Page 19 - Maths Skills - 7

Integers 17

6. In a class test containing 20 questions, 6 marks are awarded for every correct and (–2) are awarded for
every incorrect answer and 0 for answer not attempted.
(i) Astha gets 9 correct answers and 11 incorrect answers. Find her score.
(ii) Siddhi scored 36 marks though she got 8 correct answers. How many questions did she attempt
incorrectly?

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 quiet
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 O → OF OR MULTIPLICATION 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. The order of operation is therefore

Brackets → Of (multiplication) → Division → Multiplication → Addition → Subtraction
A mathematical expression with brackets is solved in the order:
Vinculum Braces

‘—’ ⇒ ( ) ⇒ { } ⇒ [ ]

Parentheses Square Brackets

Let’s Attempt

Example 1: Simplify.
(i) 10 – (5 + 3 – 2) (ii) 15 – (– 3) × (5) + 10
Solution: (i) 10 – (5 + 3 – 2) = 10 – 6 = 4 (ii) 15 – (– 3) × (5) + 10 = 15 – (– 15) + 10 = 15 + 15 + 10 = 40

Example 2: Simplify.

(i) 18 ÷ (8 – 4 + 2) (ii) 36 – [15 – {9 ÷ (17 + 3 × 2 – 20)}]
Solution: (i) 18 ÷ (8 – 4 + 2) [Removing Vinculum]
= 18 ÷ (8 – 6) [Removing Parentheses]

= 18 ÷ 2 = 9
(ii) 36 – [15 – {9 ÷ (17 + 3 × 2 – 20)}]

= 36 – [15 – {9 ÷ (17 + 6 – 20)}]
= 36 – [15 – {9 ÷ (23 – 20)}] [Removing Parentheses]
= 36 – [15 – {9 ÷ 3}] [Removing Braces]
= 36 – [15 – 3] [Removing Square Brackets]

= 36 – 12 = 24