Mathematical Operations
Here’s a list of most commonly used mathematical operators:
| Mathematical Operators | Symbol |
|---|---|
| Addition | + |
| Subtraction | - |
| Multiplication | × |
| Division | ÷ or / |
| Of | Of |
| Equal to | = |
| Less than | < |
| Greater than | > |
| Less than or Equal to | ≤ |
| Greater than or Equal to | ≥ |
Brackets - Circular Bracket ( ); Curly bracket { }; Square bracket [ ]
BODMAS
This rule gives us the correct order, in which various operations have to be performed during simplification.
B (Brackets)
Brackets are to be solved in the order given below:
- ( 1 + 2 ) circular bracket
- { 1 + 2 } curly bracket
- [ 1 + 2 ] square bracket
ODM
After that we solve for Of, Division and Multiplication, in that order.
AS
Thereafter we solve for Addition and Subtraction.
Let’s us see all the different types of questions that we may encounter in this chapter.
Types of Simple Mathematical Operations based Questions
Type 1: Symbol Substitution
In this type of questions, a candidate is provided with substitutes for various mathematical symbols. One is supposed to make all the substitutions and then simplify the given expression(s).
Q. If ‘×’ means ‘–’, ‘÷’ means ‘+’, + means ‘×’, then
18 × 5 ÷ 5 + 6 is equal to
(a) 37 (b) 43 (c) 49 (d) 58
Explanation:
‘×’ means ‘–’, ‘÷’ means ‘+’, + means ‘ב
Replacing the operators: 18 x 5 ÷ 5 + 6 = 18 - 5 + 5 x 6
Now, 18 - 5 + 5 x 6 = 18 – 5 + 30 = 43
Answer: (b)
Type 2: Balancing the Equation
In these type of questions, the operators in the given equation are missing. The signs given in one of the options have to be used in order to balance the given equation.
Q. If the following equation has to be balanced, then the signs of which of the following options will be used ?
24 $\hspace{1ex}$ 6 $\hspace{1ex}$ 12 $\hspace{1ex}$ 16 = 0
(a) ÷, + and – (b) –, + and + (c) –, – and – (d) ÷, + and ÷
Explanation:
24 $\hspace{1ex}$ 6 $\hspace{1ex}$ 12 $\hspace{1ex}$ 16 = 0
(b) –, + and + : 24 - 6 + 12 + 16 = (24 + 12 + 16) - 6 = 52 – 6 = 46
(c) –, – and – : 24 – 6 – 12 – 16 = 24 – 34 = -10
(d) ÷, + and ÷ : 24 ÷ 6 + 12 ÷ 16 (all positive numbers being added)
(a) ÷, + and – : 24 ÷ 6 + 12 – 16 = 4 + 12 – 16 = 16 – 16 = 0
Answer: (a)
Type 3: Interchange of Signs and Numbers
In these type of questions, the given equation becomes correct and fully balanced when either two signs of the equation or both the numbers and the signs of the equation are interchanged.
Q. Which one of the given interchanges in signs would make the given equation correct ?
10 – 2 + 9 × 2 ÷ 4 = 19
(a) ÷ and × (b) – and + (c) × and ÷ (d) – and ÷
Explanation:
10 – 2 + 9 × 2 ÷ 4 = 19
(d) – and ÷ : 10 ÷ 2 + 9 × 2 - 4 = 5 + 18 - 4 = 19
Answer: (d)
Type 4: Find the Resultant Number in a Row
In this type of questions, two rows of numbers are given along with certain rules. On the basis of these rules, one is required to find out resultant number in each row separately (operation of numbers progresses from left to right). Therafter, he/she has to answer the question given below the rows.
Q. In the following question two rows of numbers are given. The resultant number of each row is to be worked out separately based on the following rules:
(i) If an even number is followed by another even number, they are to be added.
(ii) If an even number is followed by a prime number, they are to be multiplied.
(iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number.
(iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number.
(v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number.
1st Row: 84 $\hspace{1ex}$ 21 $\hspace{1ex}$ 13
2nd Row: 15 $\hspace{1ex}$ 11 $\hspace{1ex}$ 44
What is the half of the sum of the resultants of the two rows ?
(a) 236 (b) 116 (c) 132 (d) 232
Explanation:
We may rewrite the question as follows:
In the following question two rows of numbers are given. The resultant number of each row is to be worked out separately based on the following rules:
(i) Even number + Even number
(ii) Even number × Prime Number
(iii) Odd number — Even number
(iv) Odd number + $(Odd \hspace{1ex} number)^2$
(v) Even number ÷ Composite odd number
1st Row (84 $\hspace{1ex}$ 21 $\hspace{1ex}$ 13): 84 ÷ 21 = 4 [Rule (v)]; 4 × 13 = 52 [Rule (ii)]
2nd Row (15 $\hspace{1ex}$ 11 $\hspace{1ex}$ 44): 15 + 112 = 136 [Rule (iv)]; 136 + 44 = 180 [Rule (i)]
Half of the sum of the resultants of the two rows = (180 + 52)/2 = 232/2 = 116
Answer: (b)