Middle School Math Quiz: Divide Multi Digit Numbers
20 questions · exam conditions
0:00
Divide Multi Digit NumbersQuestion 1 of 20

Elena calculates 8,064÷488,064 ÷ 48 using the standard algorithm. In her first step, she determines how many times 4848 goes into 8080. What should her first partial quotient digit be, and what remainder carries to the next step?

First digit is 11 with remainder 3232 carrying forward
First digit is 22 with remainder 1616 carrying forward
First digit is 11 with remainder 326326 carrying forward
First digit is 22 with remainder 44 carrying forward
← Back to quizzes

Middle School Math Quiz

Middle School Math Quiz: Divide Multi Digit Numbers

Practice Divide Multi Digit Numbers in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Divide Multi Digit Numbers, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Elena calculates 8,064÷488,064 ÷ 48 using the standard algorithm. In her first step, she determines how many times 4848 goes into 8080. What should her first partial quotient digit be, and what remainder carries to the next step?

  1. First digit is 11 with remainder 3232 carrying forward (correct answer)
  2. First digit is 22 with remainder 1616 carrying forward
  3. First digit is 11 with remainder 326326 carrying forward
  4. First digit is 22 with remainder 44 carrying forward
Explanation: 4848 goes into 8080 once (11) with remainder 3232. The 66 from the tens place combines with this remainder to make 326326 for the next step. 48×1=4848 × 1 = 48, and 80−48=3280 - 48 = 32. Choice B incorrectly uses 48×2=96>8048 × 2 = 96 > 80. Choice C confuses the carrying process. Choice D uses an impossible remainder for this step.

Question 2

Verify a division result by multiplication: If 4536÷36=1264536\div 36 = 126, which check is correct?

  1. 36×126=453636\times 126 = 4536 (correct answer)
  2. 36×126=456336\times 126 = 4563
  3. 126×36=4326126\times 36 = 4326
  4. 4536×36=1264536\times 36 = 126
Explanation: This question tests verifying division results by multiplication, a key step after using the standard algorithm to ensure accuracy. To check 4536 ÷ 36 =126, multiply 36×126: 36×100=3600, 36×20=720, 36×6=216, total 3600+720+216=4536, which equals the dividend, confirming it's correct. The proper verification is quotient × divisor = dividend (or +remainder if any), so choice A is right. Incorrect options might swap numbers or have arithmetic errors, like 4563 instead of 4536. Always perform this multiplication check after division to catch mistakes in the algorithm steps. Common division errors include wrong quotient digits or subtraction, which this verification reveals. This method applies to real-world scenarios like confirming equal shares.

Question 3

A store has 2,0192{,}019 stickers and packs them into 1616 identical packs. Divide 2,019÷162{,}019\div 16 using the standard long division algorithm. What is the quotient with remainder?

  1. 125 R19125\ \text{R}19
  2. 127 R11127\ \text{R}11
  3. 126 R3126\ \text{R}3 (correct answer)
  4. 126 R9126\ \text{R}9
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 2,019 ÷ 16, divide 16 into 20, which goes 1 time (16×1=16), subtract 20-16=4, bring down 1 to make 41; 16 into 41 goes 2 times (16×2=32), subtract 41-32=9, bring down 9 to make 99; 16 into 99 goes 6 times (16×6=96), subtract 99-96=3, quotient 126 R3. Verify: 126×16 +3=2,016+3=2,019, matches. The correct answer is 126 R3, with 3 stickers left over. Mistakes often stem from wrong trial multiplication or forgetting to bring down. Ensure remainder < divisor. This represents packing items equally with possible leftovers.

Question 4

Which equation correctly verifies the division 3,409÷27=126 R73{,}409\div 27 = 126\ \text{R}7?​

  1. 27×126+7=3,40927\times 126 + 7 = 3{,}409 (correct answer)
  2. 27×7+126=3,40927\times 7 + 126 = 3{,}409
  3. 126×7+27=3,409126\times 7 + 27 = 3{,}409
  4. 27×126−7=3,40927\times 126 - 7 = 3{,}409
Explanation: This question tests understanding verification of division with remainder, where quotient × divisor + remainder should equal the dividend. For 3,409 ÷ 27 = 126 R7, the correct equation is 27×126 +7=3,409, as 126×27=3,402 and +7=3,409 matches. Other options like 27×126 -7=3,395 do not equal 3,409. This verification confirms the division is accurate. A common mistake is confusing the order, like multiplying remainder by quotient instead. Always use the formula quotient × divisor + remainder = dividend to check. This concept ensures reliability in division results, useful in various mathematical contexts.

