# MATCHING THE PROPERTY OF RATIONAL NUMBER QUIZ

## About "Matching the Property of Rational Number Quiz"

Matching the Property of Rational Number Quiz :

Here we are going to see some example problems on operations of rational numbers.

Closure property :

The collection of rational numbers (Q) is closed under addition and multiplication. This means for any two rational numbers a and b, a + b and a × b are unique rational numbers.

Commutative property :

Addition and multiplication are commutative for rational numbers. That is, for any two rational numbers a and b,

(i) a + b = b + a and

(ii) a × b = b × a

Associative property :

Addition and multiplication are associative for rational numbers. That is, for any three rational numbers a,b and c

(i) (a + b)+ c = a + (b + c) and

(ii) (a × b)× c = a × (b × c)

Additive and Multiplicative Identity property :

For any rational number a there exists a unique rational number –a such that a + (−a) = 0 = (−a) + a (Additive Inverse property).

For any non-zero rational number b there exists a unique rational number (1/b) such that b x (1/b) = 1 = (1/b) × b (Multiplicative Inverse property).

## Matching the Property of Rational Number Quiz - Practice questions

Question 1 : Solution :

The given statement exactly matches the general form (a + b) + c  =  a + (b + c).

It is in the associative property of addition.

Question 2 : Solution :

The given statement is in the form a x (b + c)  = (a x b) + (a x c)

The name of the property is distributive property of multiplication over addition.

Question 3 : Solution :

If a = -4/9, 1/a  =  9/(-4)

a x (1/a)  =  1

Hence the given is inverse property of multiplication.

(iv)  1/0

Solution :

It is undefined.

(v)  22/7

Solution :

If is a rational number.

Question 4 :

Which of the following properties hold for subtraction of rational numbers? Why?

(a) closure (b) commutative (c) associative

(d) identity (e) inverse

Solution :

Closure property :

For any two rational numbers a and b, we may get

Commutative property :

a - b   b - a

Associative property :

a - (b - c) ≠ (a - b) - c

Inverse property :

Inverse property fails.

Identity property :

5 - 0 ≠ 0 - 5 After having gone through the stuff given above, we hope that the students would have understood, "Example Problems Based on Operation of Rational Numbers"

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