Verified Answer :
- Identify the dividend \(61,261\) and the divisor \(70\).
- Divide 612 by 70 to get 8, leaving a remainder of 52.
- Bring down 6 to get 526, divide by 70 to get 7, leaving a remainder of 36.
- Bring down 1 to get 361, divide by 70 to get 5, leaving a final remainder of 11.
- The final result is \(\boxed{875 \text{ remainder } 11}\).
Explanation
- Problem Analysis and Objective
The objective is to perform the long division of 61,261 by 70. This means we are seeking a quotient \(q\) and a remainder \(r\) such that \(61,261 = 70 \times q + r\), where \(0 \le r < 70\). We will proceed by examining the digits of the dividend from left to right.
- Dividing 612 by 70
First, we look at how many times 70 divides into the first three digits of 61,261, which is 612. Since \(70 \times 8 = 560\) and \(70 \times 9 = 630\), the largest multiple of 70 less than 612 is \(70 \times 8 = 560\). Subtracting 560 from 612 gives \(612 - 560 = 52\). So, the first digit of our quotient is 8, and the remainder is 52.
- Dividing 526 by 70
Next, we bring down the next digit of the dividend, which is 6, to form the number 526. Now, we find how many times 70 goes into 526. Since \(70 \times 7 = 490\) and \(70 \times 8 = 560\), the largest multiple of 70 less than 526 is \(70 \times 7 = 490\). Subtracting 490 from 526 gives \(526 - 490 = 36\). Thus, the second digit of our quotient is 7.
- Dividing 361 by 70
Finally, we bring down the last digit of the dividend, which is 1, to form the number 361. Now, we find how many times 70 goes into 361. Since \(70 \times 5 = 350\) and \(70 \times 6 = 420\), the largest multiple of 70 less than 361 is \(70 \times 5 = 350\). Subtracting 350 from 361 gives \(361 - 350 = 11\). Thus, the third digit of our quotient is 5, and the final remainder is 11.
- Final Answer
Combining the digits, we have the quotient 875 and the remainder 11. Therefore, the result of the division is \(\boxed{875 \text{ remainder } 11}\).
Examples
Long division is a fundamental skill used in everyday situations, such as splitting costs. Imagine you and your friends collected a total of \(\$61,261\) from a fundraiser, and you need to distribute this money into 70 equal-sized donation packets. Using long division, you determine that each of the 70 packets will contain \(\$875\), and there will be \(\$11\) left over to be donated separately. Mastering this process ensures accurate and fair distribution of resources in any budgeting scenario.