Written divisionSome reminders for written division

When you are dividing numbers you need to decide whether to use a mental method (doing sums in your head) or a written method (writing the numbers down).

A reminder about place value

Have a look at the number 623.

6 is the hundreds digit. 2 is the tens digit. 3 is the units digit.

Division sums

Division vs. Multiplication

With whole numbers when you multiply, the number gets bigger. When you divide, the number gets smaller.

There is always a link between division and multiplication sums. Have a look at these three numbers in division and multiplication sums:

Division and multiplication are opposites or 'inverses'. If you divide by an amount and then multiply the result by the same amount, you end up back where you started.

Timesavers ÷ 10 and ÷ 100

Dividing by 10

When you divide by 10 you move all the digits one place to the right and then numbers become 10 times smaller. If the number ends with a zero you can simply remove it.

Dividing by 100

When you divide by 100 you move all the digits two place to the right and then numbers become 100 times smaller. If the number ends with two zeros you simply remove them.

To learn more about multiplying and dividing by 10, 100 and 1 000 visit the Multiply and divide by 10, 100 and 1 000 module.

*NEW* Division using repeated subtraction

One way of dividing is to think of it as repeated subtraction.

For example, look at the question 20 ÷ 5    Subtract  5             20 - 5 = 15    Subtract 5 again   15 - 5 = 10    Subtract 5 again   10 - 5 = 5    Subtract 5 again     5 - 5 = 0

Count the total number of times you subtracted 5. In this question it was 4 times. As the final number after all the subtractions is 0, the 5 divides into 20 exactly with no remainder.    20 ÷ 5 = 4

Here's another example, 25 ÷ 6    Subtract  6             25 - 6 = 19    Subtract 6 again   19 - 6 = 13    Subtract 6 again   13 - 6 = 7    Subtract 6 again     7 - 6 = 1

You can't subtract another 6 as there is only 1 left, which is less than the divisor 6. This is the remainder. 6 was subtracted 4 times, but you have a remainder, 1.    25 ÷ 6 = 4 remainder 1  

Using multiples with repeated subtraction

You can also combine this method with using multiples, such as multiples of 10, as a shortcut.

For example, 400 ÷ 8As 400 is divisible exactly by 10 you can subtract 80 instead of 8.    Subtract 80 (i.e. 10 x 8)  400 - 80 = 320    Subtract 80 (i.e. 10 x 8)  320 - 80 = 240    Subtract 80 (i.e. 10 x 8)  240 - 80 = 160    Subtract 80 (i.e. 10 x 8)  160 - 80 = 80    Subtract 80 (i.e. 10 x 8)    80 - 80 = 80

Add the total number of 8s subtracted which is 10 + 10 + 10 + 10 + 10 to get the answer 50 with no remainder.    400 ÷ 8 = 50

Short division

Large numbers are difficult to divide, because we don't learn the times tables for them.

This is the traditional way of doing a division sum. You may have tried this method at school.

396 ÷ 3 can be written like this:

To work out this sum, divide 3 into 396 one digit at a time, starting from the left (with the digit 3). Put the result of each division on top of the line.

      The 3 into 3 goes 1 time exactly      3 into 9 goes 3 times      3 into 6 goes 2 times exactly      396 ÷ 3 = 132

But what if the numbers don't divide exactly? This is where you carry numbers.2 565 ÷ 5 can be written like this:

To work out this sum, divide 5 into 2 565 one digit at a time, starting from the left (with the digit 2). Put the result of each division on top of the line.

      The 5 into 2 won't go so you carry the 2      5 into 25 goes 5 times exactly      5 into 6 goes once with 1 remainder       5 into 15 goes 3 times exactly      2 565 ÷ 5 = 513

Long division

This is the traditional way of doing long division sums, which you may have been taught at school. It doesn't look much fun, but it's not so bad. Give it a go.

Have a look at the sum: 8 640 ÷ 15

8 640 ÷ 15 = 576

Spacesaver division

Spacesaver division is long division without all the written bits. With this method you're doing a division sum, but all the thinking is multiplication and subtraction! You can use it when dividing by both one digit and two digit numbers.

Have a look at the sum:22 972 ÷ 4.

Step 1: 4 into 2 won't go - so carry 2 Step 2: 4 into 22 goes 5 times (5 x 4 = 20) - so carry the remainder 2 Step 3: 4 into 29 goes 7 times (7 x 4 = 28) - so carry the remainder 1 Step 4: 4 into 17 goes 4 times (4 x 4 = 16) - so carry the remainder 1 Step 5: 4 into 12 goes exactly 3 times.

22 972 ÷ 4 = 5 743

This method also works when dividing by 2 digit numbers. Have a look at the sum 40 458 ÷ 11.

