Mathematical Operations

What this topic tests

In mathematical-operation questions the numbers are small and the sums are easy. What the examiner really checks is whether you follow the order of operations without a single slip. Think of a shop bill: 3 pens at ₹10 each and 2 notebooks at ₹40 each cost 3 × 10 + 2 × 40 = 30 + 80 = ₹110. Nobody adds 10 + 2 first. That habit of "multiply first, then add" is exactly the rule you need here.

BODMAS in simple words

BODMAS tells you which part of an expression to work out first:

Letter	Meaning	Example
B	Brackets	(6 + 2) is done first
O	Orders: powers, roots, "of"	$3^2$, $\sqrt{16}$, half of 10
D, M	Division and Multiplication	same rank
A, S	Addition and Subtraction	same rank

Example: 18 + 24 ÷ 6 × 3 − 5. First the ÷ and ×: 24 ÷ 6 = 4, then 4 × 3 = 12. Now 18 + 12 − 5 = 25.

Same rank means left to right

Division is not "before" multiplication, and addition is not "before" subtraction. When operators have the same rank, simply go from left to right.

• 96 ÷ 8 × 4 = 12 × 4 = 48 (not 96 ÷ 32 = 3).
• 60 − 12 + 8 = 48 + 8 = 56 (not 60 − 20 = 40).

This one rule decides many answers, because examiners love to put ÷ before × or − before +.

Brackets inside brackets

When brackets are nested, open them from the inside: first ( ), then { }, then [ ].

Example: 100 − [20 + {30 − (12 − 4) × 2}]. Inner bracket: 12 − 4 = 8. Curly bracket: 30 − 8 × 2 = 30 − 16 = 14. Square bracket: 20 + 14 = 34. Finally 100 − 34 = 66. Inside every bracket, BODMAS still applies (8 × 2 before 30 − ...).

Finding a missing number

Some questions hide one number: 18 + 6 × ? − 4 = 38. Undo the steps in reverse order.

1. Move the loose terms: 6 × ? = 38 + 4 − 18 = 24.
2. Undo the multiplication: ? = 24 ÷ 6 = 4.
3. Put 4 back and check: 18 + 24 − 4 = 38 ✓.

Always check the answer by putting it back. It takes five seconds and removes every doubt.

How wrong options are built

Almost every wrong option in this topic comes from one of three slips:

• Left-to-right slip: the student ignored BODMAS. For 7 + 8 × 2 − 5, left to right gives 15 × 2 − 5 = 25, but the correct value is 7 + 16 − 5 = 18.
• Sign slip: a minus sign is carried wrongly, e.g. 45 − 5 × 6 + 9 read as 45 − (30 + 9).
• Forgotten term: the last "− 5" or "+ 4" is left out.

If your answer matches an option, still ask: "Did I do × and ÷ before + and −?" If yes, mark it and move on.

Speed habits

• Circle every × and ÷ first; do those pieces; then read the line once more for + and −.
• Write the reduced line after each step (18 + 12 − 5). Short lines prevent mistakes.
• Use the last digit to check: 7 × 8 ends in 6, so 56 is right and 54 is not.

Quick revision

• Order: Brackets → Orders → ÷ and × (left to right) → + and − (left to right).
• ÷ and × have equal rank; + and − have equal rank. Same rank = left to right.
• Nested brackets: ( ) then { } then [ ]; BODMAS works inside each bracket too.
• Missing number: undo the steps backwards, then put the number back to check.
• The left-to-right value is the examiner's favourite wrong option.