Welcome to long division! Long division is a systematic method for dividing large numbers into smaller, manageable parts. It helps us solve division problems that would be difficult to do mentally. In this example, we're dividing 847 by 7 to get 121.
Long division follows a systematic four-step process known as DMSB. D stands for Divide - we divide the first digits of the dividend by the divisor. M stands for Multiply - we multiply our quotient by the divisor. S stands for Subtract - we subtract this product from our dividend. B stands for Bring Down - we bring down the next digit. We repeat these steps until we finish the problem.
Now let's start the first step: Divide. We look at the first digit of our dividend, which is 8. We ask ourselves: how many times does 7 go into 8? The answer is 1 time, with a remainder. So we write 1 above the 8 in our quotient. This is the beginning of our answer.
Now we continue with steps 2 and 3. Step 2 is Multiply: we take our quotient digit 1 and multiply it by our divisor 7. One times 7 equals 7. We write this 7 directly under the 8. Step 3 is Subtract: we subtract 7 from 8, which gives us 1. We write this 1 below the subtraction line. This remainder of 1 will be used in the next step.
Now we complete the division by repeating the DMSB process. We bring down the 4 to make 14. Fourteen divided by 7 equals 2, so we write 2 in our quotient. Two times 7 equals 14, subtract to get 0. Finally, we bring down the last digit 7. Seven divided by 7 equals 1. Our complete answer is 121. We can check: 121 times 7 equals 847, confirming our solution is correct.