Question 5

Divide 4,536÷184{,}536\div 18 using the standard long division algorithm. What is the quotient?

  1. 242
  2. 272
  3. 262
  4. 252 (correct answer)
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 4,536 ÷ 18, divide 18 into 45, which goes 2 times (18×2=36), subtract 45-36=9, bring down 3 to make 93; 18 into 93 goes 5 times (18×5=90), subtract 93-90=3, bring down 6 to make 36; 18 into 36 goes 2 times (18×2=36), subtract 0, so quotient is 252. Verify: 252×18=4,536, matching the dividend. The correct quotient is 252. Mistakes often occur from misalignment of place values or incorrect trial multiplication, like choosing 3 instead of 2 initially (18×3=54>45). The algorithm requires careful selection of each quotient digit to avoid remainders >= divisor. This helps in understanding equal sharing in various contexts, like distributing resources.

Question 6

A science club has 3,2753{,}275 beads to make bracelets. They split them equally among 2525 students. Divide 3,275÷253{,}275\div 25 using the standard long division algorithm. How many beads does each student get?​

  1. 121
  2. 131 (correct answer)
  3. 130
  4. 141
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 3,275 ÷ 25, divide 25 into 32, which goes 1 time (25×1=25), subtract 32-25=7, bring down 7 to make 77; 25 into 77 goes 3 times (25×3=75), subtract 77-75=2, bring down 5 to make 25; 25 into 25 goes 1 time (25×1=25), subtract 0, so quotient is 131. Verify: 131×25=3,275, exact match. Each student gets 131 beads. Common errors include forgetting to bring down digits or wrong subtraction, like 77-75=3. Ensure each step's remainder is less than the divisor before proceeding. This division applies to fair distribution, such as sharing beads among students.

Question 7

A science club has 3,2753{,}275 beads to make bracelets. They split them equally among 2525 students. Divide 3,275÷253{,}275\div 25 using the standard long division algorithm. How many beads does each student get?

  1. 130
  2. 141
  3. 121
  4. 131 (correct answer)
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 3,275 ÷ 25, divide 25 into 32, which goes 1 time (25×1=25), subtract 32-25=7, bring down 7 to make 77; 25 into 77 goes 3 times (25×3=75), subtract 77-75=2, bring down 5 to make 25; 25 into 25 goes 1 time (25×1=25), subtract 0, so quotient is 131. Verify: 131×25=3,275, exact match. Each student gets 131 beads. Common errors include forgetting to bring down digits or wrong subtraction, like 77-75=3. Ensure each step's remainder is less than the divisor before proceeding. This division applies to fair distribution, such as sharing beads among students.

Question 8

A classroom collected 864864 pencils to donate and wants to pack them equally into 2424 boxes. Divide 864÷24864\div 24 using the standard long division algorithm. How many pencils go in each box?

  1. 34
  2. 40
  3. 36 (correct answer)
  4. 38
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 864 ÷ 24, start by dividing 24 into 86, which goes 3 times since 24×3=72, subtract 86-72=14, bring down 4 to make 144; then 24 into 144 goes 6 times since 24×6=144, subtract 144-144=0, so the quotient is 36 with no remainder. To verify, multiply the quotient by the divisor: 36×24=864, which matches the dividend. The correct quotient is 36, meaning each box gets 36 pencils. A common mistake might be choosing a quotient digit too large, like 4 for the first step (24×4=96>86), leading to incorrect subtraction. Remember, at each step, determine how many times the divisor fits into the current number without exceeding it, then proceed with multiply, subtract, and bring down. This division context represents equally distributing pencils into boxes, ensuring fair sharing.

Question 9

Which equation correctly verifies the division 3,409÷27=126 R73{,}409\div 27 = 126\ \text{R}7?

  1. 27×126−7=3,40927\times 126 - 7 = 3{,}409
  2. 27×126+7=3,40927\times 126 + 7 = 3{,}409 (correct answer)
  3. 126×7+27=3,409126\times 7 + 27 = 3{,}409
  4. 27×7+126=3,40927\times 7 + 126 = 3{,}409
Explanation: This question tests understanding verification of division with remainder, where quotient × divisor + remainder should equal the dividend. For 3,409 ÷ 27 = 126 R7, the correct equation is 27×126 +7=3,409, as 126×27=3,402 and +7=3,409 matches. Other options like 27×126 -7=3,395 do not equal 3,409. This verification confirms the division is accurate. A common mistake is confusing the order, like multiplying remainder by quotient instead. Always use the formula quotient × divisor + remainder = dividend to check. This concept ensures reliability in division results, useful in various mathematical contexts.

