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Division

Short Division

Long Division

Key Vocabulary

Key terms

Divide

Divisible

Remainder

Share

Groups

Left over

Quotient

Dividend

Divisor

Obelus

Main Menu

Definitions

Long Division

Short Division

Definitions

To Divide is to share or group a number into

equal parts. Eg) If you divide 10 by 2 you get 5.

Divide

A number is divisible if it can be divided

without a remainder. Eg) 10 can be divided by 2,

it is divisible by 2. 10 can not be divided by 3

without a remainder so 10 is not divisible by 3.

Divisible

A remainder is the amount left over after

dividing a number. Eg) If you divide 10 by 3

the answer is 2 with 1 remainder

Remainder

To share is to divide into equal groups. Eg) If

you share 10 sweets between 2 people, each person

gets 5.

Share

Grouping is the process of dividing into equal

sets (groups). Eg) If you share 10 sweets

between 2 people, each person gets 5.

Groups

The left over is the same as the remainder. Eg)

If you divide 10 by 3, the answer is 3 with 1

left over.

Left over

The Quotient is the number resulting from

dividing one number by another (the answer) Eg)

In 10 5 2, the quotient is 2.

Quotient

Dividend

The Dividend is the number being divided. Eg)

In 10 5 2, 10 is the dividend.

Divisor

The Divisor is the number you are dividing by.

Eg) In 10 5 2, 5 is the divisor is the

dividend.

Obelus

The Obelus is the name of the sign.

Main Menu

Long Division

Short Division

Short Division

What is division?

Reversing Multiplication

Working with remainders

Repeated subtraction

The Bus Stop Method

The Grid Method

Main Menu

Long Division

Definitions

Short Division

What is division?

Division is a Mathematical Operation (like add,

subtract and multiply). Division determines how

many times one quantity is contained in another.

It is the inverse of multiplication.

Divisions can be written in many different ways

2 6 1 3

Main Menu

Long Division

Definitions

Short Division

Reversing Multiplication

Division vs Multiplication

x

25

4

100

x

4

25

100

100

25

4

100

4

25

Look at the relationship between these three

numbers

These are often called associated facts

4

25

100

Main Menu

Long Division

Definitions

Short Division

Practice

Short Division

The Bus Stop Method

3

2

1

To work out this sum, divide 963 by 3, one digit

at a time, starting from the left.

This is sometimes called the space saver method

Main Menu

Long Division

Definitions

Short Division

Practice

Short Division

The Bus Stop Method

0

6

4

2

1

To work out this sum, divide 252 by 3, one digit

at a time, starting from the left.

Main Menu

Long Division

Definitions

Short Division

Practice

Short Division

The Bus Stop Method

0

8

8

r 3

3

3

To work out this sum, divide 353 by 4, one digit

at a time, starting from the left.

Main Menu

Long Division

Definitions

Short Division

Practice

Short Division

Repeated Subtraction

You can use repeated subtraction. For example

Subtract 6 30 6 24

Subtract 6 24 6 18

30 6

Subtract 6 18 6 12

Subtract 6 12 6 6

Subtract 6 6 6 0

There is nothing left so no remainder

Count the number of subtractions

5

30 6 5

Main Menu

Long Division

Definitions

Short Division

Practice

Short Division

Repeated Subtraction

Another example

Subtract 17 90 17 73

Subtract 17 73 17 55

Subtract 17 55 17 38

Subtract 17 38 17 21

90 17

Subtract 17 21 17 4

There is 4 left over so this is the remainder

90 17 5 r 4

Count the number of subtractions

5

Main Menu

Long Division

Definitions

Short Division

Practice

Short Division

The grid method

Using a grid can be helpful if you are confident

with your times tables

Example 754 12

Draw a grid

We can make 700 12 easier

We can now divide our second column 30 12

Now, the final column

Notice that 30 12 is 2 remainder 6. This six

carries over to the next column

Therefore 754 12 62 r 10

Main Menu

Long Division

Definitions

Short Division

Practice

Short Division

- Want to practice?

NO- Im ready for long division

YES- I want to practice reversing multiplication

Reversing multiplication solutions

YES- I want to practice the bus stop method

Bus stop method solutions

YES- I want to practice the grid method

Grid method solutions

Main Menu

Long Division

Definitions

Long Division

Repeated Subtraction

The Traditional Method

Main Menu

Definitions

Short Division

Long Division

Repeated Subtraction

- Lets try 543 16

543

Start with we know 10 x 16 160

383

- 160 (10 x 16)

223

- 160 (10 x 16)

- 160 (10 x 16)

63

31

- 32 (2 x 16)

We cannot subtract another 160 so look for a

lower multiple

15 cannot be divided by 16 so this is the

remainder

15

- 16 (1 x 16)

We have used 10 10 10 2 1 lots of 16.

