1. © T Madas

2. … why …? What is 2 + 6 x 3 ? Who is right? 2 + 6 2 + 6 x 3 == 24 20
Mr Madas in Year 7
… why …?
© T Madas

3. We do not work out operations as we come to them
We always follow this order
multiplications
& divisions
additions
& subtractions
First
then
© T Madas

4. multiplications
& divisions
First
then
additions
& subtractions 23
2 + 3 x 7 =
3 x 7 = 15
18 – 12 ÷ 4 =
12 ÷ 4
18 – 3 = 47
÷ 6 =
30 ÷ 6 = 1
19 – 2 x 9 =
2 x 9
19 – 18 = 20
4 x 50 ÷ 10 =
50 ÷ 10
4 x 5 =
You must set your work this way
© T Madas

5. multiplications
& divisions
First
then
additions
& subtractions 19
2 + 4 x =
4 x 3 = 15
÷ =
12 ÷ 4 = 3
÷ 6 – 7 =
30 ÷ 6
5 + 5 – 7 = 10
19 – 2 x =
2 x 7
19 – = 6
9 – 50 ÷ =
50 ÷ 10
9 – =
You must set your work this way
© T Madas

6. This calculator does not know the order of operations
pocket
calculator
scientific
calculator
This calculator knows the order of operations
© T Madas

7. Practice
on the
Order of Operations
© T Madas

8. C a l c u l a t e :
÷ x
then
+ – 60
4 + 8 x 7 =
8 x 7 = 10
20 – 40 ÷ 4 =
40 ÷ 4
20 – 10 = 14
÷ 4 =
28 ÷ 4
7 + 7 = 5
29 – 3 x 8 =
3 x 8
29 – 24 = 20
8 x 25 ÷ 10 =
25 ÷ 10
8 x 2.5 = 56
7 + 7 x 7 =
7 x 7 = 36
8 x 4
8 x ÷ 9 =
36 ÷ 9 =
© T Madas

9. C a l c u l a t e :
÷ x
then
+ – 25
1 + 8 x 3 =
8 x 3 = 13
18 – 20 ÷ 4 =
20 ÷ 4
18 – 5 = 11
÷ 5 =
25 ÷ 5
6 + 5 = 12
17 – 3 x 3 =
3 x 3
17 – 9 = 21
3 + 4 x =
4 x 3 = 13
÷ =
12 ÷ 4 = 8
÷ 6 – 1 =
30 ÷ 6
4 + 5 – 1 =
© T Madas

10. C a l c u l a t e : 40 7 14 1 2 4 7 ÷ x + – 4 + 6 x 6 = 6 x 6 4 + 36 =
then
+ – 40
4 + 6 x 6 =
6 x 6 = 7
20 – 26 ÷ 2 =
26 ÷ 2
20 – 13 = 14
÷ 4 =
36 ÷ 4
5 + 9 = 1
49 – 6 x 8 =
6 x 8
49 – 48 = 2
÷ 6 – 7 =
42 ÷ 6
2 + 7 – 7 = 4
35 – 6 x =
6 x 6
35 – = 7
8 – 30 ÷ =
30 ÷ 10
8 – =
© T Madas

11. C a l c u l a t e :
÷ x
then
+ – 39
4 + 5 x 7 =
5 x 7 = 8
14 – 24 ÷ 4 =
24 ÷ 4
14 – 6 = 15
÷ 3 =
18 ÷ 3
9 + 6 = 15
27 – 3 x 4 =
3 x 4
27 – 12 = 16
4 x 12 ÷ 3 =
12 ÷ 3
4 x 4 = 20
4 + 4 x 4 =
4 x 4 = 40
7 x 5
7 x ÷ 9 =
45 ÷ 9 =
© T Madas

12. C a l c u l a t e :
÷ x
then
+ – 32
5 + 3 x 9 =
3 x 9 = 6
10 – 16 ÷ 4 =
16 ÷ 4
10 – 4 = 14
÷ 7 =
35 ÷ 7
9 + 5 = 4
36 – 4 x 8 =
4 x 8
36 – 32 = 7
2 x 35 ÷ 10 =
35 ÷ 10
2 x 3.5 = 90
9 + 9 x 9 =
9 x 9 = 53
5 x 9
5 x ÷ 9 =
72 ÷ 9 =
© T Madas

