Divide Divisible Remainder Share

Groups Left over

Quotient Dividend Divisor Obelus

Main MenuDefinitions Long DivisionShort Division

To Divide is to share or group a number into equal parts. Eg) If you divide 10 by 2 you get 5.

The left over is the same as the remainder. Eg) If you divide 10 by 3, the answer is 3 with 1 left over.

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

Divide

Divisible

Remainder

Share

Groups

Left over

Quotient

Dividend

Divisor

Obelus

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.

To share is to divide into equal groups. Eg) If you share 10 sweets between 2 people, each person gets 5.

Grouping is the process of dividing into equal sets (groups). Eg) If you share 10 sweets between 2 people, each person gets 5.

The Dividend is the number being divided. Eg) In 10 ÷ 5 = 2, 10 is the dividend.

The Divisor is the number you are dividing by. Eg) In 10 ÷ 5 = 2, 5 is the divisor is the dividend.

The Quotient is the number resulting from dividing one number by another (the answer) Eg) In 10 ÷ 5 = 2, the quotient is 2.

The Obelus is the name of the ÷ sign.

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What is division?

The Bus Stop Method

Reversing Multiplication

Repeated subtraction

The Grid Method

Working with

remainders

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What is division?

Divisions can be written Divisions can be written in many different waysin many different ways

3 2 6 12 6 13

2 6 1 ÷ 3

Division is a Division is a Mathematical Operation Mathematical Operation (like add, subtract (like add, subtract and multiply). Division determines how many times one and multiply). Division determines how many times one quantity is contained in another. It is the inverse of quantity is contained in another. It is the inverse of multiplication.multiplication.

Mathematical Operations include:

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Reversing Multiplication

Division vs Multiplication

These are often called associated facts

25 4 100

100 25 44 25 100

100 4 25

÷ =

÷ =

x =

x =

Look at the relationship between these three numbers

4 25 100

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The Bus Stop Method

3 9 6 3

To work out this sum, divide 963 by 3, one digit at a time, starting from the left.

3 2 1

This is sometimes called the space saver method

This is called the bus stop method. See the resemblance?

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The Bus Stop Method

4 2 5 2

To work out this sum, divide 252 by 3, one digit at a time, starting from the left.

0 6 42 1

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The Bus Stop Method

4 3 5 3

To work out this sum, divide 353 by 4, one digit at a time, starting from the left.

0 8 83 3

r 3

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Repeated Subtraction

You can use repeated subtraction. For example:

30 ÷ 6

Subtract 6 30 – 6 = 24Subtract 6 24 – 6 = 18Subtract 6 18 – 6 = 12Subtract 6 12 – 6 = 6

Subtract 6 6 – 6 = 0

Count the number of subtractions

5

There is nothing left so no remainder

30 ÷ 6 = 5

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Repeated Subtraction

Another example:

90 ÷ 17

Subtract 17 90 – 17 = 73

Subtract 17 73 – 17 = 55

Subtract 17 55 – 17 = 38

Subtract 17 38 – 17 = 21

Subtract 17 21 – 17 = 4

Count the number of subtractions

5

There is 4 left over so this is the remainder

90 ÷ 17 = 5 r 4

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The grid method

Using a grid can be helpful if you are confident with your times tables:

Example: 754 ÷ 12 Draw a grid: ÷ 700 50 4

12We can make 700 ÷ 12 easier

÷ 720 30 4

12 60

Notice that 30 ÷ 12 is 2 remainder 6. This six carries

over to the next column

÷ 720 30 4 + 6

12 60 2

We can now divide our second column 30 ÷ 12

Now, the final column:

÷ 720 30 4 + 6

12 60 2 0 r10 Therefore: 754 ÷ 12 = 62 r 10

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Want to practice?NO- I’m ready for long division

YES- I want to practice reversing multiplication Reversing multiplication solutions

YES- I want to practice the bus stop method

YES- I want to practice the grid method

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Bus stop method solutions

Grid method solutions

The Traditional Method

Repeated Subtraction

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Lets try: 543 ÷ 16

Repeated Subtraction

Start with we know 10 x 16 = 160 543- 160 (10 x 16) 383- 160 (10 x 16) 223- 160 (10 x 16) 63

