Maths: Grade 5
Numbers, Operations & Relationships: Division
DIVISION
In Grade 4, we learnt how to divide 3 digit numbers by 2 digit numbers, so now we are
going to recap on what we learned, as well as learn some new methods for division.
Division means finding out how many times a number goes into another number, e.g.
dividing 50 by 10 finds out how many groups of 10 there are in 50.
When we are dividing, we are, in fact, doing repeated subtraction.
Example
12 ÷ 3 = 4
OR
12
- 3 (1 group)
9
9
- 3 (1 group)
6
6
- 3 (1 group)
3
3
- 3 (1 group)
0
So dividing 12 by 3, means dividing 12 into 4 equal groups of 3.
Numbers cannot be divided in any order.
Example
500 ÷ 10 is not the same as 10 ÷ 500
The following symbols are used for division:
÷/
They all mean divide by.
Version 2: April 2014
© Copyright My Cyberwall 2013
1
Maths: Grade 5
Numbers, Operations & Relationships: Division
Example
500÷ 10 or 500/10 or
500
10
The number that you are dividing into is known as the dividend, the number that you are
dividing by is known as the divisor and the answer is called the quotient.
Example
500
dividend
÷
10
÷ divisor
=
50
= quotient
We cannot divide a number by 0. Any number divided by 0 is undefined. Any number
divided by 1, stays the same.
Example
500 ÷ 0 = undefined
500 ÷ 1 = 500
Halving Numbers
Halving is the same as dividing a number by 2.
Example
Half of 54 = 54 ÷ 2 = 27.
Methods of Dividing
Using Factors to Divide
To make division easier, you can break the number that needs to be divided into its
factors.
Version 2: April 2014
© Copyright My Cyberwall 2013
2
Maths: Grade 5
Numbers, Operations & Relationships: Division
Example
680 ÷ 20
Factors of 20:
We can use any of these factor pairs to divide.
For this example, we will use 2 and 10.
1. Divide 680 by the 1st factor, i.e. by 2:
680 ÷ 2 = 340
2. Next divide the answer, i.e. 340 by the 2nd factor, i.e. 10:
340 ÷ 10 = 34
So 680 ÷ 20 = 680 ÷ 2 ÷ 10
= 340 ÷ 10
= 34
Using the Halving Method to Divide
This is useful if the divisor is an even number.
Example
736÷ 16
= 368 ÷ 8, if you half both numbers
= 184 ÷ 4, if you half both numbers again
= 92 ÷ 2, if you half both numbers again
= 46
Version 2: April 2014
© Copyright My Cyberwall 2013
3
Maths: Grade 5
Numbers, Operations & Relationships: Division
In the above example, we have halved the dividend and the divisor, i.e. half of 736
(dividend) is 368 and half of 16 (divisor) is 8. Then each one has been halved again i.e.
half of 368 is 184 and half of 8 is 4. Finally half of 184 is 92 and half of 4 is 2. We then
divided the 92 by the 2 to get the answer of 46.
Breaking Down the Number Being Divided
We can break down the number being divided, i.e. the dividend, into smaller numbers
that add up to the dividend and are multiples of the divisor.
Example
266 ÷ 7
Write 266 as the sum of the multiples of 7:
266 = 210 + 56 or 140 + 70 + 56
56 ÷ 7 = 8
210 ÷ 7 = 30
266 ÷ 7 = 38
OR
140 ÷ 7 = 20
70 ÷ 7 = 10
56 ÷ 7 = 8
266 ÷ 7 = 38
Version 2: April 2014
© Copyright My Cyberwall 2013
4
Maths: Grade 5
Numbers, Operations & Relationships: Division
Short Division
Short division is used to divide one number by another whole number, which is less than
10.
Example
266 ÷ 7
1. Start on the left and divide the 7 into the 2. It does not go, because 7 is larger than 2, so
divide the 7 into 26. It goes 3 times ( 3 x 7 = 21) with a remainder of 5. Put the 3 on the
line above the first 6 and the remainder 5 must be carried over to the second 6, making
the next digit 56:
7 2
3
6
2
5
6
2. Divide the 7 into 56. It goes 8 times, so put the 8 on the line above the 6:
7 2
3
6
2
8
6
5
The answer is 38.
Long Division
Long division is usually used when the number you are dividing by is at least 2 digits
long and the number that you are dividing into is at least 3 digits long, e.g. 192 ÷ 80.
However, it can also be used for simpler division.
All the workings out are shown in long division.
Example
442 ÷ 17
1. Start on the left and divide the 17 into the 4. It does not go, because 17 is larger than 4,
so divide the 17 into 44. It goes 2 times (2 x 17 = 34) with remainder 10. Put the 2 on the
top line directly above the second 4:
2
1 7 4 4 2
Version 2: April 2014
© Copyright My Cyberwall 2013
5
Maths: Grade 5
Numbers, Operations & Relationships: Division
2. As the 17 goes into 44 twice ( 2 x 17 = 34), put 34 under the 44. Then put a minus sign
and a line under the 34:
2
1 7 4 4 2
- 3 4
3. Deduct the 34 from the 44 and put the answer, i.e. 10 under the 44:
2
1 7 4 4 2
- 3 4
1 0
4. Carry down the 2 from the 442:
2
1 7 4 4 2
- 3 4
1 0 2
5. Now divide the 17 into 102. It goes 6 times with no remainder, so write 6 in the answer
line and put 102 under the first 102. Put a minus sign and a line under the second 102:
1 7 4
- 3
1
- 1
2
4
4
0
0
6
2
2
2
6. Now deduct the second 102 from the first 102. The answer is 0 as there is no
remainder:
1 7 4
- 3
1
- 1
2
4
4
0
0
6
2
2
2
0
Version 2: April 2014
© Copyright My Cyberwall 2013
6
Maths: Grade 5
Numbers, Operations & Relationships: Division
Relationship between Multiplication and Division
Division is the inverse (opposite) of multiplication, so you can always check your
answers as shown below.
Example
139 x 53 = 7367
7367 ÷ 139 = 53
7367 ÷ 53 = 139
Using Rounding Off to Estimate Division
We can estimate the answer by rounding off both the dividend and divisor to the nearest
10 before dividing. The actual answer may be worked out using any other method.
Example
168 ÷ 12 ≈ 170 ÷ 10 ≈ 17
1
1 2 1 6
- 1 2
4
- 4
4
8
8
8
0
Using Strategies to Check Solutions
You can use any of the above methods to check your answer to any division sum.
Example
528 ÷ 22
Version 2: April 2014
© Copyright My Cyberwall 2013
7
Maths: Grade 5
Numbers, Operations & Relationships: Division
Method 1 – Using Factors to Divide
Factors of 22:
We will use factor pairs 2 and 11.
528 ÷ 22
= (528 ÷ 2) ÷ 11
= 264 ÷ 11
= 24
Method 2 – Using the Halving Method
528 ÷ 22
= (528 ÷ 2) ÷ (22 ÷ 2)
= 264 ÷ 11
= 24
Method 3 – Breaking down the Number being Divided
528 = 220 + 198 + 110
220 ÷ 22 = 10
198 ÷ 22 =9
110 ÷ 22 = 5
528 ÷ 22= 24
Version 2: April 2014
© Copyright My Cyberwall 2013
8
Maths: Grade 5
Numbers, Operations & Relationships: Division
Method 4 – Long Division
2
2 2 5 2
- 4 4
8
8
4
8
8
8
0
Version 2: April 2014
© Copyright My Cyberwall 2013
9