13. ( )
Brackets
© T Madas

14. Calculate this sum
( )
then
÷ x
then
+ –
2 + 3 x 7 =
3 x 7 = 23
How do we write this if we want the addition to take place before the multiplication?
( )
2 + 3 x 7 =
5 x 7 = 35
Do the sum inside the bracket first
© T Madas

15. Examples ( ) ÷ x + – (2 + 3) x 4 = ( ) 5 x 4 = 20 9 x (17 – 12) = ( )
then
÷ x
then
+ –
(2 + 3) x 4 = ( )
5 x 4 = 20
9 x (17 – 12) = ( )
9 x 5 = 45
20 ÷ (16 – 12) = ( )
20 ÷ 4 = 5
(6 + 4) x (18 – 6) = ( ) ( )
10 x 12 =
120
You must set your work this way
© T Madas

16. The Order Of OperationsB I D M A S
Brackets
Indices
Division
Addition
Subtraction
Multiplication
Powers
© T Madas

17. BIDMAS
Practice
© T Madas

18. Calculate: ( ) ÷ x + – 8 x (5 + 3) = ( ) 8 x 8 = 64 7 x (8 – 4) + 4 =
then
÷ x
then
+ –
8 x (5 + 3) = ( )
8 x 8 = 64
7 x (8 – 4) + 4 = ( )
7 x 4
7 x = = 32
72 ÷ (5 + 7) = ( )
72 ÷ 12 = 6
80 ÷ (5 x 8) = ( )
80 ÷ 40 = 2
11 x (5 + 3) – 8 = ( )
11 x 8
11 x 8 – 8 =
88 – 8 = 80
30 ÷ (5 + 1) = ( )
30 ÷ 6 = 5
60 ÷ (5 x 6) = ( )
60 ÷ 30 = 2
9 x (2 + 3) – 5 = ( )
9 x 5 – 5 =
9 x 5
45 – 5 = 40
© T Madas

19. Calculate: ( ) ÷ x + – 4 x (5 + 4) = ( ) 4 x 9 = 36 8 x (7 – 4) + 5 =
then
÷ x
then
+ –
4 x (5 + 4) = ( )
4 x 9 = 36
8 x (7 – 4) + 5 = ( )
8 x 3
8 x = = 29
40 ÷ (2 + 3) = ( )
40 ÷ 5 = 8
90 ÷ (3 x 6) = ( )
90 ÷ 18 = 5
12 x (5 + 1) – 8 = ( )
12 x 6
12 x 6 – 8 =
72 – 8 = 64
36 ÷ (9 – 3) = ( )
36 ÷ 6 = 6
48 ÷ (8 x 2) = ( )
48 ÷ 16 = 3
7 x (2 + 3) – 4 = ( )
7 x 5
7 x 5 – 4 =
35 – 4 = 31
© T Madas

20. BIDMAS
with
Indices
© T Madas

21. Calculate:
( )
then
a 2
then
÷ x
then
+ – ( ) ( ) ( )
© T Madas

22. Calculate:
( )
then
a 2
then
÷ x
then
+ – ( ) ( ) ( )
© T Madas

23. © T Madas

24. C a l c u l a t e :
÷ x
then
+ – 60
4 + 8 x 7 =
8 x 7 = 10
20 – 40 ÷ 4 =
40 ÷ 4
20 – 10 = 14
÷ 4 =
28 ÷ 4
7 + 7 = 5
29 – 3 x 8 =
3 x 8
29 – 24 = 20
8 x 25 ÷ 10 =
25 ÷ 10
8 x 2.5 = 56
7 + 7 x 7 =
7 x 7 = 36
8 x 4
8 x ÷ 9 =
36 ÷ 9 =
© T Madas

25. C a l c u l a t e :
÷ x
then
+ – 25
1 + 8 x 3 =
8 x 3 = 13
18 – 20 ÷ 4 =
20 ÷ 4
18 – 5 = 11
÷ 5 =
25 ÷ 5
6 + 5 = 12
17 – 3 x 3 =
3 x 3
17 – 9 = 21
3 + 4 x =
4 x 3 = 13
÷ =
12 ÷ 4 = 8
÷ 6 – 1 =
30 ÷ 6
4 + 5 – 1 =
© T Madas

