Why does $3 + 4 \times 2$ equal 11 and not 14? The answer lies in BIDMAS, the universal rule book for the order of operations in maths. Just like following a recipe, performing calculations in the correct order is crucial for getting the right result every time.
The BIDMAS Rule Explained
BIDMAS tells you the sequence in which to perform operations. Work down the pyramid, dealing with each level before moving to the next.
B — Brackets ( )
Anything inside brackets must be calculated first. Work from the innermost brackets outwards.
I — Indices
Next, deal with any powers (e.g., $5^2$) or roots (e.g., $\sqrt{25}$).
DM — Division (÷) & Multiplication (×)
These are on the same level. Work from left to right, doing any division or multiplication as you encounter them.
AS — Addition (+) & Subtraction (−)
These are also on the same level and are the last to be done. Work from left to right.
Worked Examples
Example 1: Basic BIDMAS
Calculate: $8 + 3 \times 5$
$= 8 + 15$
$= 23$
Example 2: With Brackets
Calculate: $(12 – 4) \div 2$
$= 8 \div 2$
$= 4$
Example 3: With Indices
Calculate: $20 – 3^2 + 5$
$= \underline{20 – 9} + 5$
$= 11 + 5$
$= 16$
Example 4: Left-to-Right Rule
Calculate: $24 \div 6 \times 2 + 7$
$= \underline{4 \times 2} + 7$
$= 8 + 7$
$= 15$
Example 5: Combining Everything
Calculate: $4 \times (5+3) – 10 \div 2^2$
$= 4 \times 8 – 10 \div \underline{2^2}$
$= \underline{4 \times 8} – \underline{10 \div 4}$
$= 32 – 2.5$
$= 29.5$
Tutor Insights
🤔 Common Misunderstandings
- D before M: The biggest mistake is thinking Division always comes before Multiplication. They are a pair, solved left-to-right.
- Forgetting Brackets: Not completing the calculation inside the brackets fully before moving on.
- Index Errors: Calculating $3^2$ as $3 \times 2 = 6$ instead of $3 \times 3 = 9$.
📝 Common Exam Mistakes
- Not showing working: Writing down each step (one operation per line) is the best way to avoid errors and get method marks.
- Simple Calculation Errors: Basic arithmetic mistakes made under pressure. Double-check your work!
- Misinterpreting the question: Not reading carefully and missing a power or a sign.
Practice Questions
- $7 + 2 \times 5$
- $(15 – 3) \div 4$
- $10 – 2^2 + 1$
- $30 \div 5 \times 3$
- $5 \times (6 – 2)^2$
- $\sqrt{25} + 3 \times 4 – 2$
- $18 \div (3 + 3) + 7 \times 2$
Show Answers
- $7 + 10 = \mathbf{17}$
- $12 \div 4 = \mathbf{3}$
- $10 – 4 + 1 = \mathbf{7}$
- $6 \times 3 = \mathbf{18}$
- $5 \times 4^2 = 5 \times 16 = \mathbf{80}$
- $5 + 12 – 2 = \mathbf{15}$
- $3 + 14 = \mathbf{17}$
FAQs
Q: What’s the difference between BIDMAS and BODMAS?
A: They are exactly the same rule. ‘I’ stands for Indices, while ‘O’ stands for Orders. Both refer to powers and roots.
Q: How do I remember BIDMAS?
A: Many students use a mnemonic (memory aid). A popular one is: Big Insects Don’t Multiply As Slowly. Try making up your own!
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