Like us!

Have a Look!

WhatsApp Message

Share Link

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 - RRB Technician Grade III 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 of rational numbers illustrated by : (2/9 + 4/9) = (4/9 + 2/9)
A. Distributive property	B. Associative property	C. Commutative property	D. Closure property
Right Option : C
View Explanation

Question : 2

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

Question : 3

7a + 2 = a(7) + 2, is explained by which property?
A. Associative over addition	B. Associative over multiplication	C. Commutative over multiplication	D. Commutative over Addition
Right Option : C
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Exponents and Power 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

Exponents and Power II

Mensuration I

Direct and Inverse Variation II

Direct and Inverse Variation I

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Andhra Bank

Class / Course

RRB Technician Grade I Signal

Railways

RRB Technician Grade III

RPF Constable

RPF Sub Inspector

RPF Constable Test Series

Students / Parents Reviews [10]

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from m...

Prisha Gupta

8th

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak poi...

Shivam Rana

7th

My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.

Hiya Gupta

8th

About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has...

Shreya Shrivastava

8th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.

Om Umang

10th

View All

Attention !!!!!

Commutative Property

Commutative Property

Students / Parents Reviews [10]

Yatharthi Sharma

Prisha Gupta

Archit Segal

Shivam Rana

Hiya Gupta

Shreya Shrivastava

Manish Kumar

Aman Kumar Shrivastava

Cheshta

Om Umang