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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3. Definitions Short Division Long Division Main Menu Divide Divisible
To Divide is to share or group a number into equal parts. Eg) If you divide 10 by 2 you get 5.
A number is divisible if it can be divided without a remainder. Eg) 10 can be divided by 2, it is divisible by 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.
Short Division
Long Division
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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
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5. Mathematical Operations include:
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.
Mathematical Operations include:
Divisions can be written in many different ways
2 6 1 3
÷ 3
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Long Division
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6. Short Division x = x = ÷ = ÷ = 25 4 100 4 25 100 100 25 4 100 4 25 4
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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7. Short Division 3 9 6 3 3 2 1 The Bus Stop Method
This is called the bus stop method. See the resemblance? 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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8. Short Division 4 2 5 2 6 4 The Bus Stop Method 2 16 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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9. Short Division 4 3 5 3 8 8 The Bus Stop Method r 3 3 38 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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10. Short Division 30 ÷ 6 5 30 ÷ 6 = 5 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 90 ÷ 17 90 ÷ 17 = 5 r 4 5 Repeated Subtraction
Another example:
Subtract – 17 = 73
Subtract – 17 = 55
Subtract – 17 = 38
Subtract – 17 = 21
90 ÷ 17
Subtract – 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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12. We can now divide our second column 30 ÷ 12
Short Division
The grid method
Using a grid can be helpful if you are confident with your times tables:
Example: 754 ÷ 12 ÷
700 50 4 12
Draw a grid:
We can make 700 ÷ 12 easier
We can now divide our second column 30 ÷ 12 ÷
720 30 4 12 60 ÷
720 30
4 + 6 12 60 2
Now, the final column: ÷
720 30
4 + 6 12 60 2
0 r10
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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13. Short Division 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
Bus stop method solutions
YES- I want to practice the grid method
Grid method solutions
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Long Division
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14. The Traditional Method
Long Division
Repeated Subtraction
The Traditional Method
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Short Division
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15. Long Division 543 ÷ 16 = 33 remainder 15 Lets try: 543 ÷ 16 543 383
Repeated Subtraction
Lets try: 543 ÷ 16
543
Start with we know 10 x 16 = 160
(10 x 16)
383
223
(10 x 16)
(10 x 16) 63
(2 x 16) 31
We cannot subtract another 160 so look for a lower multiple
15 cannot be divided by 16 so this is the remainder
(1 x 16) 15
We have used lots of 16. This means we divided 33 times
543 ÷ 16 = 33 remainder 15
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16. Long Division 1748 ÷ 42 = 41 remainder 26 Lets try: 1748 ÷ 42 1748
Repeated Subtraction
Lets try: ÷ 42
1748
Start with we know 10 x 42 = 420
(10 x 42)
1328
(10 x 42)
908
(10 x 42)
488
(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
(1 x 42) 26
We have used lots of 42. This means we divided 41 times
1748 ÷ 42 = 41 remainder 26
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17. Long Division 9265 ÷ 37 = 250 remainder 15 Lets try: 9265 ÷ 37 9265
Repeated Subtraction
Lets try: ÷ 37
9265
Start with we know 100 x 37 = 3700
(100 x 37)
5564
1865
(100 x 37)
We cannot subtract another 3700 so look for a lower multiple
(20 x 37)
1125
(20 x 37)
385
We cannot subtract another 740 so look for a lower multiple
(10 x 37) 15
15 cannot be divided by 37 so this is the remainder
We have used lots of 37. This means we divided 250 times
9265 ÷ 37 = 250 remainder 15
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18. Notice DMS is alphabetical. This might help you remember the order!
Long Division
The Divide - Multiply – Subtract Cycle
Notice DMS is alphabetical. This might help you remember the order!
Start
Divide
Multiply
Subtract
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19. Long Division 1 8 4 7 2 4 3 2 3 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.
Step 2 is to divide 7 by 4 1 8
Step 3 is to multiply 4 x 1, this will show us what we’ve worked out so far. 4
7 2
7 ÷ 4 = 1 r 3
Step 4. Now we subtract this to see what we’ve 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
Finished!
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20. Long Division 3 9 4 1 5 6 1 5 1 2 3 6 3 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. 3 9
Let’s try 156 ÷ 4 4 1 5
1 2 3 6
Finished!
3 6
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21. Long Division 5 5 5 2 7 5 2 7 2 5 2 5 2 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. 5 5
Let’s try 156 ÷ 4 5 2 7
2 5
Finished! 2 5
2 5
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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
Let’s try 3749 ÷ 12 12
3 6 1 4
1 2
Finished! 2 9
2 4 5
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23. We may find this useful:
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
r 5
Let’s try 3749÷ 31 31
We may find this useful: 31 62 93
124
155
186
217
248
279
310
3 1 6 4
6 2 2 9
Finished!
2 4 5
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24. Long Division 6 9 7 4 8 9 The space saver method Traditional method
Let’s try 489 ÷ 7 6 9
r 6 7 4 6
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25. Long Division 1 6 8 28 4 7 2 9 The space saver method
Traditional method
The space saver method
Let’s try 4729 ÷ 28 1 6 8
r 25 28 4 19 24
These might be useful: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280
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26. Long Division 1 2 8 5 36 4 6 2 8 3 The space saver method
Traditional method
The space saver method
Let’s try ÷ 36 1 2 8 5
r 23 36 4 10 30 20
These might be useful: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360
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27. Division practise 613 r 4 561 r 9 64 r 17 163 r 15
3682 divided by divided by divided by divided by 24
613 r 4
561 r 9
64 r 17
163 r 15
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28. Division practise 1278 r 2 490 r 2 108 r 13 1104 r 1
6392 divided by divided by divided by divided by 23
1278 r 2
490 r 2
108 r 13
1104 r 1
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29. Division practise 1761 r 1 7004 r 6 86 r 14 1486 r 28
5284 divided by divided by divided by divided by 43
1761 r 1
7004 r 6
86 r 14
1486 r 28
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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