Long Division with 3-Digit Dividends and Remainders

Long Division with 3-Digit Dividends and Remainders

Long division is an essential mathematical technique to help us solve problems involving multi-digit numbers. As we delve into long division with 3-digit dividends, we'll focus on understanding how to compute the quotient and remainder accurately.

Step-by-Step Process

1. Write the division problem: Start with the dividend (the number being divided) and the divisor (the number by which we're dividing). For example, if we're dividing 645 by 17, the problem would be (645 ÷ 17).

2. Prepare to subtract: Write the divisor below the dividend and draw a line below the divisor.

3. Find the highest digit in the dividend that is less than or equal to the divisor: In our example, the highest digit is 6, which is less than or equal to 17.

4. Multiply the divisor by the highest digit and write the product in the quotient's first position: Multiplying 17 by 6, we get 102. Write this as the first digit in the quotient.

5. Subtract the product from the dividend: Subtract 102 from 645, which leaves us with 543.

6. Write the remainder below the dividend: Write 543 as the new dividend and move to step 3 to find the next digit of the quotient.

7. Repeat steps 3-6: Continue this process until there are no more digits left in the dividend.

8. Write the remainder: Once you reach the last digit in the dividend, write the remainder below the dividend and stop.

Remainder in Long Division

The remainder is the value that's left over after you've divided the dividend by the divisor as many times as possible. In our example, the remainder is 543.

Long Division and 3-Digit Dividends

As we've seen, long division with 3-digit dividends follows the same process as long division with single-digit dividends, but it involves more steps and digits. The process remains the same, but the calculations and the recording of the quotient and remainder become more complex.

By mastering this process, we can accurately solve problems involving 3-digit dividends and remainders, laying the foundation for more advanced mathematics.