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 .

 

  1. Chapter 1 Class 7 Integers
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.