Page 82 - Ganit Kaushal

3. Square Brackets [ ]: These are used to enclose additional groups of terms when parentheses and curly
brackets are already in use.
4. Vinculum or Bar (a line over a group of numbers): Though less common, it also works like brackets.

_________ Æ ( ) Æ { } Æ [ ]
Bar or Vinculum Round brackets Curly brackets Square brackets

To simplify a problem having all the brackets, we first perform the operation under the bar, then in the round
brackets, then in curly brackets and lastly in square brackets.

Order of Operations with Brackets: BODMAS Rule

To solve mathematical problems involving multiple operations (addition, subtraction, multiplication, division),
we follow the BODMAS rule, which stands for (in this order):
® B: Brackets first

® O: Orders (like squares or square roots, powers) or ‘Of’
9
For example: 9% of 200 = × 200 = 18
100
® D: Division Note

® M: Multiplication For Class 6 students, the focus is mainly
® A: Addition on parentheses (.) and understanding
how to use them in basic operations.
® S: Subtraction
This rule tells us the correct order to perform the operations, ensuring the result is accurate.

Examples with Four Operations

1. Addition and Subtraction:
Without brackets: 8 + 5 – 3 = 10. With brackets: 8 + (5 − 3) = 8 + 2 = 10
In this case, both expressions give the same result, but brackets help avoid confusion when the
expressions get more complex.
2. Multiplication and Division:
When multiplication or division appears inside the brackets, it must be performed first.
• Without brackets: 20 ÷ 5 × 2 = 4 × 2 = 8

• With brackets: 20 ÷ (5 × 2) = 20 ÷ 10 = 2
Here, the brackets change the meaning of the expression and give a different result.
3. Mixed Operations (Addition, Subtraction, Multiplication, and Division):
Brackets dictate which operation is to be performed first in a mix of operations.

• Example without brackets:
12 + 8 ÷ 2 × 3 = 12 + 4 × 3 = 12 + 12 = 24
3 × 3 – 3 ÷ 3 + 3 = 3 × 3 – 1 + 3 = 9 – 1 + 3 = 9 + 2 = 11
• Example with brackets:
12 + (8 ÷ 2) × 3 = 12 + 4 × 3 = 12 + 12 = 24

3 × 3 – (3 ÷ 3) + 3 = 3 × 3 – 1 + 3 = 9 – 1 + 3 = 9 + 2 = 11

80 Mathematics-6