Key ideas
When a calculation has more than one operation, you must do them in the right order. Use BODMAS:
| B | Brackets first | (3 + 2) × 4 = 5 × 4 |
|---|---|---|
| O | Orders: powers like 3² | 3² = 3 × 3 = 9 |
| D M | Division and Multiplication | work left to right |
| A S | Addition and Subtraction | work left to right |
- Division and multiplication are equal. Do whichever comes first, reading left to right. The same goes for addition and subtraction.
- Rewrite the calculation after every step. It keeps your working tidy and stops mistakes.
- In worded questions, words like sum (add), difference (subtract), product (multiply) and shared equally (divide) tell you the operation.
Calculations using BODMAS
Calculate 7 + 4 × 5(2 marks)
Find the operation to do first.7 + 4 × 5= 7 + 20✓1
In plain EnglishThere are no brackets or powers. Multiplication comes before addition, so work out 4 × 5 = 20 first. Rewrite the line with 20 in its place.
Do what is left.= 27✓2
In plain EnglishNow it's just 7 + 20 = 27.
⚠ Common mistake. Working left to right gives 7 + 4 = 11, then 11 × 5 = 55. That's wrong: multiplication comes first.
Calculate 18 − 12 ÷ 3 + 2(2 marks)
Divide first.18 − 12 ÷ 3 + 2= 18 − 4 + 2✓1
In plain EnglishDivision comes before addition and subtraction, so 12 ÷ 3 = 4 first.
Add and subtract from left to right.= 14 + 2= 16✓2
In plain EnglishAddition and subtraction are equal, so go left to right: 18 − 4 = 14, then 14 + 2 = 16.
⚠ Watch out. Doing the addition first (4 + 2 = 6, then 18 − 6 = 12) gives the wrong answer. Go left to right.
Calculate (9 − 3) × 4 − 3²(3 marks)
Brackets and powers first.(9 − 3) × 4 − 3²= 6 × 4 − 9✓1
In plain EnglishB: the bracket first, 9 − 3 = 6. O: the power next. 3² means 3 × 3 = 9 (not 3 × 2). Rewrite the line with both answers in.
Then multiply.= 24 − 9✓2
In plain English6 × 4 = 24.
Then subtract.= 15✓3
In plain English24 − 9 = 15.
Worded examples
Multiply the sum of 8 and 4 by 3.(2 marks)
Write it as one calculation.(8 + 4) × 3✓1
In plain English"The sum of 8 and 4" means 8 + 4. We must multiply that whole answer by 3, so it goes in brackets. Without brackets, 8 + 4 × 3 would only multiply the 4.
Work it out.= 12 × 3= 36✓2
In plain EnglishBrackets first: 8 + 4 = 12. Then 12 × 3 = 36.
At the rainforest gift shop, Ellie buys 4 postcards at 35p each and a keyring costing 120p. Write one calculation for the total cost, and work it out in pounds.(2 marks)
Write one calculation.120 + 4 × 35✓1
In plain EnglishThe postcards cost 4 × 35. The keyring is 120 on top. BODMAS makes sure 4 × 35 is worked out first, so no brackets are needed.
Work it out.= 120 + 140= 260p= £2.60✓2
In plain English4 × 35 = 140, then 120 + 140 = 260p. There are 100p in £1, so 260p is £2.60.
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