Final answer:
To find the quotient of 8,688 ÷ 24 via long division, divide each part of the dividend successively by the divisor and write the entire solution as 362. The process illustrates how division can be broken down into steps and reciprocals help understand the relationship between multiplication and division.
Step-by-step explanation:
To find the quotient of 8,688 ÷ 24, we can perform long division. Here are the steps:
- First, set up the division, with 8,688 being the dividend (inside the division bar) and 24 as the divisor (outside the division bar).
- Divide the first two digits of the dividend (86) by the divisor (24), which goes 3 times since 24 times 3 is 72, which is close to 86 without going over.
- Write 3 at the top, multiply 3 by 24, and write 72 below 86, then subtract 72 from 86, leaving us with 14.
- Bring down the next digit (8) to get 148.
- Divide 148 by 24, which goes 6 times. Write 6 at the top, multiply 6 by 24, get 144, and write it below 148.
- Subtract 144 from 148, which leaves 4.
- Bring down the last digit (8) to get 48.
- Finally, divide 48 by 24, which is exactly 2.
- Write 2 at the top, multiply 2 by 24, get 48, and write it below 48.
- The division has no remainder. Our final answer is 362.
As a quick review, reciprocals help us understand that dividing by a number is the same as multiplying by its reciprocal. This concept is useful when working with division in different forms, whether with whole numbers or with powers of ten, as illustrated with the provided examples.
It's always good to remember that there are various methods to arrive at the same solution as we have seen in this and the other example of division with powers of ten. Different strategies might be employed, but the end result remains constant, which can reinforce our understanding and accuracy.