Welcome to long division! Today we'll learn how to divide a three-digit number by a two-digit number. Long division is a systematic method that breaks down complex division into manageable steps. Let's use four hundred fifty-six divided by twenty-three as our example.
Now let's start the division process. First, we look at the first two digits of four hundred fifty-six, which is forty-five. We ask ourselves: how many times does twenty-three go into forty-five? Twenty-three times one equals twenty-three, and twenty-three times two equals forty-six, which is too big. So twenty-three goes into forty-five exactly one time, with a remainder of twenty-two.
Next, we bring down the last digit, which is six. This gives us two hundred twenty-six. Now we ask: how many times does twenty-three go into two hundred twenty-six? Twenty-three times nine equals two hundred seven, and twenty-three times ten equals two hundred thirty, which is too big. So twenty-three goes into two hundred twenty-six exactly nine times, with a remainder of nineteen.
Excellent! Our division is now complete. Four hundred fifty-six divided by twenty-three equals nineteen with a remainder of nineteen. Let's verify our answer by checking: twenty-three times nineteen equals four hundred thirty-seven, and four hundred thirty-seven plus nineteen equals four hundred fifty-six. Perfect! Our answer is correct.
To summarize what we've learned: Long division is a systematic method that breaks complex division problems into manageable steps. We start by dividing the first part of the dividend, then multiply, subtract, and bring down digits one by one. This process continues until we've used all digits, and we always verify our answer through multiplication.