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This page sets out the method for BIDMAS in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the BIDMAS topic page.
When you see more than one operation in a calculation, rewrite the whole line each time you do one step.
When you see 'put brackets in to make this correct', try bracketing the part that BIDMAS would normally do last.
Brackets, then indices, then division and multiplication, then addition and subtraction.
Division does not beat multiplication. They share a level and run left to right.
2 + 3 × 4 is 2 + 12 = 14, not 5 × 4.
Brackets are how you force the addition to happen first.
(2 + 3) × 4 = 5 × 4 = 20. The bracket is one value.
Without the bracket the same symbols would make 14.
20 ÷ 4 × 2 is 5 × 2 = 10. You do not do 4 × 2 first.
Jumping to a later multiplication is the usual slip.
3 × 2² = 3 × 4 = 12. Only the 2 is squared.
A bracket such as (3 × 2)² would square the whole product.
Replace the piece you have just done, then read what is left.
8 − 3 + 2 becomes 5 + 2, not 8 − 5.
A bracket is one value. Work inside it, using BIDMAS again if the inside has more than one operation, and replace the bracket with that value. (8 - 2)^2 starts as 6^2. The power is outside, so it applies to the whole result of the bracket. Without the bracket, 8 - 2^2 would square only the 2, giving 8 - 4 = 4.
An index is done before multiplication, division, addition or subtraction. In 2 × 5^2 only the 5 is squared: 5^2 = 25, then 2 × 25 = 50. It is not (2 × 5)^2 = 100. If the question wants the whole product squared, it has to say so with a bracket.
Nested work still follows the same list. In 2 × 5^2 - (18 ÷ 3 + 1), the power and the bracket are both high priority. 5^2 = 25, so 2 × 25 = 50. Inside the bracket, division comes before addition: 18 ÷ 3 = 6, then 6 + 1 = 7. The last step is 50 - 7 = 43.
Method: 1. Work inside any brackets first, and treat the result as one number. 2. Do powers next, before you multiply or add. 3. Replace each finished bracket or power before you move on.
Multiplication does not beat division. They are one level. 48 ÷ 6 × 2 is 8 × 2 = 16. Doing 6 × 2 first would invent a bracket that is not there and would give 48 ÷ 12 = 4. Read along the line and replace each piece as you finish it.
The same left-to-right rule applies when a division comes second. 8 × 6 ÷ 4 is 48 ÷ 4 = 12. A string of only multiplications and divisions never jumps to a later sign because it 'feels like division should wait'. Write the new line after each step so the next operation is obvious.
Once the multiplications and divisions are finished, the line should contain only additions and subtractions, plus any values you have already substituted. 48 ÷ 6 × 2 + 9 becomes 16 + 9 after the multiply-divide stage. The addition is still waiting. Do not add the 2 and the 9 while the division is still on the line.
Method: 1. After powers, do multiplication and division from left to right. 2. Do not let multiplication jump ahead of a division on its left. 3. Write the value so far before you meet the next operation.
Addition does not beat subtraction. 20 - 18 + 2 is worked as 2 + 2 = 4. The common wrong step is to do 18 + 2 = 20 first and then write 20 - 20 = 0. That treats the expression as 20 - (18 + 2), and those brackets are not in the question.
A longer line uses the same habit. 16 + 9 - 4 is 25 - 4 = 21. Here either order happens to give 21, but that is luck with the signs. Build the habit of moving left to right. A line such as 10 - 4 + 3 becomes 6 + 3 = 9. Doing 4 + 3 first would wrongly give 10 - 7 = 3.
Negative results are allowed. 4 - 9 + 2 is -5 + 2 = -3. Stopping at zero, or swapping the subtraction into 9 - 4, changes the question. If a power or a product is still on the line, finish that before any of these additions. BIDMAS is a queue, not a suggestion.
Method: 1. Do addition and subtraction last, still from left to right. 2. Do not do the subtraction first just because it looks smaller. 3. Check the running total after each plus or minus.
First work out the expression with no extra brackets, so you know what BIDMAS does on its own. 3 + 6 × 2 + 4 = 3 + 12 + 4 = 19. If the target is 19, no brackets are needed. If the target is something else, the brackets must pull an addition or subtraction in front of a multiplication.
