Operation

Commutative

True / False

Addition

a  + b = b + a

True

Subtraction

a  − b = b − a

False

Multiplication

a × b = b × a

True

Division

a/b=b/a

False

Commutativity for Integers.jpg

So commutativity is always possible for addition &

multiplication, but not for subtraction & division.

 

For Integers

Let us take two integers 2 & 3

Operation

Number

Remark

  Addition

a + b = b + a

Take a = 2 & b = 3

 

L.H.S

a + b

= 2 + 3

= 5

 

R.H.S

b + a

= 3 + 2

= 5

 

∴ a + b = b + a

 

Since a + b = b + a,

∴ Addition is commutative.

Subtraction

 

a − b = b − a

Take a = 2 & b = 3

 

L.H.S

a − b

= 2 − 3

= −1

 

R.H.S

b – a

= 3 − 2

= 1


∴ a − b ≠ b – a

Since a − b ≠ b − a,

∴ Subtraction is
not
commutative .

Multiplication

 

a ×  b =  b × a

Take a = 2 & b = 3

 

L.H.S

a × b

= 2 × 3

= 6

 

R.H.S

b × a

= 3 × 2

= 6

 

∴ a × b = b × a

 

 

Since, a × b = b × a

∴ Multiplication is commutative.

Division

 

a/b=b/a

Take a = 2, b = 3

 

L.H.S

 a/b

= 2/3

 

R.H.S

 b/a

= 3/2

 

∴ a/b≠b/a

Since a/b≠b/a

 ∴ Division is
not commutative .

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.