is addition of commutative on rational numbers?????
please tell me
Answers
Step-by-step explanation:
Properties of Rational Numbers
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.
Introduction to Natural and Whole Numbers
Introduction to rational numbers
Properties of rational numbers
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.
\frac{1}{2}
2
1
+ \frac{3}{4}
4
3
= \frac{4 + 6}{8}
8
4+6
= \frac{10}{8}
8
10
Or, = \frac{5}{4}
4
5
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.
\frac{1}{2}
2
1
– \frac{3}{4}
4
3
= \frac{4 – 6}{8}
8
4–6
= \frac{-2}{8}
8
−2
Or, = \frac{-1}{4}
4
−1
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.
\frac{1}{2}
2
1
× \frac{3}{4}
4
3
= \frac{6}{8}
8
6
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.
\frac{1}{2}
2
1
÷ \frac{3}{4}
4
3
= \frac{1 ×4}{2 ×3}
2×3
1×4
= \frac{2}{3}
3
2
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.
Step-by-step explanation: