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Chapter 1: Q1. (page 37)

Explain why it is not necessary to state a division property for inequalities.

Short Answer

Expert verified

It is not necessary to state division properties for inequalities because it is same as multiplication with a reciprocal of a number.

Step by step solution

01

- Write division properties of inequality

For any real numbers a,b,andc

Let cbe a positive number, if a>bthen ac>bcand if a<bthen ac<bc

Now let c be a negative number, if a>b then ac<bcand if a<b then ac>bc

02

- Write multiplication properties of inequality

For any real numbers a,b,andc

Let c be a positive number, if a>b then ac>bcand if a<b then ac<bc

Now let c be a negative number, if a>b then ac<bc and if a<b then ac>bc

03

- compare both properties

From step 1 and 2,

On taking reciprocal of number c in multiplicative properties of inequalities it becomes same as division properties of inequalities.

Thus, it is not necessary to state division properties separately.

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