26. C a l c u l a t e : 40 7 14 1 2 4 7 ÷ x + – 4 + 6 x 6 = 6 x 6 4 + 36 =
then
+ – 40
4 + 6 x 6 =
6 x 6 = 7
20 – 26 ÷ 2 =
26 ÷ 2
20 – 13 = 14
÷ 4 =
36 ÷ 4
5 + 9 = 1
49 – 6 x 8 =
6 x 8
49 – 48 = 2
÷ 6 – 7 =
42 ÷ 6
2 + 7 – 7 = 4
35 – 6 x =
6 x 6
35 – = 7
8 – 30 ÷ =
30 ÷ 10
8 – =
© T Madas

27. C a l c u l a t e :
÷ x
then
+ – 39
4 + 5 x 7 =
5 x 7 = 8
14 – 24 ÷ 4 =
24 ÷ 4
14 – 6 = 15
÷ 3 =
18 ÷ 3
9 + 6 = 15
27 – 3 x 4 =
3 x 4
27 – 12 = 16
4 x 12 ÷ 3 =
12 ÷ 3
4 x 4 = 20
4 + 4 x 4 =
4 x 4 = 40
7 x 5
7 x ÷ 9 =
45 ÷ 9 =
© T Madas

28. C a l c u l a t e :
÷ x
then
+ – 32
5 + 3 x 9 =
3 x 9 = 6
10 – 16 ÷ 4 =
16 ÷ 4
10 – 4 = 14
÷ 7 =
35 ÷ 7
9 + 5 = 4
36 – 4 x 8 =
4 x 8
36 – 32 = 7
2 x 35 ÷ 10 =
35 ÷ 10
2 x 3.5 = 90
9 + 9 x 9 =
9 x 9 = 53
5 x 9
5 x ÷ 9 =
72 ÷ 9 =
© T Madas

29. Calculate: ( ) ÷ x + – 8 x (5 + 3) = ( ) 8 x 8 = 64 7 x (8 – 4) + 4 =
then
÷ x
then
+ –
8 x (5 + 3) = ( )
8 x 8 = 64
7 x (8 – 4) + 4 = ( )
7 x 4
7 x = = 32
72 ÷ (5 + 7) = ( )
72 ÷ 12 = 6
80 ÷ (5 x 8) = ( )
80 ÷ 40 = 2
11 x (5 + 3) – 8 = ( )
11 x 8
11 x 8 – 8 =
88 – 8 = 80
30 ÷ (5 + 1) = ( )
30 ÷ 6 = 5
60 ÷ (5 x 6) = ( )
60 ÷ 30 = 2
9 x (2 + 3) – 5 = ( )
9 x 5 – 5 =
9 x 5
45 – 5 = 40
© T Madas

30. Calculate: ( ) ÷ x + – 4 x (5 + 4) = ( ) 4 x 9 = 36 8 x (7 – 4) + 5 =
then
÷ x
then
+ –
4 x (5 + 4) = ( )
4 x 9 = 36
8 x (7 – 4) + 5 = ( )
8 x 3
8 x = = 29
40 ÷ (2 + 3) = ( )
40 ÷ 5 = 8
90 ÷ (3 x 6) = ( )
90 ÷ 18 = 5
12 x (5 + 1) – 8 = ( )
12 x 6
12 x 6 – 8 =
72 – 8 = 64
36 ÷ (9 – 3) = ( )
36 ÷ 6 = 6
48 ÷ (8 x 2) = ( )
48 ÷ 16 = 3
7 x (2 + 3) – 4 = ( )
7 x 5
7 x 5 – 4 =
35 – 4 = 31
© T Madas

31. Calculate:
( )
then
a 2
then
÷ x
then
+ – ( ) ( ) ( )
© T Madas

32. Calculate:
( )
then
a 2
then
÷ x
then
+ – ( ) ( ) ( )
© T Madas

33. © T Madas