiring proper regrouping to get the correct difference. Choice A is correct because following the standard algorithm with proper regrouping: ones 18-9=9 (after borrowing across zeros), tens 9-7=2, hundreds 9-5=4, thousands 9-6=3, ten thousands 6-4=2, giving 23,429. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice C represents misalignment of place values or incorrect borrowing, which happens when students don't handle borrowing across zeros properly. To help students: Use graph paper or place value columns to align digits correctly. For subtraction, check each column—if top digit is less than bottom digit, borrow 10 from the next left column (reducing that column's top digit by 1). Practice borrowing across zeros (like 5,003 - 2,456) by borrowing from the next non-zero place. Have students estimate first (round to nearest thousand) to check if answer is reasonable. Watch for: subtracting smaller from larger in each column without borrowing, not reducing the borrowed-from digit, and misaligning place values.
Question 8
What is 39,784+6,509?
- 46,293 (correct answer)
- 46,393
- 46,283
- 45,293
Explanation: The correct answer is 46,293, since 39,784 + 6,509 = 46,293. Choice B, 46,393, comes from misreading a digit in the hundreds place during addition. Choice C, 46,283, is off by 10 from a small addition slip in the tens place. Choice D, 45,293, comes from forgetting to carry a thousand when adding the thousands digits.
Question 9
What is 81,640−26,875?
- 64,765
- 54,765 (correct answer)
- 55,765
- 54,775
Explanation: Subtracting 26,875 from 81,640 gives 54,765, making Choice B correct. Choice A, 64,765, comes from a borrowing error in the ten-thousands place. Choice C, 55,765, comes from a small regrouping slip in the hundreds place. Choice D, 54,775, comes from a small error in the tens place during subtraction.
Question 10
Elena collected 2,679 bottle caps for recycling. She gave 845 to her brother and 567 to her sister. Her cousin then gave her 429 more bottle caps. If Elena needs 2,000 bottle caps for a school project, how many more does she need?
- Elena needs 1,696 more bottle caps.
- Elena needs 304 more bottle caps. (correct answer)
- Elena needs 133 more bottle caps.
- Elena needs 429 more bottle caps.
Explanation: Choice B is correct because Elena has 2,679 minus 845 minus 567 plus 429, which equals 1,696 bottle caps, and she needs 2,000 minus 1,696, or 304 more. Choice A is incorrect because it is the number of bottle caps Elena currently has, not the number she still needs. Choice C is incorrect because it does not match the difference between 2,000 and 1,696. Choice D is incorrect because it is the number of bottle caps her cousin gave her, not the number still needed.
Question 11
Find the difference: 600,040−285,967
- 314,073 (correct answer)
- 314,083
- 315,073
- 324,173
Explanation: This question tests 4th grade fluency with adding and subtracting multi-digit whole numbers using the standard algorithm (CCSS.4.NBT.4). The standard algorithm for subtraction involves aligning numbers by place value, subtracting each place starting from the ones, and regrouping (borrowing) when the top digit is less than the bottom digit. Regrouping means taking 10 from the next left place and adding it to the current place. To subtract 285,967 from 600,040, align places and subtract ones (0-7 requires borrow, resulting in 10-7=3), tens (3-6 requires borrow across zeros, resulting in 13-6=7 after adjusting), hundreds (9-9=0), thousands (9-5=4), ten thousands (9-8=1), and hundred thousands (5-2=3), requiring proper regrouping to get the correct difference. Choice C is correct because following the standard algorithm with proper regrouping: ones 10-7=3 (after borrow), tens 13-6=7 (after borrow across zeros), hundreds 9-9=0, thousands 9-5=4, ten thousands 9-8=1, hundred thousands 5-2=3, giving 314,073. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice D represents misalignment or incorrect borrowing, which happens when students don't handle zeros properly. To help students: Use graph paper or place value columns to align digits correctly. For subtraction, check each column—if top digit is less than bottom digit, borrow 10 from the next left column (reducing that column's top digit by 1). Practice borrowing across zeros (like 5,003 - 2,456) by borrowing from the next non-zero place. Have students estimate first (round to nearest thousand) to check if answer is reasonable. Watch for: not continuing borrowing across zeros, misaligning places.
Question 12
What is 48,679+27,458?
- 76,027
- 76,147
- 75,137
- 76,137 (correct answer)
Explanation: Choice D is correct because 48,679 plus 27,458 equals 76,137. Choice A is incorrect because it does not match the actual sum. Choice B is incorrect because it is close to the correct answer but reflects a small addition error. Choice C is incorrect because it is off by exactly 1,000, suggesting a misplaced digit.
Question 13
What is 81,640−26,875?
- 54,765 (correct answer)
- 54,775
- 64,765
- 55,765
Explanation: Subtracting 81,640−26,875 gives 54,765. Choice B has an error in the tens place (54,775 instead of 54,765). Choice C has an error in the ten-thousands place (64,765 instead of 54,765). Choice D has an error in the thousands place (55,765 instead of 54,765). Question 14
A school library had 3,508 books at the beginning of the year. During the year, they bought 1,276 new books and removed 847 damaged books. At the end of the year, they counted 3,925 books. How many books were lost or stolen during the year?
