Divide $25 \longdiv {1,658}$.
To find the quotient, start by dividing □ 25 into □.
The task is to perform the long division of 1658 by 25. In the long division algorithm, we divide the dividend (1658) by the divisor (25). We proceed by examining the digits of the dividend from left to right.
First, consider the first two digits of the dividend, 16. Since 16 is smaller than 25, we cannot divide 25 into 16. Therefore, we include the next digit and consider the number 165.
Next, we determine how many times 25 fits into 165. By checking multiples of 25:
\(25 \times 6 = 150\)
\(25 \times 7 = 175\)
Since 175 is greater than 165, the largest multiple of 25 that is less than or equal to 165 is 150. Thus, the first digit of the quotient is 6. We subtract 150 from 165 to get a remainder of 15.
Now, bring down the next digit of the dividend, which is 8, and place it next to the remainder 15 to form the number 158.
We then divide 158 by 25. Checking multiples of 25 again:
\(25 \times 6 = 150\)
\(25 \times 7 = 175\)
Since 175 is greater than 158, the largest multiple of 25 that is less than or equal to 158 is 150. Thus, the next digit of the quotient is 6. We subtract 150 from 158 to get a remainder of 8.
The division process is complete as there are no more digits in the dividend to bring down. We have found a quotient of 66 and a remainder of 8.
We can express the result as:
\(\frac{1658}{25} = 66 \text{ remainder } 8\)
Or, in decimal form:
\(66 + \frac{8}{25} = 66 + 0.32 = 66.32\)
Therefore, the result of dividing 1658 by 25 is \(\boxed{66.32}\).
Long division is a fundamental skill used in many everyday situations, such as managing a budget or sharing items. For instance, if you have a total of \(\$1658\) and you want to split it equally among 25 people, you would perform this division to determine that each person receives \(\$66.32\). This skill ensures accurate calculations when dealing with larger numbers and fractional amounts in daily financial or logistical tasks.