We cannot subtract another 160 so look for a lower multiple

- 32 (2 x 16) 31- 16 (1 x 16) 15

15 cannot be divided by 16 so this is the remainder

543 ÷ 16 = 33 remainder 15

We have used 10 + 10 + 10 + 2 + 1 lots of 16. This means we divided 33 times

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Lets try: 1748 ÷ 42

Repeated Subtraction

Start with we know 10 x 42 = 420 1748- 420 (10 x 42)

1328

- 420 (10 x 42)908- 420 (10 x 42)

488We cannot subtract another 420 so look for a lower multiple

- 420 (10 x 42) 68- 42 (1 x 42) 26

26 cannot be divided by 42 so this is the remainder

1748 ÷ 42 = 41 remainder 26

We have used 10 + 10 + 10 + 10 + 1 lots of 42. This means we divided 41 times

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Lets try: 9265 ÷ 37

Repeated Subtraction

Start with we know 100 x 37 = 3700 9265- 3700 (100 x 37) 556

4- 3700 (100 x 37) 1865- 740 (20 x 37) 1125

We cannot subtract another 3700 so look for a lower multiple

- 740 (20 x 37) 385- 370 (10 x 37) 15

15 cannot be divided by 37 so this is the remainder

9265 ÷ 37 = 250 remainder 15

We have used 100 + 100 + 20 + 20 + 10 lots of 37. This means we divided 250 times

We cannot subtract another 740 so look for a lower multiple

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• The Divide - Multiply – Subtract CycleNotice DMS is alphabetical.

This might help you remember

the order!

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4 7 2

Traditional method

This is a similar method to 'short' division, but, rather than writing the remainder at the top, we work it out underneath. Don’t forget the DMS cycle Starting with 72 ÷ 4

The first step is write out the division.

7 ÷ 4 = 1 r 3

Step 2 is to divide 7 by 4

1

4 x 1 = 4 43 2

32 ÷ 4 = 8

8

4 x 8 = 32

3 20 Finished!

Step 3 is to multiply 4 x 1, this will show us what we’ve worked out so far.

Step 4. Now we subtract this to see what we’ve still got to divide

Step 5. Divide 32 by 4

Step 6: Multiply 8 x 4

Step 7: Subtract this to see if we need to continue to divide

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4 1 5 6

Traditional method

This is a similar method to 'short' division, but, rather than writing the remainder at the top, we work it out underneath.

Let’s try 156 ÷ 4 0

01 5

3

1 23 Finished!6

9

3 60

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5 2 7 5

Traditional method

This is a similar method to 'short' division, but, rather than writing the remainder at the top, we work it out underneath.

Let’s try 156 ÷ 4 0

02 7

5

2 52

Finished!

5

5

2 50

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12 3 7 4 9

Traditional method

This is a similar method to 'short' division, but, rather than writing the remainder at the top, we work it out underneath.

Let’s try 3749 ÷ 12 3

3 61

4

1

1 22

Finished!

9

2

2 45

r 5

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31 3 7 4 9

Traditional method

This is a similar method to 'short' division, but, rather than writing the remainder at the top, we work it out underneath.

Let’s try 3749÷ 31 1

3 16 4

2

6 22 Finished! 9

0

2 45

r 5We may find We may find this useful: this useful:

313162629393

124124155155186186217217248248279279310310

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The space saver method

Traditional method

7 4 8 9

Let’s try 489 ÷ 7

046

69 r 6

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The space saver method

Traditional method

28 4 7 2 9

Let’s try 4729 ÷ 28

041

19

6 r 25

These might be useful: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280

24

8

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The space saver method

Traditional method

36 4 6 2 8 3

Let’s try 46283 ÷ 36

04

110

2 r 23

These might be useful: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360

30

8 520

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3682 divided by 6

6741 divided by 12

2065 divided by 32

3927 divided by 24

613 r 4

561 r 9

64 r 17

163 r 15

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6392 divided by 5

5392 divided by 11

5629 divided by 52

25393 divided by 23

1278 r 2

490 r 2

108 r 13

1104 r 1

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5284 divided by 3

63042 divided by 9

1390 divided by 16

63926 divided by 43

1761 r 1

7004 r 6

86 r 14

1486 r 28

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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