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”
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
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