1. Introduction to Division
Mathematics
Introduction to Division

2. The aim of this powerpoint is to teach you about division and its link to multiplication.
EITHER
Take notes as you go along, include some examples and write down any questions and your answers (which you can mark as you go along) OR
At the end of the next powerpoint, printout the notes called Calc7a

3. Symbols of Division
There are THREE symbols which represent division.
For simple division we use:
For long division we use:
For any division we can use the line in a fraction: or ÷

4. What is division? Division is the opposite of multiplication
It asks the question…
If I share a number equally into groups, how many will there be in each group? OR
How many groups of a number are there in another number?

5. 24/8 So 24 ÷ 8 could also be written as… 8 24
8 24
and this particular division is either asking…
If I divide 24 into 8 equal groups, how many will there be in each group? OR
How many groups of 8 are there in 24?
As division and multiplication are linked, if you learn your times tables and know that 3 × 8 = 24, you also know that 24 ÷ 8 = 3 and that 24 ÷ 3 = 8. 24 8
24/8 OR or

6. Terms which tell you to divide
Words that tell you to divide are as follows:
‘share’ ‘divide’ ‘quotient’
The word ‘per’ also tells you to divide particularly when the calculation involves rates, e.g. miles per hour (i.e. divide distance by time).
Other special terms are…
Halve which tells you to divide by 2
Third which tells you to divide by 3
Quarter which tells you to divide by 4
The bottom number in a fraction tells you the ‘type’ of fraction and also tells you what number to divide by.

7. Learning your tables The best way to learn your tables is by rote…
This is repeating them out loud, over and over to yourself again and again, until your brain simply remembers them.
You should have had plenty of practice of learning your tables when you were looking at ‘multiplication’.
If you learn your tables inside-out then dividing by those values should not be a problem.
Remember: If you know that 4 × 5 = 20 then you also know… 20 ÷ 4 = and ÷ 5 = 4

8. Formula Triangles – Creating one…
Formula triangles can help you to link your knowledge of your times tables to help you with simple divisions.
To create a formula triangle, write the multiplication along the bottom and the answer above them.
E.g. For 7 × 9 = 63 …. 63
7 × 9

9. Formula Triangles – Using one…
To use a formula triangle just remember that…
the two bottom numbers multiply together to give the top number OR
the top number divided by either of the bottom numbers gives the other bottom number
So this triangle shows…
72/9 = 8
72/8 = 9
9 x 8 (or 8 x 9) = 72 72
9 8

10. Mental Divisions
Learning your tables off by heart and understanding the link between multiplication and division is the first step to being able to divide well mentally
To help work out answers to small number divisions, you can use tallies by writing them alternately in a number of columns (equal to the number you are dividing by) until you have the a total number of tallies equal to the number you are dividing.
E.g. 12 ÷ 4
If we divide 12 into 4 groups, each group will contain 3
I am dividing by 4 so I will need 4 separate columns or groups of tallies | | | | | |
Click, count and observe… | | | | | |
I will need 12 tallies in total

11. Dealing with Remainders
Sometimes a number cannot be shared out exactly between the required number of groups
E.g. 17 ÷ 4 =
You may need to give your answer and quote a remainder as a value after the letter r.
You may quote the answer as a fraction by writing the remainder over the divisor
You may use the bus shelter method to divide and give your answer as a decimal (demonstrated in a future presentation)
There is only 1 tally left which cannot be split ‘wholly’ between the 4 groups!!!
I am dividing by 4 so I will need 4 separate columns or groups of tallies
4 r.1
4.25
4 ¼
| | | | | | | | | | | | | | | |
I will need 17 tallies in total

12. Practice Mental Divisions (no remainders)
What are the answers to each of these divisions?
1) 16 ÷ 2 =
2) 15 ÷ 3 =
3) 24 ÷ 6 =
4) 35 ÷ 5 =
HINT 1: What number multiplied by 2 gives 16?
HINT 2: If you split 16 peas into 2 equal groups
how many peas would be in each group?
HINT 1: What number multiplied by 3 gives 15?
HINT 2: If you split 15 peas into 3 equal groups
how many peas would be in each group?
HINT 1: What number multiplied by 6 gives 24?
HINT 2: If you split 24 peas into 6 equal groups
how many peas would be in each group?
HINT 1: What number multiplied by 5 gives 35?
HINT 2: If you split 35 peas into 5 equal groups
how many peas would be in each group?

13. Answers 16
1) 16 ÷ 2 = 2) 15 ÷ 3 = 3) 24 ÷ 6 = 4) 35 ÷ 5 = 8
2 ?
2 × 8
Divide 15 tallies into 3 equal groups…
| | | | | | | | | | | |
How many tallies in each group? 5
6 × 4 = 24
6 × ? = 24 4
Share 35 tallies between 5 groups…
|||| || |||| || |||| || |||| || |||| ||
How many tallies in each group? 7

14. Practice Mental Divisions (with remainders)
What are the answers to each of these divisions?
1) 23 ÷ 7 =
2) 29 ÷ 9 =
3) 63 ÷ 10 =
4) 76 ÷ 8 =
HINT 1: 7 times what gives you a value near 23?
HINT 2: If you split 23 peas into 7 equal groups
how many peas would be in each group and what is the remainder?
HINT 1: 9 times what gives a value near 50?
HINT 2: If you split 50 peas into 9 equal groups
how many peas would be in each group
and what is the remainder?
HINT 1: 10 times what gives a value near 63?
HINT 2: If you split 63 peas into 10 equal groups
how many peas would be in each group
and what is the remainder?
HINT 1: 8 times what gives a value near 76?
HINT 2: If you split 76 peas into 8 equal groups
how many peas would be in each group
and what is the remainder?

15. 7 × 3 = 21 10 × 6 = 60 Answers |||| |||| |||| |||| |||| |||| |||| ||||
1) 23 ÷ 7 = 2) 29 ÷ 9 = 3) 63 ÷ 10 = 4) 76 ÷ 8 =
3 r.2
We started with 23 which means we have 2 left over
Put 50 tallies into 9 equal groups…
| | | | | | | | | | | | | | |
| | | | | | | | | | | | (+ 2)
How many tallies in each group?
3 2/9
10 × 6 = 60
6 r.3
Divide 76 tallies into 8 ‘equal’ groups…
|||| |||| |||| |||| |||| |||| |||| ||||
|||| |||| |||| |||| |||| |||| |||| |||| (+4)
How many tallies in each group?
We started with 63 which means we have 3 left over
9 4/8

16. What next?
If you haven’t made any notes or copied any examples, questions and answers out during this presentation, print out the notes called Calc7a. Read through them and make sure you answer any questions.
Complete a new multiplication grid (Mult12.xlsx). Remember to time yourself and write the date, your name and the number 2 on the back of the sheet. Have you improved your time?
Now move on to the Calc7b-MentalD powerpoint