Mathematical Operations

**Category : **9th Class

**Type-I**

**Solving by Substitution**

In this type of problems, you are required to simplify the given statement by substituting various signs and numerals as per given terms. To simplify a statement, the BODMAS rule is very useful.

**Type-II**

**Interchanging of Signs and Numbers**

In this type of problems, you would require to interchange the pair(s) of symbols/numbers. Simplify if asked the given statement(s) using BODMAS rule.

**Type-III**

**Analysing the Conclusions**

In this type of problems, relations between different statements are given in terms of mathematical operations (less than, more than etc.) A student is required to analyse amongst them to get correct conclusions.

**EXAMPLE**

**Consider the following statements.**

**'A @ B' means 'A is not greater than B'.**

**'A © B' means 'A is not smaller than B'.**

**'A # B' means "A is neither greater than nor equal to B'.**

**'A $ B' means "A is neither smaller than nor equal to B'.**

**Assuming the given below statements to be true, analyse which of the two conclusions I and II is/are definitely true and choose your option accordingly.**

**Statements:** P @ Q, Q © R, R # S.

**Conclusions:** 1. P $ R II. R $ P

(a) Only I is true (b) Only II is true (c) None is true (d) Both are true

**Explanation (c):**

We have

A@B AB A < B

A©B A B A > B

A # B A B and A B A < B

A $ B A B and A B A > B

Given statements: P < Q, Q >. R, R < S.

Relationship between P and R: P < Q, Q >. R

No definite relationship between P and R.

Hence none of I and II is true.

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