Short division with a remainder in the quotient

When we divide a number by another number, we can use a method called short division. Here’s an example: 67 divided by three. We look at one digit at a time in the dividend. Start from the left... ...with the six. Three fit into six two times.

After the equals sign, we write two, as the first digit in the quotient. Then we take the next digit in the dividend, seven. Three fits into seven two times. Write another two in the quotient. But three doesn’t fit evenly into seven two times — there’s something left over.

We get a remainder: seven minus six, is one. So 67 divided by 3 is 22 with a remainder of 1. If there is a remainder, we show it in the answer by writing ‘remainder’ and what we have left, after the quotient, like this. Here is another example: 839 divided by four. Use short division and start from the left with eight.

Four fits into eight two times. Write two. Then we look at the three in the dividend. Four doesn’t fit into three. Write zero after the two.

Instead, let’s try using both the 3 and the 9: 39. We use the four times table. Four times nine is 36. Four times ten is 40. So four fits into 39 nine times.

And now we have a remainder of 39 minus 36, that’s three. Write remainder three in the answer. Let’s look at one last example: 1442 divided by 3. Pause the video and calculate this one yourself. Let’s find out what the quotient is by using short division.

First, the digit one in the dividend. Three doesn’t fit into one. We don’t need to write a zero in the answer — because zero at the beginning of a number does not change the size of it. Now we look at two digits in the dividend, one and four, 14. Three fits into 14 four times.

Write four. But there are 2 left over. Write a two after the first four in the dividend, as a remainder. Now, use the remainder and the next digit in the dividend, four. That is 24.

Three fits into 24 eight times. Write eight in the quotient. The last digit to be divided by three is two. Three doesn’t fit into two, so we write a zero after the eight in the answer. Here, the zero is the ones in 480, so here it is needed!

Two minus zero is two, so there are two left over. The answer to 1442 divided by 3 is 480 remainder 2. Now we have practised ‘short division with a remainder in the quotient’.