First, divide total flour by days: $$4,368 ÷ 24 = 182$$ pounds per day. Then divide daily amount by bag capacity: $$182 ÷ 18 = 10$$ remainder $$2$$. So they need $$10$$ bags with $$2$$ pounds left over. Choice A uses incorrect daily amount ($$4,368 ÷ 26 = 168$$). Choice C assumes $$216$$ pounds per day. Choice D uses $$174$$ pounds per day.

First verify: $$72 × 117 = 8,424$$ ✓. For $$8,424 ÷ 73$$: Start with estimate $$117$$, but $$73 × 117 = 8,541 > 8,424$$, so try $$116$$: $$73 × 116 = 8,468 > 8,424$$. Try $$115$$: $$73 × 115 = 8,395$$. Remainder: $$8,424 - 8,395 = 29$$. So quotient $$115$$, remainder $$29$$. Choice B has calculation error. Choice C has impossible remainder ($$> 73$$). Choice D shows correct arithmetic.

To find the remainder: $$r = 9,576 - 37 × 258$$. Calculate $$37 × 258 = 9,546$$, so $$r = 9,576 - 9,546 = 30$$. Check: $$37 × 258 + 30 = 9,546 + 30 = 9,576$$ ✓. Choice A gives the right answer but with incorrect arithmetic shown. Choice B uses wrong calculation. Choice D also uses incorrect multiplication.

$$48$$ goes into $$80$$ once ($$1$$) with remainder $$32$$. The $$6$$ from the tens place combines with this remainder to make $$326$$ for the next step. $$48 × 1 = 48$$, and $$80 - 48 = 32$$. Choice B incorrectly uses $$48 × 2 = 96 > 80$$. Choice C confuses the carrying process. Choice D uses an impossible remainder for this step.

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 $$324$$ pencils per classroom with $$12$$ remaining is correct. If each of the $$18$$ classrooms receives $$324$$ pencils, the total distributed would be $$18 \times 324 = 5,832 - 12 = 5,820$$ pencils. Adding back the $$12$$ remaining pencils gives us $$5,820 + 12 = 5,832$$ total pencils, which matches perfectly. Answer D is correct.

Now let's see why the other options fail. Choice A suggests $$322$$ pencils per classroom: $$18 \times 322 = 5,796$$, leaving $$36$$ pencils remaining, not $$12$$. Choice B claims $$320$$ pencils per classroom: $$18 \times 320 = 5,760$$, which would leave $$72$$ pencils remaining—this option even acknowledges the remainder would be different. Choice C proposes $$323$$ pencils per classroom: $$18 \times 323 = 5,814$$, leaving $$18$$ pencils remaining, not $$12$$.

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.

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 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 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.

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.