Mathematical operations

Mathematical operations are basically the simplification of an expression containing numbers and different Mathematical operations. In this chapter, we deal with questions having four fundamental Mathematical operations– addition (+), subtraction (–), multiplication (×) and division (÷) and also statements such as ‘less than (<)’, ‘greater than (>)’, ‘equal to (=)’, ‘not equal to (≠)’, etc. All these operations are represented by symbols, different from usual ones. The candidate is required to substitute the real signs in place of artificial symbols to solve the questions. We need to follow the BODMAS rule for simplification of Mathematical operations.

B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction. Mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.

There are four types of questions based on mathematical operations which are usually asked in various competitive examinations.

Type 1 : Problem Solving by Substitution

In this type of questions, you have substitutes for various mathematical symbols or numerals followed by a question involving calculation of an expression or choosing the correct/incorrect equation.

Example1: If ‘÷’ means ‘+’, ‘–’ means ‘÷’, ‘×’ means ‘–’ and ‘+’ means ‘×’ then, 62 ÷ 8 – 4 × 12 + 4 =
(A)16

(B)36

(C)1/6
(D)26
Answer : (A) Given expression, 62 ÷ 8 – 4 × 12 + 4 = ?
According to question, after replacement of mathematical sign
62 + 8 ÷ 4 – 12 × 4 = ?
= 64 – 48 = 16

Example 2. If ‘–‘ stands for ‘÷’, ‘+’ stands for ‘×’, ‘÷’ stand for ‘–‘ and ‘×’ stands for ‘+’, which one of the following question is correct?
(A) 30 – 6 + 5 × 4 ÷ 2 = 27.
(B) 30 + 6 – 5 ÷ 4 × 2 = 30.
(C) 30 × 6 ÷ 5 – 4 + 2 = 32.
(D) 30 ÷ 6 × 5 + 4 – 2 = 40.

Answer (A)
30 ÷ 6 × 5 + 4 – 2 = 27
→ 5 × 5 + 4 – 2 = 27.
→ 29 – 2 = 27.
→ 27 = 27.

Type 2:Interchanging the Signs and Numbers Type

In this type of questions, certain signs or numbers interchange among each other. The candidate is required to change the given signs or numbers with each other and select the equation which is correct from the given alternatives. It can also be asked to find the correct pair of signs and numbers to be interchanged from the alternatives to make the given equation correct.

Example 3:If signs ‘+’ and ‘−’ and numbers 4 and 8 interchange between each other, then which one of the following four equations would be correct?

(A) 4- 8+ 12 =0

(B)8 − 4 ÷ 12 = 8

(D) 8 ÷ 4 − 12 = 24

Answer (A) Given, 4 -8 +12= 0 On interchanging signs ‘+’ and ‘−’ and numbers 4 and 8 in option (A), we get 8+ 4- 12 =0 ⇒12 -12 = 0

Example 4: Which one of the four interchanges in signs and numbers would make the given equation correct?

6× 4+2 =16

(A) + and ×, 2 and 4

(B) + and ×, 4 and 6

(D)None of these

Answer (B):Given, 6× 4+2 =16 On interchanging signs ‘+’ and ‘×’ and number 4 and 6

4 +6 ×2 =4 +12= 16

Replacement of signs by alphabets or symbols

In this type of questions signs are replaced by alphabets or symbols. You have to substitute corresponding signs and find the solution of the given equation.

Example5 :If ‘R’ stands for ‘–‘, ‘A’ stands for ‘+’, ‘B’ stands for ‘÷’ and ‘C’ stands for ‘×’, then what is the value of the given equation ?
25 A 37 C 8 B 4 R 1 = ?

(A) 99
(B) 100
(C) 98
(D) 199

Answer (C)= 25 + 37 × 8 ÷ 4 – 1

Example 6. If P denotes ‘÷’, Q denotes ‘×’, R denotes ‘+’ and S denotes ‘−’,

then 18 Q 12 P 4 R 5 S 6 =?

(A) 95

(B) 53

(D) 57

Answer:(B)

18 ×12÷ 4+ 5− 6 = 53 (Apply BODMAS rule)

EXAMSPIRE

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