- 12 books were lost or stolen (correct answer)
- 24 books were lost or stolen
- 36 books were lost or stolen
- 48 books were lost or stolen
Explanation: Starting with 3,508 books, adding the 1,276 bought and subtracting the 847 removed gives an expected 3,937 books, but only 3,925 were actually counted, meaning 12 books were lost or stolen. Choice B could come from a borrowing error while subtracting 3,925 from the expected 3,937. Choice C compounds a similar subtraction slip, roughly tripling the true difference. Choice D could result from misreading one of the four-digit numbers by a small amount before subtracting. Choice A correctly finds the gap between the expected count and the actual count.
Question 15
A farmer harvested 6,425 apples from his orchard. He sold 2,847 apples at the farmers market and 1,956 apples to a local grocery store. He then picked 834 more apples from trees he had missed. How many apples does the farmer have now?
- The farmer has 1,622 apples now.
- The farmer has 3,622 apples now.
- The farmer has 2,456 apples now. (correct answer)
- The farmer has 2,290 apples now.
Explanation: Choice C is correct because 6,425 minus 2,847 minus 1,956 plus 834 equals 2,456 apples. Choice A is incorrect because it does not account for the apples picked after the sales. Choice B is incorrect because it does not correctly combine all four amounts. Choice D is incorrect because it does not match the result of the full sequence of subtractions and addition.
Question 16
What is 6,807+9,958?
- 16,675
- 15,665
- 16,765 (correct answer)
- 16,665
Explanation: The correct sum is 16,765. Choice A, 16,675, has two digits swapped in the hundreds and tens places. Choice B, 15,665, comes from forgetting to carry a 1 into the thousands place. Choice D, 16,665, comes from adding 6 plus 9 as 15 without carrying the 1 into the hundreds place.
Question 17
Find the difference: 50,000−18,746
- 31,254 (correct answer)
- 32,254
- 41,254
- 31,364
Explanation: The correct answer is 31,254, because 50,000 minus 18,746 equals 31,254. Choice B, 32,254, comes from a borrowing error of 1,000 during subtraction. Choice C, 41,254, comes from a borrowing error of 10,000 in the ten-thousands place. Choice D, 31,364, comes from transposing two digits in the hundreds and tens places.
Question 18
Marcus is saving money for a bicycle that costs $485. He has already saved $127 and his grandmother gives him $95. His uncle gives him twice as much as his grandmother gave him. How much more money does Marcus need to buy the bicycle?
- $95 more is needed for the bicycle
- $168 more is needed for the bicycle
- $263 more is needed for the bicycle
- $73 more is needed for the bicycle (correct answer)
Explanation: This is a multi-step word problem that requires you to track money coming in and then calculate how much more is needed. The key is organizing the information and working through each step carefully.
Let's calculate how much money Marcus has total. He starts with $127 that he already saved. His grandmother gives him $95, so now he has $\127 + $95 = $222. His uncle gives him twice as much as his grandmother, which means 2 \times $95 = $190. Adding the uncle's money: $222 + $190 = $412 total.
Since the bicycle costs 485, Marcus still needs $$\485 - $412 = $73$$ more. This confirms answer choice D is correct.
Looking at the wrong answers: Choice A (95)mighttemptyouifyouonlycountedthegrandmother′sgiftandforgotabouttheuncle′scontribution.ChoiceB(168) could result from forgetting to include Marcus's initial savings of 127inyourtotal.ChoiceC(263) appears if you only counted Marcus's original $127 and ignored both relatives' gifts entirely.
When solving multi-step money problems, write down each amount clearly and add them step by step. Don't try to do all the mental math at once. Also, pay close attention to phrases like "twice as much" – they require an extra calculation that's easy to miss when you're rushing through the problem. Question 19
Find the sum: 46,785+29,469
- 76,254 (correct answer)
- 75,254
- 76,244
- 76,154
Explanation: 46,785 + 29,469 = 76,254. Adding each place with proper regrouping (ones, tens, hundreds, thousands, then ten-thousands) gives this total. Choice B is 1,000 too low, suggesting a missed regrouping in the thousands place. Choice C is 10 too low. Choice D is 100 too low, from a missed carry in the hundreds place.
Question 20
Maya is collecting stickers for a school project. She starts with 1,247 stickers. Her friend gives her 386 more stickers, but then she uses 529 stickers for her project. How many stickers does Maya have left?
- 1,104 stickers (correct answer)
- 1,162 stickers
- 1,014 stickers
- 1,204 stickers
Explanation: The correct answer is 1,104 stickers, because 1,247 plus 386 equals 1,633, and 1,633 minus 529 equals 1,104. Choice B, 1,162 stickers, comes from adding 1,247 and 386 incorrectly as 1,691 before subtracting 529. Choice C, 1,014 stickers, comes from a subtraction slip after finding the correct sum of 1,633. Choice D, 1,204 stickers, comes from a small addition error in the tens place before subtracting.