Rules for calculation (BODMAS) and practice

Understanding the Components of BODMAS:

1. B – Brackets

There are three types of brackets:

• Parentheses ( )

• Curly Brackets { }

• Square Brackets [ ]

Always solve expressions inside the innermost bracket first.

Example:

$(2+3)\times 4=5\times 4=20$

2. O – Orders

Orders include:

• Exponents (Powers): e.g., 2² = 4

• Roots: e.g., √16 = 4

Solve any exponent or root immediately after brackets.

3. D & M – Division and Multiplication

Division and multiplication have equal priority. Perform them from left to right as they appear.

Example:

$20÷4\times 3=5\times 3=15$

4. A & S – Addition and Subtraction

Addition and subtraction are also equal in priority. Solve them from left to right.

Example:

$15-4+2=11+2=13$

Importance of Following BODMAS:

Without following BODMAS, answers can vary drastically. Consider:

Expression:

$8+2\times 5$

Without BODMAS:

$(8+2)\times 5=10\times 5=50$

With BODMAS:

$8+(2\times 5)=8+10=18$

Common BODMAS Mistakes

• Solving addition before multiplication.
• Ignoring the order of nested brackets.
• Confusing subtraction with a negative sign.
• Forgetting that division and multiplication are left to right.
• Always rewrite the expression step-by-step to reduce errors.

Step-by-Step Examples:

Example 1:

$7+3\times 2$

Step 1: Multiply → 3 × 2 = 6

Step 2: Add → 7 + 6 = 13

Example 2:

(5+4)2(5 + 4)²(5+4)2

Step 1: Bracket → 5 + 4 = 9

Step 2: Order → 9² = 81

Example 3:

$30÷5\times 3$

Step 1: Division → 30 ÷ 5 = 6

Step 2: Multiply → 6 × 3 = 18

Example 4:

25−(2+3)225 – (2 + 3)²25−(2+3)2

Step 1: Bracket → 2 + 3 = 5

Step 2: Order → 5² = 25

Step 3: Subtract → 25 – 25 = 0

Real-Life Applications of BODMAS

• Finance: Calculating compound interest or tax.

• Engineering: Solving formulas and design equations.

• Programming: Coding calculators or logic systems.

• Science: Balancing chemical equations or working with formulas.

• Daily Math: Estimating bills or measurements.