Let's solve the division problem 811 divided by 8. In this problem, 811 is the dividend, 8 is the divisor, and we're looking for the quotient and remainder.
We'll use long division to solve 811 divided by 8. First, we see how many times 8 goes into the first digit, 8. It goes exactly 1 time. We multiply 8 by 1 to get 8, then subtract to get 0. Next, we bring down the 1 to make 1. Since 8 doesn't go into 1, we write 0 and bring down the next digit to make 11. Finally, 8 goes into 11 once with a remainder. We multiply 8 by 1 to get 8 and subtract from 11 to get a remainder of 3.
Let's break down each step in detail. First, 8 divided by 8 equals 1 with no remainder. Next, we look at 81 divided by 8. Eight goes into 81 ten times because 8 times 10 is 80, leaving a remainder of 1. Then we have 11 divided by 8, which goes 1 time with a remainder of 3. So our quotient is 101 and remainder is 3. To verify, we can check that 1 times 8 is 8, 10 times 8 is 80, and 1 times 8 is 8. Adding these gives 96, and when we account for place values correctly, we get our original number 811.
Let's verify our answer of 101 remainder 3 using two methods. First, the multiplication check: we multiply 101 by 8 to get 808, then add our remainder 3 to get 811, which matches our original dividend. Second, estimation: we know 8 times 100 is 800, which is close to 811. The difference is 11. Since 8 goes into 11 once with remainder 3, our total is 100 plus 1, which is 101, with remainder 3. Both methods confirm our answer is correct.
Our final answer to 811 divided by 8 can be expressed in three different ways. First, as a whole number with remainder: 101 remainder 3. This is useful for grouping problems, like determining how many groups of 8 items we can make from 811 items with 3 left over. Second, as a mixed number: 101 and 3/8. This is useful when we need to express the exact fractional value. Third, as a decimal: 101.375. This is useful for calculations and measurements where decimal values are preferred. All three representations are mathematically equivalent and correct.