Question

Does the associated property for division hold for rational number justify your answer with the help of an example using the rational numbers 1 /5,1/12,1/15

Answer 1

Answer:

Properties of Rational Numbers: Every one of us knows what natural numbers are. The number of pages in a book, the fingers on your hand or the number of students in your classroom. These numbers are rational numbers. Now let us study in detail about the properties of rational numbers.

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Properties of Rational Numbers

The major properties of rational numbers are:

Closure Property

Commutativity Property

Associative Property

Distributive Property

Let us now study these properties in detail.

Closure Property

Properties of Rational Numbers

Source: Solving math problems

1) Addition of Rational Numbers

The closure property states that for any two rational numbers a and b, a + b is also a rational number.

12 + 34

= 4+68

= 108

Or, = 54

The result is a rational number. So we say that rational numbers are closed under addition.

2) Subtraction of Rational Numbers

The closure property states that for any two rational numbers a and b, a – b is also a rational number.

12 – 34

= 4–68

= −28

Or, = −14

The result is a rational number. So the rational numbers are closed under subtraction.

3) Multiplication of Rational Numbers

The closure property states that for any two rational numbers a and b, a × b is also a rational number.

12 × 34

= 68

The result is a rational number. So rational numbers are closed under multiplication.

4) Division of Rational Numbers

The closure property states that for any two rational numbers a and b, a ÷ b is also a rational number.

12 ÷ 34

= 1×42×3

= 23

The result is a rational number. But we know that any rational number a, a ÷ 0 is not defined. So rational numbers are not closed under division. But if we exclude 0, then all the rational numbers are closed under division.

Commutative Property

1. Addition

For any two rational numbers a and b, a + b = b+ a

−23+ 57 and 57+ −23 = 121

so, −23+ 57 = 57+ −23

We see that the two rational numbers can be added in any order. So addition is commutative for rational numbers.

2. Subtraction

For any two rational numbers a and b, a – b ≠ b – a. Given are the two rational