Try the bracket around the first addition: (3 + 6) × 2 + 4 = 9 × 2 + 4 = 22. That hits 22. A bracket around the end, 3 + 6 × (2 + 4) = 3 + 36 = 39, hits a different target. Brackets around both additions, (3 + 6) × (2 + 4) = 54, hit another. Each placement is a different calculation. Check by working it out, not by hoping.
In an exam line, one pair is often enough. Put the bracket around the part that must be treated as a single number, then apply the operations outside from the left, still obeying indices and multiply-divide. If your checked value misses the target, move the bracket. Do not change the numbers or the signs that were printed.
Method: 1. Work out the expression with no extra brackets first. 2. Place brackets so the target operation happens earlier. 3. Calculate the bracketed version and compare it with the target.
Exam questions often hide a BIDMAS line inside a story. A group buys several tickets and a snack each, then uses a voucher. The cost is a bracket multiplied by the number of people, with the voucher taken off at the end. Write the story as one line, such as 4 × (7.50 + 3.25) - 5, before you calculate. That line is what earns the method mark.
The words give you the structure. "Each" and "per" mean multiply. "Total" or "altogether" for several items means add inside a bracket. "Off" or "discount" means subtract at the end. Write the bracket first for the amount that is the same for every person, then multiply, then subtract. Work out each stage on its own line so a slip in the arithmetic does not spoil the method.
Method: 1. Underline the amounts and the words that tell you to add, multiply or take off. 2. Write the whole story as one calculation, with brackets where a total is multiplied. 3. Work out the bracket first, then the multiplication, then the final add or subtract. 4. Write the answer with the unit, for example pounds.
Tip: Money answers need two decimal places in the working, such as 10.75 and not 10.7.
A power comes straight after brackets. In 5^2 - 3 × 4 the square is done first: 25 - 12 = 13. A square root sign behaves like a bracket as well. In √(9 + 16) you must work out 9 + 16 = 25 before you take the root, which gives 5. Taking √(9) + √(16) = 7 is a different calculation.
A fraction bar is also a bracket in disguise. In (15 + 9)/(2 × 3) the top is one number and the bottom is another, so you work out 15 + 9 = 24 and 2 × 3 = 6 and then divide to get 4. Typing 15 + 9 ÷ 2 × 3 would give a different answer, so on a calculator put brackets round the top and the bottom. Without a calculator, work out each part and write it on its own line.
Method: 1. Treat the top and the bottom of a fraction bar as two separate brackets. 2. Work out anything under a square root sign before taking the root. 3. Do powers before multiplication, division, addition and subtraction. 4. Divide the top by the bottom at the end.
Negative numbers follow the same order, with the sign rules for each step. In 6 - 2 × (-3) the multiplication is first: 2 × (-3) = -6. Then 6 - (-6) = 12. The two minus signs next to each other make a plus. It is a very common slip to subtract 2 from 6 first and then multiply, which gives -12.
Be careful with a power of a negative number. (-3)^2 = 9 because the bracket is squared. Without the bracket, -3^2 = -9 because only the 3 is squared and the minus sign is applied afterwards. A division with a negative gives a negative: 12 ÷ (-3) = -4. Write each stage on a new line and check the sign of each product or quotient before you add or subtract.
Method: 1. Do brackets and powers first, remembering that (-3)^2 = 9. 2. Then multiply and divide, working out the sign of each answer. 3. Rewrite subtracting a negative as adding. 4. Finish with the adding and subtracting from left to right.
Some questions give a calculation with the wrong answer and ask for brackets that make it right. For 4 + 6 × 2 = 20, the unbracketed value is 4 + 12 = 16. To reach 20 the addition has to happen first, so write (4 + 6) × 2 = 20. Try the brackets round each pair of neighbouring numbers until the answer matches. You must show that the bracketed version works.
Another style is "Mia says 8 + 4 × 3 = 36. Is she correct?" She added first and then multiplied: 12 × 3 = 36. The correct value is 8 + 12 = 20. A good explanation names the rule: multiplication is done before addition, so the 4 × 3 must be worked out first. Then you can say which brackets would make her answer right, which is (8 + 4) × 3.
Method: 1. Work out the calculation without brackets using BIDMAS. 2. If it does not match the target, move the brackets round an addition or subtraction. 3. Recalculate with the brackets and compare with the target. 4. In an explanation, name the rule that was broken.
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