Division

1
Division
Short Division
Long Division
Key Vocabulary
2
Key terms
Divide
Divisible
Remainder
Share
Groups
Left over
Quotient
Dividend
Divisor
Obelus
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Definitions
Long Division
Short Division
3
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.
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Long Division
Short Division
4
Short Division
What is division?
Reversing Multiplication
Working with remainders
Repeated subtraction
The Bus Stop Method
The Grid Method
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Long Division
Definitions
5
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
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Long Division
Definitions
6
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
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Long Division
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Short Division
Practice
7
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
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Short Division
Practice
8
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.
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Short Division
Practice
9
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.
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Short Division
Practice
10
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
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11
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
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Short Division
Practice
12
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
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Short Division
Practice
13
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
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Long Division
Definitions
14
Long Division
Repeated Subtraction
The Traditional Method
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Short Division
15
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
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Practice
16
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
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Practice
17
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
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Long Division
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Short Division
Practice
18
Long Division

• The Divide - Multiply Subtract Cycle

Notice DMS is alphabetical. This might help you
remember the order!
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Long Division
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Short Division
Practice
19
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!
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Long Division
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Short Division
Practice
20
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
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Long Division
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Short Division
Practice
21
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
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Long Division
Definitions
Short Division
Practice
22
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
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Long Division
Definitions
Short Division
Practice
23
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
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Long Division
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Short Division
Practice
24
Long Division
Traditional method

• The space saver method

Lets try 489 7
0
6
9
r 6
6
4
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Long Division
Definitions
Short Division
Practice
25
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
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Definitions
Short Division
Practice
26
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
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Short Division
Practice
27
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
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Short Division
Practice
28
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
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Practice
29
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
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Long Division
Definitions
Short Division
Practice
30
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