Question 10

Divide using the standard long division algorithm: 4,536÷124{,}536\div 12. What is the quotient?

  1. 358358
  2. 388388
  3. 37 R 837\text{ R }8
  4. 378378 (correct answer)
Explanation: This question tests dividing multi-digit numbers using the standard long division algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 4,536 ÷ 12, divide 12 into 45 (3 times since 12×3=36 ≤45 <12×4=48), write 3, multiply 36, subtract 9, bring down 3 to make 93; 12 into 93 goes 7 times (12×7=84), subtract 9, bring down 6 to make 96; 12 into 96 goes 8 times (12×8=96), subtract 0, so quotient 378 with no remainder. Verify: 378×12=4,536, which matches. The correct quotient is 378, as in option A. A mistake like 37 R8 might come from not bringing down properly or subtraction error. Always align quotient digits with place values. This example highlights repeating steps until all digits are processed.

Question 11

A club earned \1{,}596$ from a fundraiser and wants to share it equally among 14 members. Using the standard long division algorithm, how much does each member get? (Assume dollars only, no cents.)

  1. $104
  2. $114 (correct answer)
  3. $140
  4. $124
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, repeat until complete, resulting in a quotient. For 1596 ÷ 14, divide 14 into 15 (goes 1 time, 14×1=14≤15<14×2=28), write 1, multiply 14, subtract 1, bring down 9 to make 19; 14 into 19 goes 1 time (14×1=14≤19<14×2=28), multiply 14, subtract 5, bring down 6 to make 56; 14 into 56 goes 4 times (14×4=56), multiply 56, subtract 0, so quotient 114. Verify: 114×14=1596, correct. The correct answer is $114, as in choice A. A mistake might be incorrect trial multiplication, like thinking 14×2=28 fits in 19 (it doesn't). Always align place values properly and check remainder < divisor. In sharing money, each of 14 members gets $114 exactly.

Question 12

Divide using the standard long division algorithm: 5724÷185724\div 18. Give the quotient and remainder.

  1. 308 R 0308\text{ R }0
  2. 318 R 6318\text{ R }6
  3. 318 R 0318\text{ R }0 (correct answer)
  4. 317 R 18317\text{ R }18
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, repeat until complete, with quotient and remainder. For 5724 ÷ 18, divide 18 into 57 (goes 3 times, 18×3=54≤57<18×4=72), write 3, multiply 54, subtract 3, bring down 2 to make 32; 18 into 32 goes 1 time (18×1=18≤32<18×2=36), multiply 18, subtract 14, bring down 4 to make 144; 18 into 144 goes 8 times (18×8=144), multiply 144, subtract 0, so quotient 318 R0. Verify: 318×18=5724, exact match. The correct answer is 318 R0, as in choice A. Errors could be subtraction mistakes, like 57-54=4 instead of 3, or choosing too small a quotient digit. The remainder must be less than the divisor; here it's zero, meaning exact division. This algorithm is useful for equal sharing, like distributing items evenly.

Question 13

Divide using the standard long division algorithm: 2,835÷152{,}835\div 15. What is the quotient?

  1. 180180
  2. 180 R 135180\text{ R }135
  3. 189189 (correct answer)
  4. 159159
Explanation: This question tests dividing multi-digit numbers using the standard long division algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 2,835 ÷ 15, divide 15 into 28 (1 time since 15×1=15 ≤28 <15×2=30), write 1, multiply 15, subtract 13, bring down 3 to make 133; 15 into 133 goes 8 times (15×8=120), subtract 13, bring down 5 to make 135; 15 into 135 goes 9 times (15×9=135), subtract 0, so quotient 189 with no remainder. Verify: 189×15=2,835, which matches. The correct quotient is 189, as in option B. Mistakes like 180 R135 might occur from stopping early or misalignment. Ensure remainder is always less than divisor. This shows exact division in practice.

Question 14

A school orders 5,8325,832 pencils to distribute equally among 1818 classrooms. After distribution, they find they have 1212 pencils remaining. How many pencils did each classroom receive?

