The Correct Answer and Explanation is:
Of course. Here are the correct answers to the division problems, followed by a detailed explanation of the long division process used to solve them.
Correct Answers
- 38 200 ÷ 56 = 682 with a remainder of 8
- 3 209 ÷ 18 = 178 with a remainder of 5
- 4 567 ÷ 93 = 49 with a remainder of 10
- 7 331 ÷ 47 = 155 with a remainder of 46
- 9 536 ÷ 82 = 116 with a remainder of 24
Explanation of the Method
These problems are solved using the process of long division, which is a systematic way to divide multi-digit numbers. The process involves a repeating cycle of steps: dividing, multiplying, subtracting, and bringing down the next digit. Let’s walk through the first problem, 38,200 ÷ 56, as a detailed example.
First, we look at the dividend (38,200) and see how many times the divisor (56) can fit into its first few digits. 56 cannot go into 3 or 38, so we look at 382. We estimate that 56 goes into 382 about 6 times. We write “6” as the first digit of our answer.
Next, we multiply this digit by the divisor: 6 × 56 = 336. We write 336 under 382 and subtract: 382 – 336 = 46.
Then, we bring down the next digit from the dividend, which is 0, placing it next to our result of 46. This gives us the new number 460.
We repeat the cycle: How many times does 56 go into 460? It goes in 8 times. We write “8” as the next digit of our answer. We multiply 8 × 56 = 448 and subtract it from 460, which leaves 12.
We bring down the final digit, another 0, to make the number 120.
Finally, we repeat the cycle one last time. How many times does 56 go into 120? It goes in 2 times. We write “2” as the last digit of our answer. We multiply 2 × 56 = 112 and subtract it from 120, which leaves a final value of 8.
Since there are no more digits to bring down, 8 is our remainder. The quotient (the main part of the answer) is 682, with a remainder of 8. This same methodical process is applied to solve the other four problems.
