# Symbols Notations: Interchange of signs and numbers based Tricks with Problem (Question) and Solutions

### Interchange of signs based

In this type of questions are provided with substitutes for various mathematical symbols or numerals followed by a question involving calculation of an expression.
Note: While solving mathmatical expression according to the BODMAS rule.

### Solved Problems

Q.1.If ÷ means ×, × means +, + means – and – means ÷, then find the value of 16 × 3 + 5 – 2 ÷ 4.

(a) 9

(b) 10

(c) 19

(d) None of these

Sol-

Using the correct symbols,

we have

Given expression :

16 + 3 – 5 ÷ 2 × 4 = 16 + 3 –5/2 × 4

= 19 – 10 = 9

Q.2.If + means ÷, ÷ means –, – means ×, × means +, then 12 + 6 ÷ 3 – 2 × 8 = ?

(a) –2

(b) 2

(c) 4

(d) 8

Sol.

Using the correct symbols,

we have

Given expression

= 12 ÷ 6 – 3 × 2 + 8 = 2 – 6 + 8 =

10 – 6 = 4

Q.3.If + means –, – means ×, ÷ means + and × means ÷, then 15 – 3 + 10 × 5 + 5 = ?

(a) 5

(b) 22

(c) 38

(d) 52

Sol.

Using the correct symbols,

we have

Given expression

= 15 × 3 – 10 ÷ 5 – 5 = 45 – 2 – 5

= 45 – 7 = 38

### Interchange of signs and numbers based

each of the following questions, if the given interchanges are made in signs and numbers, which one of the four equations would be correct?

Q.1.Given interchanges : Signs – and ÷ and numbers 4 and 8.

(a) 6–8÷4 = –1

(b) 8–6÷4 = 1

(c) 4÷8–2 = 6

(d) 4–8÷6 = 2

Sol.

On interchanging – and ÷ and 4 and 8 in (c), we get the

equation as :

8–4÷2=6 or 8 – 2 = 6 or 6 = 6, which is true.

Q.2.Given interchanges : Signs + and × and numbers 4 and 5.

(a) 5×4+20=40

(b) 5×4+20=85

(c) 5×4+20=104

(d) 5×4+20=95

Sol.

On interchanging + and × and 4 and 5 in (c), we get the

equation as :

4+5×20=104

104 = 104, which is true.