Does the associated property for division hold for rational number justify your answer with the help of an example using the ratio

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

1 thought on “Does the associated property for division hold for rational number justify your answer with the help of an example using the ratio”

  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.

    Suggested Videos

    Introduction to Natural and Whole Numbers

    Play

    Introduction to rational numbers

    Play

    Properties of rational numbers

    Play

    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

Leave a Comment