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Commutative Property

Rational Numbers II - Concepts

Identity Property

Commutative Property

Multiplicative Inverse

Division of Rational Numbers

Multiplication of Rational Numbers

Rational Numbers between Two Rational Numbers

Properties of Rational Numbers

Simplification of Rational Numbers

Class - 8th CBSE Subjects

Concept Explanation

Commutative Property

Commutative property of addition in rational numbers:

The addition of rational numbers is commutative i.e. if $large frac{a}{b};and;frac{c}{d}$ are any two ratoinal numbers, then

$large frac{a}{b}+frac{c}{d}=frac{c}{d}+frac{a}{b}$

Verification: In order to verify this property, let us consider two expressions

$large frac{5}{6}+frac{-4}{9}=frac{-4}{9}+frac{5}{6}$

We have,

$large frac{-4}{9}+frac{5}{6}=frac{-8+15}{18}=frac{7}{18}$ and, $large frac{5}{6}+frac{-4}{9}=frac{15}{18}+frac{-8}{18}=frac{15+(-8)}{18}=frac{7}{18}$

$large therefore ;frac{5}{6}+frac{-4}{9}=frac{-4}{9}+frac{5}{6}$

Similarly, it can be verified for others pairs of rational numbers.

Commutative property of subtraction in rational numbers:

The subtraction of rational numbers is not always commutative. That is, for any two rational numbers $large frac{a}{b}$ and $large frac{c}{d}$ , we have

$large frac{a}{b}-frac{c}{d}neq frac{c}{d}-frac{a}{b}$

For example, $large frac{2}{3}-frac{1}{6}=frac{2}{3}+frac{-1}{6}=frac{2times 2+(-1)times 1}{6}=frac{3}{6}=frac{1}{2}$

and, $large frac{1}{6}-frac{2}{3}=frac{1}{6}+frac{-2}{3}=frac{1+(-2)times 2}{6}=frac{1-4}{6}=frac{-3}{6}=frac{-1}{2}$

$large therefore ;frac{2}{3}-frac{1}{6}neq frac{1}{6}-frac{2}{3}$

Commutative property of multiplication in rational numbers:

The multiplication of rational numbers is commutative. That is, if $large frac{a}{b}$ and $large frac{c}{d}$ are any two raitonal numbers, then

$large frac{a}{b}times frac{c}{d}=frac{c}{d}times frac{a}{b}$

Verification: We have,

(i) $large frac{3}{4}times frac{5}{7}=frac{3times 5}{4times 7}=frac{15}{28}$ and, $large frac{5}{7}times frac{3}{4}=frac{5times 3}{7times 4}=frac{15}{28}$

$large therefore ;frac{3}{4}times frac{5}{7}=frac{5}{7}times frac{3}{4}$

(ii) $large frac{-5}{12}times frac{-3}{4}=frac{-5times -3}{12times 4}=frac{15}{48}=frac{5}{16}$ and, $large frac{-3}{4}times frac{-5}{12}=frac{-3times -5}{4times 12}=frac{15}{48}=frac{5}{16}$

$large therefore ;frac{-5}{12}times frac{-3}{4}=frac{-3}{4}times frac{-5}{12}$

Commutative property of division in rational numbers:

For any rational number $large frac{a}{b}$ , we have

$large frac{a}{b}div 1=frac{a}{b}$ and $large frac{a}{b}div (-1)=-frac{a}{b}=frac{-a}{b}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Name the property illustrated by: (5/9 x 2/9) = (2/9 x 5/9)
A. Distributive property	B. Associative property	C. Commutative property	D. Closure property
Right Option : C
View Explanation

Question : 2

The commutative property of ADDITION states _____________________________
A. that you can multiply the factors in any order.	B. that you can divide the numbers in any order.	C. that up can add the numbers in any order.	D. that you can group the numbers in any order.
Right Option : C
View Explanation

Question : 3

Which of the following is an example of the Commutative Property of Addition?
A. 1/7 x 1/5= 1/5 x 1/7	B. 1/2 + 0 = 1/2	C. 5/7 + 3/4 = 3/4 + 5/7	D. 8 (2/5 + 3/4) = (8 x 2/5) + (8 x 3/4)
Right Option : C
View Explanation

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Language - English

Chapters

Rational Numbers I

Rational Numbers II

Linear Equations in One Variable I

Square and Square Root I

Square and Square Root II

Cube and Cube Roots

Comparing Quantities I

Comparing Quantities II

Comparing Quantities III

Algebraic Expressions

Algebraic Identities

Mensuration I

Mensuration II

Exponents and Power I

Exponents and Power II

Direct and Inverse Variation I

Direct and Inverse Variation II

Factorisation

Introduction to Graphs

Constructions

Prerequiste

Playing With Numbers

Linear Equations in One Variable II

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Commutative Property

Commutative Property

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