Order of Operations (BIDMAS)

Spec reference: Number - Structure and calculation
Key idea: Apply the correct order of operations when evaluating expressions.

---

▶ BODMAS - Order of Operations

---

BIDMAS

BIDMAS (also known as BODMAS) gives the order in which operations must be performed:

Letter	Operation	Example
B	Brackets	$(3+2)$
I	Indices (powers and roots)	$3^2$, $\sqrt{16}$
D	Division	$÷$
M	Multiplication	$\times$
A	Addition	$+$
S	Subtraction	$-$

TIP

Division and Multiplication have equal priority - work left to right.
Addition and Subtraction have equal priority - work left to right.

---

Worked examples

Example 1

Calculate $3+4\times 2$

Multiplication before addition:

$3+(4\times 2)=3+8=\boxed{{\displaystyle 11}}$

(Not $7\times 2=14$)

Example 2

Calculate $20-12÷4+3^2$

Step 1 - Indices: $3^2=9$

Step 2 - Division: $12÷4=3$

Step 3 - Left to right: $20-3+9=\boxed{{\displaystyle 26}}$

Example 3

Calculate ${\displaystyle \frac{6+14}{2+3}}$

The fraction bar acts as brackets for both numerator and denominator:

$$\frac{(6+14)}{(2+3)}=\frac{20}{5}=\boxed{{\displaystyle 4}}$$

Example 4

Calculate $(2+3{)}^2-\sqrt{16}\times 3$

Step 1 - Brackets: $(2+3)=5$

Step 2 - Indices: $5^2=25$ and $\sqrt{16}=4$

Step 3 - Multiplication: $4\times 3=12$

Step 4 - Subtraction: $25-12=\boxed{{\displaystyle 13}}$

---

Common mistakes

Watch out for

• $3+4\times 2\ne 14$ - multiplication happens before addition
• $10-3+2=9$ (left to right), not $10-5=5$
• Division and multiplication are equal priority, so $12÷4\times 3=3\times 3=9$, not $12÷12=1$

---

Test Yourself

Question 1 of 5

Calculate $5 + 3 \times 4$