Mathematics (Core)Exam code: 0580
Operations with Numbers and Decimals
Number
BIDMAS
- Operations are carried out in a fixed order, remembered as BIDMAS or BODMAS
| Letter | Stands for | Note |
|---|---|---|
| B | Brackets | Innermost brackets first |
| I | Indices | Powers and roots |
| D M | Division and Multiplication | Equal rank, worked left to right |
| A S | Addition and Subtraction | Equal rank, worked left to right |
- Division and multiplication share a rank, so 24 ÷ 6 × 2 is 8, not 2
- Addition and subtraction likewise share a rank, so 10 − 4 + 3 is 9, not 3
Hidden brackets in fractions and roots
- A fraction line acts as a bracket around the whole numerator and the whole denominator
- (7 + 5)/(9 − 3) is worked as 12 ÷ 6 = 2
- A root sign acts as a bracket around everything underneath it
- √(9 + 16) is √25 = 5, which is not the same as √9 + √16 = 7
- These brackets have to be typed in explicitly on a calculator, because the layout that makes them obvious on paper is lost on the keypad
Worked example
Applying BIDMAS
Work out (9 − 4) + 3 × 2³.
Solution:
- Brackets first: 9 − 4 = 5, so the calculation becomes 5 + 3 × 2³
- Indices next: 2³ = 8, giving 5 + 3 × 8
- Multiplication before addition: 3 × 8 = 24, giving 5 + 24
- Addition last: 5 + 24 = 29
Worked example
Putting in one pair of brackets
Insert one pair of brackets in each line so that it is true.
(a) 3 + 9 × 4 − 2 = 21
(b) 3 + 9 × 4 − 2 = 46
Solution:
- Without brackets, BIDMAS gives 3 + 36 − 2 = 37, so the brackets have to change the order of working
- (a) 21 is less than 37, so make the multiplication smaller by bracketing the subtraction: 9 × (4 − 2) = 9 × 2 = 18
- Check the whole line: 3 + 18 = 21, so the answer is 3 + 9 × (4 − 2) = 21
- (b) 46 is more than 37, so make the multiplication bigger by bracketing the addition: (3 + 9) × 4 = 12 × 4 = 48
- Check the whole line: 48 − 2 = 46, so the answer is (3 + 9) × 4 − 2 = 46