Step 1: 11 into 4 won't go - so carry the remainder 4 Step 2: 11 into 40 goes 3 times(3 x 11 = 33) - so carry the remainder 7 Step 3: 11 into 74 goes 6 times (6 x 11 = 66) - so carry the remainder 8 Step 4: 11 into 85 goes 7 times (7 x 11 = 77) - so carry the remainder 8 Step 5: 11 into 88, goes exactly 3 times (8 x 11 = 88)

40 458 ÷ 11 = 3 678

If you need some help with times tables...

Have a look at the times tables module.

Division Glossary

Here are some of the words which will crop up when doing division sums.

Have a look below to see how they can be used in the simple sums 6 ÷ 3 = 2 and 7 ÷ 3.

Divide If you divide 6 by 3 you get 2.

Divisible 6 is exactly divisible by 3. 7 is not exactly divisible by 3.

Left over If you divide 7 by 3 the answer is 2 with 1 left over.

Remainder If you divide 7 by 3 the answer is 2 with 1 remainder.

Share If you share 6 toffees between 3 people, each person gets 2.

Groups There are 3 groups of 2 in 6.

Carry If you write out the sum 2 565 ÷ 5 you have to carry some numbers. In this sum you first carry the 2 over to the 5. The 5 into 25 goes 5 times exactly. Then 5 into 6 goes once with 1 remainder which you carry over. Then 5 goes into 15 exactly 3 times.

'Written division' tutor notes

This module can be used as a starting point for: learning different methods of written division.

Students may find it useful to look at the Times tables and Mental division sections of the site before tackling this module.

Please let us know what you think of this module and the factsheets, worksheets, quiz and game at skillswise.feedback@bbc.co.uk

How does this tie in with the new curriculums?

England N1/L1.3 - Add, subtract, multiply and divide using efficient written methods.N1/L1.4 - Multiply and divide whole numbers by 10 and 100.N1/L1.5 - Recall multiplication facts up to 10 x 10 and make connections with division facts.

Wales As England.

Northern Ireland As England.

Scotland See www.aloscotland.com for details of the Scottish curriculum.

In the Skillswise module you'll find:

Written division factsheets There are six sheets in this section which can be printed out and kept.

Factsheet 1 - Some reminders for written division. Factsheet 2 - Timesavers ÷10 and ÷100. Factsheet 3 - Division using repeated subtraction. Factsheet 4 - Short division. Factsheet 5 - Long division. Factsheet 6 - Spacesaver division. Factsheet 7 - A glossary of terms for division.

The Amoeba Division Games In this game, learners can practise spacesaver division as shown in Factsheet 5. There are three levels, A being the easiest and C the hardest. Learners fill gaps in the division sum by typing in. For each sum they can look at a times table reminder to help them with their division. At the end of the game they are given a summary of how they got on in each section and an overall score. You might find it useful to visit the 'How to play' section of the game before showing it to your learners.

If they get 75% or more, they get a bonus game - 'Shoot the Amoebas'

TOP TIP! To see the game completely full screen, press the F11 key on the keyboard. This takes away the distraction of the top browser bar. To bring the browser bar back, just press F11 again!

Written division quiz The learner can choose their level. Level A is the easiest, level C the hardest.The division question and answer is shown as an image on the feedback page. The method used to show the working out of the answer is long division. Students can print out a certificate if they score 50% or more in the quiz. This will appear as a link on the results page - click on the link and the certificate will appear in a new window. Students can write their name on the certificate once it's printed.

Written division worksheets There are five printable worksheets in this section for learners to carry on the work done online.

Worksheet 1 - Written division puzzle 1 - a crossword. Worksheet 2 - Written division puzzle 2 - a crossword. Worksheet 3 - Spacesaver division worksheet 1 - dividing by 1-digit numbers. Worksheet 4 - Spacesaver division worksheet 2 - dividing by 2-digit numbers. Worksheet 5 - Long division worksheet.

Technical help:

To get the most out of this topic area you need the following 'plug-ins':

Flash The game in this topic section uses Flash. This is free to download and should only take a few minutes. You can follow the BBC WebWise instructions to download it to your machine.Find out more.

If you don't have Flash the same learning points are covered in the quiz and in the worksheets and factsheets.If you are new to the web, why not try the BBC WebWise online course, Becoming WebWise? It's free, you can do it in your own time from any computer and it will take you through everything you need to know to use the web successfully in your teaching.Get WebWise.

You can find out more about the technical requirements for Skillswise in our Help - Technical Information section.

Taking it further:

Here's a suggestion of another place on the web where you might find useful resources that you can adapt for teaching written division.

AAA Math - division An American site containing many pages demonstrating different division skills, with interactive activities and games.