Elena completed this division problem:

Question

A long division problem shows 4,297 under the division symbol. 38 is outside to the left of the symbol. The digit 1 is located above the 2 in the hundreds place of the dividend. The digit 0 is located above the 9 in the tens place of the dividend. The digit 7 is located above the 7 in the ones place of the dividend. There is a R to the right of the quotient with the remainder 31 following it. The number 38 is subtracted from the 4 in the thousands place and the 2 in the hundreds place. The digit 2 is below the 8 in the 38 being subtracted. The digit 9 is next to the 2, below the 9 in the tens place of the dividend. The digit 7 is next to the 9, below the 7 in the ones place of the dividend. 266 is subtracted from 297. The difference is 31.

Answer 1

Let’s break down the division problem based on the information provided.

1. Set Up the Problem: We will divide 4,297 by 38 using long division.

2. Quotient: You mentioned that the quotient starts with a 1 above the 2 in the hundreds place of 4,297. This indicates that 38 goes into 42 (the first two digits of 4,297) once. Thus, we write 1 above the 2.

3. First Subtraction: Multiply 1 (the quotient) by 38: \[ 1 \times 38 = 38 \] We subtract this from 42: \[ 42 - 38 = 4 \]

4. Bring Down Next Digit: Next, bring down the 9 (the digit in the tens place): Now we have 49 (formed by bringing down the 9).

5. Determine Next Digit: We need to figure out how many times 38 fits into 49. This goes in once (1) as well. We write another 1 above the 9 in the tens place. Thus, we have 11 so far.

6. Second Subtraction: Multiply 1 (the new quotient) by 38 again: \[ 1 \times 38 = 38 \] Subtract this 38 from 49: \[ 49 - 38 = 11 \]

7. Bring Down Next Digit: Now, bring down the 7 (the last digit of 4,297), giving us 117.

8. Determine Next Digit: Next, we see how many times 38 fits into 117. It fits 3 times (as \( 3 \times 38 = 114 \)). We write 3 above the 7, leading to a current quotient of 113.

9. Third Subtraction: Multiply 3 by 38: \[ 3 \times 38 = 114 \] Now subtract: \[ 117 - 114 = 3 \]

10. Remainder: Now, we have completed the long division with a quotient of 113 and a remainder of 3.

So far, the long division reveals that: \[ 4,297 \div 38 = 113 \quad R3 \]

However, you indicated a remainder of 31. It's possible that the numbers were misunderstood at some point, as the calculations show a remainder of 3 rather than 31. Here's the final conclusion based on the given descriptions:

The division of 4,297 by 38 yields a quotient of 113 with a remainder of 3. If the remainder mentioned was indeed supposed to be 31, it indicates some miscalculation or perhaps an incorrect initial dividend or divisor in the problem context provided.