SSC CGL Maths · Surds, Indices and Simplification

BODMAS and Brackets

A long expression has one right value only when everyone works it in the same order: the bar, brackets from the inside out, 'of', then division and multiplication, then addition and subtraction.

All Surds, Indices and Simplification notes

Why this matters

Forty-four questions in the bank, 39 EASY and 5 MODERATE, all from the 2023 and 2024 shifts. Every one is a single chain of operations, and the wrong options are the values you get by doing one step out of order. Seventeen of them use the word 'of', which SSC uses to catch students who treat it as a plain multiplication.

Concept 1 of 3: The order of operations (BODMAS)

If one person divides first and another multiplies first, the same line gives two answers. BODMAS is the agreement that fixes one order, so the expression means one number.

Definition

Brackets first, then Orders (powers and roots), then Division and Multiplication, then Addition and Subtraction.
Division and multiplication are one level. Work them left to right, whichever comes first. The same holds for addition and subtraction.
So $12 \div 4 \times 3 = 3 \times 3 = 9$ , not $12 \div 12 = 1$ .
Fast route: once every $\div$ and $\times$ is done, add all the positive terms, add all the negative terms, and subtract once. This avoids a long run of small signed steps.
Fast check: the four options often differ in the last digit or the sign. Work out just the last digit, or just the sign, and two options usually fall away.

Order of operations

\text{Brackets} \to \text{Orders} \to \div,\ \times\ (\text{left to right}) \to +,\ -\ (\text{left to right})

Worked example

Simplify

48 \div 6 \times 2 + 35 - 9 \times 4 \div 12

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 13 Sep 2024, Shift 3 · Q72Easy

Example 1 · Surds, Indices and Simplification · BODMAS and Brackets

Simplify the following.

16 \div 2 - 7 \times 15 \div 3 + 5 \times 5 + 4 \times 3 - 10

Multiplying before dividing

36 \div 6 \times 2

the division is on the left, so it goes first:

6 \times 2 = 12

. Doing

6 \times 2

first gives

36 \div 12 = 3

, which is wrong. Division and multiplication share one level and go left to right.

Adding before subtracting

20 - 5 + 3

15 + 3 = 18

, not

20 - 8 = 12

. Addition and subtraction also share one level and go left to right.

Drill 11 more on the order of operations (bodmas)

Concept 2 of 3: Removing nested brackets from the inside out

A bracket says: do this part first. When brackets sit inside brackets, the innermost one needs nothing else, so it is always the place to start. Each bracket you finish turns into a single number for the bracket around it.

Definition

The usual nesting is ( ) inside { } inside [ ]. Open the innermost bracket first, whatever its shape.
Inside each bracket, BODMAS applies as usual.
A minus before a bracket changes the sign of every term inside it: $a - (b - c + d) = a - b + c - d$ .
Two minus signs make a plus: $8 - (-3) = 11$ .
A number written right next to a bracket multiplies it: $13(-3)$ means $13 \times (-3) = -39$ .

Minus before a bracket

a - (b - c) = a - b + c \qquad a - (-b) = a + b

Worked example

Simplify

40 - [12 + \{18 - (9 - 4)\}]

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 9 Sep 2024, Shift 3 · Q66Easy

Example 2 · Surds, Indices and Simplification · BODMAS and Brackets

Simplify:

13 - [7 - (4 + 7) - \{7 - (7 - 4 + 7)\} + 14]

Flipping only the first sign after a minus

30 - (12 - 5 + 2)

30 - 12 + 5 - 2 = 21

. A minus before a bracket flips every sign inside it. Flipping only the 12 gives

30 - 12 - 5 + 2 = 15

, a typical wrong option.

Losing a negative bracket

4 - (6 - 6 - 8)

the bracket is

-8

, so the value is

4 + 8 = 12

. Writing

4 - 8 = -4

drops the minus that the bracket carries.

Drill 13 more on removing nested brackets from the inside out

Concept 3 of 3: The word 'of' and the bar in BODMAS

SSC prints two signs that older textbooks use. 'Of' means multiply, but it binds two numbers more tightly than ÷ or ×. A bar drawn over some terms (the vinculum) groups them even before ordinary brackets.

Definition

'Of' means multiply, and it is done before division and multiplication: $24 \div 4 \text{ of } 3 = 24 \div 12 = 2$ , while $24 \div 4 \times 3 = 18$ .
The full order SSC uses: the bar, then brackets, then of, then $\div$ and $\times$ left to right, then $+$ and $-$ .
A bar over terms makes them one number: $\overline{9 - 5} = 4$ .
A bracket after 'of' is still worked first: $3 \text{ of } (2 + 5) = 3 \times 7 = 21$ .
'Of' with a fraction is the usual fraction of a number: $\frac{2}{3} \text{ of } 27 = 18$ .

Of against times after a division

a \div b \text{ of } c = \frac{a}{bc} \qquad a \div b \times c = \frac{ac}{b}

Worked example

Simplify

96 \div 4 \text{ of } 6 + 3 \text{ of } 5 \times 2 - \overline{11 - 4}

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 10 Sep 2024, Shift 1 · Q75Easy

Example 3 · Surds, Indices and Simplification · BODMAS and Brackets

The value of

15 \div 3 \text{ of } 2 \times 2 + 9 \div 18 \text{ of } 2 \times 4 - 4 \div 8 \times 2

is:

Treating 'of' as an ordinary multiplication

48 \div 8 \text{ of } 2

48 \div 16 = 3

. Reading 'of' as a plain

\times

gives

48 \div 8 \times 2 = 12

, and SSC prints that as a wrong option.

Ignoring the bar

A bar over

4 - 9

makes it one number,

-5

, so

10 - \overline{4 - 9} = 10 + 5 = 15

. Without the bar the minus would touch only the 4, giving

10 - 4 - 9 = -3

Doing 'of' before its own bracket

3 \text{ of } (2 + 5)

the bracket still comes first:

3 \times 7 = 21

. 'Of' outranks division, not brackets.

Drill 17 more on the word 'of' and the bar in bodmas

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

The order of operations (BODMAS)
Order of operations
$\text{Brackets} \to \text{Orders} \to \div,\ \times\ (\text{left to right}) \to +,\ -\ (\text{left to right})$
Removing nested brackets from the inside out
Minus before a bracket
$a - (b - c) = a - b + c \qquad a - (-b) = a + b$
The word 'of' and the bar in BODMAS
Of against times after a division
$a \div b \text{ of } c = \frac{a}{bc} \qquad a \div b \times c = \frac{ac}{b}$

Watch out for (7)

Multiplying before dividing
→ The order of operations (BODMAS)
Adding before subtracting
→ The order of operations (BODMAS)
Flipping only the first sign after a minus
→ Removing nested brackets from the inside out
Losing a negative bracket
→ Removing nested brackets from the inside out
Treating 'of' as an ordinary multiplication
→ The word 'of' and the bar in BODMAS
Ignoring the bar
→ The word 'of' and the bar in BODMAS
Doing 'of' before its own bracket
→ The word 'of' and the bar in BODMAS

Test yourself on Surds, Indices and Simplification

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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