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.

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.

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.

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.

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.

This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, repeat until complete, with quotient and remainder. For 3065 ÷ 7, divide 7 into 30 (goes 4 times, 7×4=28≤30<7×5=35), write 4, multiply 28, subtract 2, bring down 6 to make 26; 7 into 26 goes 3 times (7×3=21≤26<7×4=28), multiply 21, subtract 5, bring down 5 to make 55; 7 into 55 goes 7 times (7×7=49≤55<7×8=56), multiply 49, subtract 6, so quotient 437 R6. Verify: 437×7 +6=3059+6=3065, matches. The correct answer is 437 R6, as in choice A. Common errors include subtraction mistakes or choosing a quotient digit too large, like 8 for 55 (56>55). Ensure each remainder is less than the divisor before proceeding. This helps in contexts like grouping items evenly.

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.

This question tests dividing multi-digit numbers using the standard algorithm: divide, multiply, subtract, bring down, repeat until complete, with quotient and remainder. For 2478 ÷ 23, divide 23 into 247 (goes 10 times, but step-by-step: 23 into 24 goes 1, 23×1=23≤24, subtract 1, bring down 7 to 17; actually, properly: 23 into 24 (1 time), but often combine; full: 23 into 247 (10 times, 23×10=230≤247<23×11=253), write 10 (but typically one digit at a time, adjust), multiply 230, subtract 17, bring down 8 to 178; 23 into 178 goes 7 times (23×7=161≤178<23×8=184), multiply 161, subtract 17, so quotient 107 R17. Verify: 107×23 +17=2461+17=2478, correct. The correct answer is 107 R17, as in choice A. Mistakes might include place value errors or wrong multiplication in steps. Trial multiply carefully to pick the right digit. For stickers in bags, 107 per bag with 17 left over.

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 864 ÷ 24, start by dividing 24 into 86 (3 times since 24×3=72 ≤86 <24×4=96), write 3 above, multiply 24×3=72, subtract 86-72=14, bring down 4 to make 144; then 24 into 144 goes 6 times (24×6=144), multiply and subtract to get 0, so quotient is 36 with no remainder. Verify by multiplying: 36×24=864, which matches the dividend. The correct answer is 36 pencils per box, as chosen in option B. A common mistake might be choosing 34 if subtracting incorrectly, like 86-72=16 instead of 14, leading to a wrong quotient. Remember, at each step, choose the largest digit where the product is less than or equal to the current number, and always check that the remainder is less than the divisor. This context of packing pencils equally demonstrates fair distribution, and verification ensures accuracy.

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.