dividedivisibleremaindershare groupsleft over quotientdividenddivisorobelus main menudefinitionslong...
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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
Main MenuLong DivisionDefinitions
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