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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 IMO 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

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 : 2

Name the property of multiplication illustrated by the following: -11/13 × -17/5 = -17/5 × -11/13
A. Distributive property	B. Associative property	C. Commutative property	D. Closure property
Right Option : C
View Explanation

Question : 3

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

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Chapters

Exponents and Power II

Prerequiste

Visualising Soild Shapes

Ratio and Proportion

Introduction to Trigonometry

Constructions

Quadrilaterals II

Quadrilaterals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Rational Numbers II

Rational Numbers I

Mensuration I

Exponents and Power I

Direct and Inverse Variation II

Direct and Inverse Variation I

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

Playing With Numbers

Introduction to Graphs

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Commutative Property

Commutative Property

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