Long division with decimal quotient

Let's calculate 67 divided by 5 using the ‘long division’ method. Draw a horizontal line. Place the divisor below the line, to the left. Write the dividend to the right. Time to calculate.

Start with the leftmost digit in the dividend, 6. 5 fits into 6 one time. Write 1 in the quotient. 5 times 1 is 5 and 6 minus 5 is 1. This leaves a remainder of 1 to carry to the next calculation.

Move the next digit down from the dividend. 1 and 7 - this forms the number 17. 5 fits into 17 three times. Write 3 after the one in the quotient. Now there are no more digits in the dividend.

And what is the remainder? 5 times 3 is 15 and 17 minus 15 is 2. We can write 13, remainder 2 as an answer. But we can be more precise. We can split the remainder into decimals.

The first thing to do is to add a decimal point and a zero. The zero does not change the value when it is after the decimal point. We add a decimal point in the quotient too. We remove the remainder 2, since we’re starting to calculate with tenths instead. We move the zero down and read the two and the zero as 20.

We divide this by 5. 5 fits into 20 four times. Write 4 after the decimal point. 5 times 4 is 20, and 20 minus 20 is 0. Now there is no remainder left.

So 67 divided by 5 equals 13.4 Let’s have a look at one last example. 43 divided by 4. First, we draw the line as usual. The divisor, 4, goes below the line to the left. The dividend, 43, goes to the right.

Start with the left digit in the dividend, 4. 4 fits into 4 once. Write a one in the quotient, above the line. 4 times 1 is 4, And 4 minus 4 is 0. Then the next digit in the dividend, 3.

Move the three down, next to the zero. 4 fits into 3 zero times. Write a zero in the quotient. 4 times 0 is 0, and 3 minus 0 is 3. We have a remainder of 3.

And now we are out of digits in the dividend. Just as we did earlier, we write a decimal point followed by a zero, to get more digits in the dividend. Now, as we start to use tenths, we write a decimal point in the quotient too. Move the zero down next to the three. Now divide 3 and 0, that is 30, by 4.

4 fits into 30 7 times. Write a seven after the decimal point in the quotient. 4 times 7 is 28, and 30 minus 28 is 2. We get a remainder again, which is 2. So we add another zero to the dividend.

This zero is also added after the decimal point, so it does not affect the value of the dividend. We move the other zero down and read 2 and 0 as 20. Then we divide by 4. 4 fits into 20 5 times. Write 5 in the quotient.

4 times 5 is 20, and 20 minus 20 is 0. Now we have no remainder left! 43 divided by 4 equals 10.75.