This means we divided 33 times

543 16 33 remainder 15

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Repeated Subtraction

- Lets try 1748 42

1748

Start with we know 10 x 42 420

- 420 (10 x 42)

1328

- 420 (10 x 42)

908

- 420 (10 x 42)

488

- 420 (10 x 42)

68

We cannot subtract another 420 so look for a

lower multiple

26 cannot be divided by 42 so this is the

remainder

- 42 (1 x 42)

26

We have used 10 10 10 10 1 lots of 42.

This means we divided 41 times

1748 42 41 remainder 26

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Repeated Subtraction

- Lets try 9265 37

9265

Start with we know 100 x 37 3700

5564

- 3700 (100 x 37)

1865

- 3700 (100 x 37)

We cannot subtract another 3700 so look for a

lower multiple

- 740 (20 x 37)

1125

385

- 740 (20 x 37)

We cannot subtract another 740 so look for a

lower multiple

15

- 370 (10 x 37)

15 cannot be divided by 37 so this is the

remainder

We have used 100 100 20 20 10 lots of 37.

This means we divided 250 times

9265 37 250 remainder 15

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

- The Divide - Multiply Subtract Cycle

Notice DMS is alphabetical. This might help you

remember the order!

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

This is a similar method to 'short' division,

but, rather than writing the remainder at the

top, we work it out underneath. Dont forget the

DMS cycle

Starting with 72 4

The first step is write out the division.

Step 2 is to divide 7 by 4

1

8

Step 3 is to multiply 4 x 1, this will show us

what weve worked out so far.

7 4 1 r 3

Step 4. Now we subtract this to see what weve

still got to divide

4

4 x 1 4

3

2

Step 5. Divide 32 by 4

3 2

Step 6 Multiply 8 x 4

4 x 8 32

32 4 8

Step 7 Subtract this to see if we need to

continue to divide

0

Finished!

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

This is a similar method to 'short' division,

but, rather than writing the remainder at the

top, we work it out underneath.

0

3

9

Lets try 156 4

0

1

5

1 2

3

6

Finished!

3 6

0

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

This is a similar method to 'short' division,

but, rather than writing the remainder at the

top, we work it out underneath.

5

5

0

Lets try 156 4

0

2

7

2 5

Finished!

2

5

2 5

0

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

This is a similar method to 'short' division,

but, rather than writing the remainder at the

top, we work it out underneath.

3

1

2

r 5

Lets try 3749 12

3 6

1

4

1 2

Finished!

2

9

2 4

5

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

This is a similar method to 'short' division,

but, rather than writing the remainder at the

top, we work it out underneath.

1

2

0

r 5

Lets try 3749 31

We may find this useful 31 62 93 124 155 186 217

248 279 310

3 1

4

6

6 2

2

9

Finished!

2 4

5

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

- The space saver method

Lets try 489 7

0

6

9

r 6

6

4

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

- The space saver method

Lets try 4729 28

0

1

6

8

r 25

4

19

24

These might be useful 28, 56, 84, 112, 140, 168,

196, 224, 252, 280

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

Traditional method

- The space saver method

Lets try 46283 36

0

1

2

8

5

r 23

4

10

30

20

These might be useful 36, 72, 108, 144, 180,

216, 252, 288, 324, 360

Main Menu

Long Division

Definitions

Short Division

Practice

Division practise

613 r 4

- 3682 divided by 6
- 6741 divided by 12
- 2065 divided by 32
- 3927 divided by 24

561 r 9

64 r 17

163 r 15

Main Menu

Long Division

Definitions

Short Division

Practice

Division practise

1278 r 2

- 6392 divided by 5
- 5392 divided by 11
- 5629 divided by 52
- 25393 divided by 23

490 r 2

108 r 13

1104 r 1

Main Menu

Long Division

Definitions

Short Division

Practice

Division practise

1761 r 1

- 5284 divided by 3
- 63042 divided by 9
- 1390 divided by 16
- 63926 divided by 43

7004 r 6

86 r 14

1486 r 28

Main Menu

Long Division

Definitions

Short Division

Practice

Long Division

- Want to practice more?

NO. All finished.

YES- I want to practice repeated subtraction

Repeated subtraction solutions

YES- I want to practice the traditional method

Traditional method solutions

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