- 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?
Answer: $73 more is needed for the bicycle
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×$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) might tempt you if you only counted the grandmother's gift and forgot about the uncle's contribution. Choice B ($168) could result from forgetting to include Marcus's initial savings of $127 in your total. Choice C ($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. - What is 39,784+6,509?
Answer: 46,293
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.
- What is 6,807+9,958?
Answer: 16,765
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.
- What is 81,640−26,875?
Answer: 54,765
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). - 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?
Answer: 12 books were lost or stolen
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. - The attendance at a baseball game was 4,863 people, out of a stadium capacity of 6,410. During the game, 729 people left early. What was the attendance when the game ended?
Answer: 4,134 people attended when the game ended
Since 729 people left early, subtract that from the reported attendance: 4,863 - 729 = 4,134. The stadium's capacity is extra information that isn't needed to answer this question. Choices B (4,681) and C (5,139) come from adding instead of subtracting or from mixing in the capacity number. Choice D (4,863) forgets to account for the people who left early.
- Find the sum: 3,895+7,468
Answer: 11,363
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.
- 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?
Answer: The farmer has 2,456 apples now.
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.
- Find the difference: 600,040−285,967
Answer: 314,073
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.
- Find the difference: 60,500−24,786
Answer: 35,714
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 subtract 24,786 from 60,500, align places and subtract ones (borrowing if needed), tens (borrowing if needed), continuing through all places, requiring proper regrouping to get the correct difference. Choice A is correct because following the standard algorithm with proper regrouping: ones 10-6=4 (after borrowing), tens 9-8=1, hundreds 14-7=7 (after borrowing), thousands 9-4=5 (after borrowing), ten thousands 5-2=3, giving 35,714. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice B represents not borrowing across the zero in thousands correctly, which happens when students forget to adjust after chain borrowing. 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.
- Keisha had 70,002 tickets. She sold 38,679 tickets. How many tickets are left?
Answer: 31,323 tickets
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. This problem requires subtracting 38,679 from 70,002 by aligning places and subtracting ones (borrowing if needed), tens (borrowing if needed), hundreds, and so on to find tickets left, requiring proper regrouping across multiple zeros to get the correct difference. Choice A is correct because following the standard algorithm with proper regrouping: ones 12-9=3 (after borrowing across zeros), tens 9-7=2, hundreds 9-6=3, thousands 9-8=1, ten thousands 6-3=3, giving 31,323. Choice B represents not borrowing across the zeros properly, which happens when students fail to propagate the borrow through multiple zero places. 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: forgetting to add carried values, subtracting smaller from larger in each column without borrowing, not reducing the borrowed-from digit, and misaligning place values.
- A toy store received three shipments of toys. The first shipment had 2,345 toys, the second had 1,789 toys, and the third had 1,056 toys. If the store sold 2,817 toys, how many toys are left in the store?
Answer: 2,373 toys are left in the store
When you see a word problem involving multiple additions and subtractions, break it down into clear steps: first find what came in, then subtract what went out.
Start by adding all three shipments to find the total toys received: 2,345+1,789+1,056. Let's add step by step: 2,345+1,789=4,134, then 4,134+1,056=5,190 total toys received.
Now subtract the toys sold: 5,190−2,817=2,373 toys remaining. This matches answer choice D.
Let's see why the other answers are wrong. Choice A (2,473) likely comes from a calculation error when adding the shipments—perhaps mixing up digits or making an arithmetic mistake. Choice B (2,283) suggests an error in the final subtraction step, possibly subtracting incorrectly or using the wrong total. Choice C (3,127) is too high and might result from forgetting to subtract the sold toys entirely, or making a major addition error.
The key strategy for multi-step word problems like this is to organize your work clearly: write down what you're finding at each step (total received, then amount remaining), and double-check your arithmetic. Many students rush and make calculation errors, so take time to verify each step. Remember that "left" or "remaining" always means you need to subtract what was used or sold from what you started with. - What is 81,640−26,875?
Answer: 54,765
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.
- A school has 54,006 students. 28,947 students ride the bus. How many students do not ride the bus?
Answer: 25,059
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.
- What is 5,406+3,895?
Answer: 9,301
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.
- Find the sum: 46,785+29,469
Answer: 76,254
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.
- What is 48,679+27,458?
Answer: 76,137
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.
- A school district has 54,006 students. 28,947 students ride the bus. How many students do not ride the bus?
Answer: 25,059
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. - A theater printed 70,008 tickets. It sold 46,579 tickets. How many tickets are left?
Answer: 23,529 tickets
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.
- Find the difference: 50,000−18,746
Answer: 31,254
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.