  1. 322322 pencils per classroom, with calculation error in the problem
  2. 320320 pencils per classroom, with 7272 pencils actually remaining
  3. 323323 pencils per classroom, but the remainder should be 1818
  4. 324324 pencils per classroom, confirming the given remainder (correct answer)
Explanation: When you encounter a division problem with remainders, you need to verify that the quotient and remainder work together correctly. This question tests your understanding of the division algorithm: dividend = (divisor × quotient) + remainder. Let's check if 324324 pencils per classroom with 1212 remaining is correct. If each of the 1818 classrooms receives 324324 pencils, the total distributed would be 18×324=5,832−12=5,82018 \times 324 = 5,832 - 12 = 5,820 pencils. Adding back the 1212 remaining pencils gives us 5,820+12=5,8325,820 + 12 = 5,832 total pencils, which matches perfectly. Answer D is correct. Now let's see why the other options fail. Choice A suggests 322322 pencils per classroom: 18×322=5,79618 \times 322 = 5,796, leaving 3636 pencils remaining, not 1212. Choice B claims 320320 pencils per classroom: 18×320=5,76018 \times 320 = 5,760, which would leave 7272 pencils remaining—this option even acknowledges the remainder would be different. Choice C proposes 323323 pencils per classroom: 18×323=5,81418 \times 323 = 5,814, leaving 1818 pencils remaining, not 1212. The key strategy here is to work backwards: multiply the proposed quotient by the divisor, then add the stated remainder to see if you get the original dividend. This verification step helps you catch calculation errors and confirms your division is correct. Always check that your remainder is less than the divisor—if it's not, you can divide further.

Question 15

A library received 1,8481{,}848 new bookmarks and wants to place them equally into 77 bins. Divide 1,848÷71{,}848\div 7 using the standard long division algorithm. How many bookmarks go in each bin?

  1. 284
  2. 274
  3. 264 (correct answer)
  4. 254
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 1,848 ÷ 7, divide 7 into 18, which goes 2 times (7×2=14), subtract 18-14=4, bring down 4 to make 44; 7 into 44 goes 6 times (7×6=42), subtract 44-42=2, bring down 8 to make 28; 7 into 28 goes 4 times (7×4=28), subtract 0, quotient 264. Verify: 264×7=1,848, matches. Each bin gets 264 bookmarks. A frequent mistake is incorrect quotient selection, like 3 for 18 (7×3=21>18). Always trial multiply to find the largest fitting digit. This context shows equal distribution of items into groups.

Question 16

A classroom collected 864864 pencils to donate and wants to pack them equally into 2424 boxes. Divide 864÷24864\div 24 using the standard long division algorithm. How many pencils go in each box?​

  1. 36 (correct answer)
  2. 38
  3. 40
  4. 34
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, and repeat until complete, resulting in a quotient and possibly a remainder. For 864 ÷ 24, start by dividing 24 into 86, which goes 3 times since 24×3=72, subtract 86-72=14, bring down 4 to make 144; then 24 into 144 goes 6 times since 24×6=144, subtract 144-144=0, so the quotient is 36 with no remainder. To verify, multiply the quotient by the divisor: 36×24=864, which matches the dividend. The correct quotient is 36, meaning each box gets 36 pencils. A common mistake might be choosing a quotient digit too large, like 4 for the first step (24×4=96>86), leading to incorrect subtraction. Remember, at each step, determine how many times the divisor fits into the current number without exceeding it, then proceed with multiply, subtract, and bring down. This division context represents equally distributing pencils into boxes, ensuring fair sharing.

Question 17

A school store has 457 pencils to put into packs of 12. Using the standard long division algorithm, what is 457÷12457\div 12 expressed as a quotient with a remainder?

  1. 38 R 138\text{ R }1 (correct answer)
  2. 39 R 139\text{ R }1
  3. 38 R 1338\text{ R }13
  4. 37 R 137\text{ R }1
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, repeat until complete, with quotient and remainder. For 457 ÷ 12, divide 12 into 45 (goes 3 times, 12×3=36≤45<12×4=48), write 3, multiply 36, subtract 45-36=9, bring down 7 to make 97; 12 into 97 goes 8 times (12×8=96≤97<12×9=108), multiply 96, subtract 97-96=1, so quotient 38 with remainder 1. Verify: 38×12 +1 =456+1=457, matching the dividend. The correct answer is 38 R1, as in choice A. Errors might include wrong quotient digit, like 4 initially (48>45), or subtraction mistake, such as 45-36=11. The algorithm ensures the remainder is always less than the divisor; if not, increase the quotient digit. This applies to distributing pencils, where 38 packs of 12 are made, with 1 pencil left over.

