The Correct Answer and Explanation is:
The correct answer is 51.
To find the quotient of 1591 divided by 31 using the long division algorithm, we follow a systematic, step by step process.
First, we set up the division problem. The divisor, 31, is placed to the left of the division bracket, and the dividend, 1591, is placed inside it.
The initial step is to determine how many times the divisor, 31, can fit into the first part of the dividend. We see that 31 cannot go into 1 or 15, so we consider the first three digits, 159. We need to estimate how many times 31 goes into 159. A helpful estimation trick is to round the numbers. Rounding 31 to 30 and 159 to 150, we can see that 30 goes into 150 five times. Let’s try 5. We multiply 5 by 31, which equals 155. This number is less than 159, so 5 is the correct first digit of our quotient. We write the 5 above the 9 in the dividend.
Next, we subtract 155 from 159, which leaves a remainder of 4. We then bring down the next digit from the dividend, which is 1, placing it next to the 4 to form the new number 41.
Now, we repeat the process. We need to find out how many times our divisor, 31, goes into the new number, 41. It is clear that 31 can go into 41 only one time. We write 1 as the next digit in our quotient, next to the 5.
Finally, we multiply this new digit, 1, by the divisor, 31. The result is 31. We write 31 below 41 and subtract. The difference is 10 (41 minus 31 equals 10). Since there are no more digits to bring down from the dividend, our calculation is complete. The number on top is the quotient, and the final number at the bottom is the remainder.
Thus, the quotient of 1591 divided by 31 is 51, with a remainder of 10. The question asks for the quotient, which is 51.
