Page 22 - Start Up Mathematics_7

Order of Operations and Use of Brackets
So far we have learnt the basic fundamental operations of addition, subtraction, multiplication and
division. Mathematical expressions having only one operation can be simplified starting from left
to right as shown: 5 + 7 + 6 + 10 = 28 or 2 × 3 × 4 × 5 = 120
When we have many operations to be performed then simplifying as we did in the above examples
can be quite confusing and may give wrong results. For example, does 24 ÷ 6 × 2 mean (24 ÷ 6) ×
2 = 4 × 2 = 8 or 24 ÷ (6 × 2) = 24 ÷ 12 = 2? In such a situation we need to use B O D M A S rule.

B → BRACKETS (+, ×, ÷, –)
or [{(...) + 2} + 2]
O → OF (÷, ×, +, –) [()]
D → DIVISION

M → MULTIPLICATION

A → ADDITION
S → SUBTRACTION

BODMAS denotes the order of operations to be performed. According to it, first the brackets are
solved, then ‘of’ followed by the four operations of division, multiplication, addition and subtraction.
The operations cannot be performed in the order in which they appear in an expression.

Brackets

Let’s learn about different type of brackets used in Arithmetic. The brackets are removed in the
order mentioned below:
Symbol Name

____ Vinculum

( ) Round brackets or parenthesis
{ } Curly brackets or braces
[ ] Square or box brackets

To simplify expressions having brackets the following order is used:
(a) If a vinculum is present, then first perform operations under it.
(b) If there are brackets within brackets, remove the innermost brackets first by doing all calculations
inside it. Then solve within the next innermost bracket and so on.

Important Rules for Solving the Brackets

• If there is a ‘+’ sign outside the bracket remove it keeping the signs of the terms inside the
bracket as it is.
• If there is a ‘–’ sign outside the bracket remove it and change the signs of all the terms inside
the bracket.

• If there is a number just outside the bracket with no sign between the number and the bracket,
we multiply the number with all the terms inside the bracket as it means multiplication.

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