Add and Subtract Multi-Digit Numbers
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4th Grade Math › Add and Subtract Multi-Digit Numbers
What is $6,807 + 9,958$?
16,765
15,665
16,665
16,675
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 6,807 and 9,958, 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 B is correct because following the standard algorithm with proper regrouping: ones 7+8=15 (write 5, carry 1), tens 0+5+1=6, hundreds 8+9=17 (write 7, carry 1), thousands 6+9+1=16 (write 6, carry 1), ten thousands 0+0+1=1, giving 16,765. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice A represents forgetting to carry over in the thousands place, which happens when students add 6+9=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.
Find the difference: $50,000 - 18,746$
31,364
32,254
41,254
31,254
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 subtract 18,746 from 50,000, align places and subtract ones (borrowing if needed), tens (borrowing if needed), hundreds, and so on, 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 across zeros), tens 9-4=5, hundreds 9-7=2, thousands 9-8=1, ten thousands 4-1=3, giving 31,254. Choice B represents not borrowing across all zeros properly, which happens when students fail to propagate the borrow to the ten thousands place. 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 school has 54,006 students. 28,947 students ride the bus. How many students do not ride the bus?
35,059
25,159
25,059
26,059
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 subtract 28,947 from 54,006, 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 16-7=9 (after borrowing), tens 9-4=5, hundreds 9-9=0, thousands 13-8=5 (after borrowing), ten thousands 4-2=2, giving 25,059. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice B represents not borrowing in the thousands place correctly, which happens when students subtract 3-8 without regrouping 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.
Find the sum: $3,895 + 7,468$
11,253
10,363
11,363
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.
Find the sum: $3,895 + 7,468$
11,364
10,363
11,363
11,253
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.
What is $39,784 + 6,509$?
46,393
46,293
45,293
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.
What is $48,679 + 27,458$?
75,137
76,147
76,027
76,137
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 48,679 and 27,458, 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 9+8=17 (write 7, carry 1), tens 7+5+1=13 (write 3, carry 1), hundreds 6+4+1=11 (write 1, carry 1), thousands 8+7+1=16 (write 6, carry 1), ten thousands 4+2+1=7, giving 76,137. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice B represents forgetting to carry over in the ten thousands place, which happens when students add 4+2=6 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.
A library has 84,305 books. 47,986 books are checked out. How many books are not checked out?
36,329 books
37,419 books
46,319 books
36,319 books
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 47,986 from 84,305, align places and subtract ones (5-6 requires borrow, resulting in 15-6=9), tens (9-8=1), hundreds (2-9 requires borrow, resulting in 12-9=3), thousands (3-7 requires borrow, resulting in 13-7=6), and ten thousands (7-4=3), requiring proper regrouping to get the correct difference. Choice A is correct because following the standard algorithm with proper regrouping: ones 15-6=9 (after borrow), tens 9-8=1, hundreds 12-9=3 (after borrow), thousands 13-7=6 (after borrow), ten thousands 7-4=3, giving 36,319. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice D represents not borrowing in the hundreds place, which happens when students subtract without adjusting. 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 places. Have students estimate first (round to nearest thousand) to check if answer is reasonable. Watch for: subtracting without borrowing, not reducing borrowed-from digits.
What is $39,784 + 6,509$?
45,293
46,393
46,283
46,293
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.
A school has 54,006 students. 28,947 students ride the bus. How many students do not ride the bus?
25,159
25,059
26,059
35,059
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 subtract 28,947 from 54,006, 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 16-7=9 (after borrowing), tens 9-4=5, hundreds 9-9=0, thousands 13-8=5 (after borrowing), ten thousands 4-2=2, giving 25,059. This demonstrates fluent use of the standard algorithm with proper place value alignment and regrouping. Choice B represents not borrowing in the thousands place correctly, which happens when students subtract 3-8 without regrouping 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.