Long division introduction

Let’s calculate some division problems! 48 divided by 4. Since we are dividing by 4, we will look at the four times table. But, this does not go all the way to 48. Therefore, we need to use another method of calculating: We start by drawing a horizontal line.

The number we are about to divide with, the divisor, we write here. Below the line, to the left. We also write the dividend, 48, below the line, but to the right. Now, we’re ready to start calculating. We take one digit at a time in the number to be divided, the dividend.

And we start from the left! So the first number we are going to divide is four. Four goes into four one time. And we write that one here, above the line. Here the answer, the quotient, will gradually appear.

Let’s continue! Four times one is four. We write that four underneath the dividend’s four. Now let’s see if there is a remainder left, after having divided the tens. Use the four you just wrote.

Subtract it from the four in 48. 4 minus 4. This is zero. Write zero in the same column. Before we divide the next digit from the dividend, the eight, move it down next to the zero.

Now, we are ready to divide. Four goes into eight twice. Write a two after the one in the quotient. Four times two is eight. Write an eight under the eight you wrote beside the zero.

Now, subtract the eight you just wrote from the next digit in the dividend. This is 8 too. Will there be any remainder left? No, because eight minus eight is zero. No remainder.

Now, there are no more digits in the number we are dividing, so we are done. Here is the answer, the quotient. 48 divided by four is 12. This method of calculating is called long division. Long division is practical: It is easier to keep track of what you are doing when the tens are written in their separate column, the ones in their column, and so on.

Let’s look at another example! 688 divided by 2. First, the horizontal line. Write the divisor, 2, to the left, below the line. The dividend to the right.

We start with the leftmost digit in the dividend, six. Two goes into six three times. Write a three in the quotient, above the line. Two times three is six. Write it under the dividend’s six.

Take the six you just wrote, and subtract it from the six in the dividend. Six minus six is zero. The next digit is eight. Move the eight down next to the zero. Two goes into eight four times.

Write a four after the three in the quotient. Two times four is eight. Write it under the eight you just moved down. Eight minus eight is zero. Move down the next eight in the dividend.

Keep calculating. Two goes into eight four times. Add another four in the quotient. Two times four is eight… and eight minus eight is zero, … so there is no remainder. The answer to 688 divided by two is 344. – There’s the method: One horizontal line.

The divisor to the left below the line. The dividend to the right. And then for each digit in the dividend: Divide. Multiply. Subtract.

Move down. Until you run out of digits. That’s the way it’s done. Now all you need is practice.