Question 18

Marcus divides 7,2457,245 by 3535 and gets a quotient of 207207. To check his work, he multiplies 207×35207 × 35 and gets 7,2457,245. What can you conclude about his division?

  1. His division is completely correct with no remainder needed (correct answer)
  2. His division is incorrect because the quotient should be 270270, not 207207
  3. His division is correct but incomplete since there should be a remainder
  4. His division is incorrect because 207×35=7,235207 × 35 = 7,235, not 7,2457,245
Explanation: When checking division problems, you need to verify that the multiplication actually works out correctly. Let's examine Marcus's work step by step. Marcus claims that 7,245÷35=2077,245 ÷ 35 = 207, and he checks this by multiplying 207×35207 × 35. However, when you actually calculate 207×35207 × 35, you get 7,2357,235, not 7,2457,245. You can verify this: 207×35=207×(30+5)=207×30+207×5=6,210+1,035=7,245207 × 35 = 207 × (30 + 5) = 207 × 30 + 207 × 5 = 6,210 + 1,035 = 7,245. Wait, let me recalculate: 207×30=6,210207 × 30 = 6,210 and 207×5=1,035207 × 5 = 1,035, so 6,210+1,035=7,2456,210 + 1,035 = 7,245. Actually, Marcus's multiplication is correct. Let me check the division properly: 7,245÷357,245 ÷ 35. Using long division or a calculator, 35×207=7,24535 × 207 = 7,245 exactly. So Marcus's work is actually completely correct. Looking at the answer choices: Choice A suggests his division is completely correct, which appears true. Choice B claims the quotient should be 270270, but 270×35=9,450270 × 35 = 9,450, which is way too large. Choice C suggests there should be a remainder, but since 207×35=7,245207 × 35 = 7,245 exactly, there's no remainder. Choice D claims that 207×35=7,235207 × 35 = 7,235, but this is incorrect—the actual product is 7,2457,245. Study tip: Always double-check your multiplication when verifying division. Calculate step-by-step rather than assuming, and remember that if division is exact, there will be no remainder.

Question 19

A class collected 3,125 cans for a food drive and wants to divide them equally among 25 boxes. Using the standard long division algorithm, find 3125÷253125\div 25.

  1. 125 (correct answer)
  2. 115
  3. 250
  4. 12.5
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, repeat until complete, resulting in a quotient. For 3125 ÷ 25, divide 25 into 31 (goes 1 time, 25×1=25≤31<25×2=50), write 1, multiply 25, subtract 6, bring down 2 to make 62; 25 into 62 goes 2 times (25×2=50≤62<25×3=75), multiply 50, subtract 12, bring down 5 to make 125; 25 into 125 goes 5 times (25×5=125), multiply 125, subtract 0, so quotient 125. Verify: 125×25=3125, correct. The correct answer is 125, as in choice A. A common mistake is misalignment or forgetting to bring down, leading to wrong quotients like 115. Ensure remainder < divisor at each step. For cans in boxes, each of 25 boxes gets 125 cans exactly.

Question 20

A science teacher pours 3,432 milliliters of solution equally into 16 cups. Using the standard long division algorithm, find 3432÷163432\div 16 as a quotient with a remainder.

  1. 213 R 8213\text{ R }8
  2. 214 R 8214\text{ R }8 (correct answer)
  3. 215 R 8215\text{ R }8
  4. 214 R 12214\text{ R }12
Explanation: This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, repeat until complete, with quotient and remainder. For 3432 ÷ 16, divide 16 into 34 (goes 2 times, 16×2=32≤34<16×3=48), write 2, multiply 32, subtract 34-32=2, bring down 3 to make 23; 16 into 23 goes 1 time (16×1=16≤23<16×2=32), multiply 16, subtract 7, bring down 2 to make 72; 16 into 72 goes 4 times (16×4=64≤72<16×5=80), multiply 64, subtract 8, so quotient 214 R8. Verify: 214×16 +8=3424+8=3432, correct. The correct answer is 214 R8, as in choice A. Common mistakes include misalignment of place values or forgetting to bring down digits, leading to wrong quotients like 215. Always trial multiply to choose the right quotient digit, ensuring the product doesn't exceed the current number. In pouring solution, this means each of 16 cups gets 214 ml, with 8 ml left over.