Operation

Commutative

True / False

Addition

a  + (b + c) = (a + b) + c

True

Subtraction

a  − (b − c) = (a − b) − c

False

Multiplication

(a × b) × c = a × (b × c)

True

Division

(a ÷ b) ÷ c = a ÷ (b ÷ c)

False

 

For Integers

Let us take three integers 2, 3, 4

Operation

Number

Remark

Addition

  

a  + (b + c) = (a + b) + c

Take a = 2, b = 3 & c = 4

 

L.H.S

a + (b + c)

= 2 + (3 + 4)

= 2 + 7

= 9

 

∴ (a + b) + c = 9

 

R.H.S

(a + b) + c

= (2 + 3) + 4

= 5 + 4

= 9

 

∴ a + (b + c) = 9

 

Since

a  + (b + c) = (a + b) + c

 

∴ Addition is associative.

Subtraction

 

a − (b − c) = (a − b) − c

Take a = 2, b = 3 & c = 4

 

L.H.S

a − (b − c)

= 2 − (3 − 4)

= 2 − (−1)

= 2 + 1

= 3

 

∴ (a − b) − c = 3

 

R.H.S

(a − b) − c

= (2 − 3) − 4

= −1 − 4

= −(1 + 4)

= −5

 

∴ a − (b − c) = −5

Since

 a − (b − c) ≠ (a − b) − c

 

∴ Subtraction is not associative.

Multiplication

 

a × (b × c) = (a × b) × c

Take a = 2, b = 3 & c = 4

 

L.H.S

a × (b × c)

= 2 × (3 × 4)

= 2 × 12

= 24

 

∴ (a × b) × c = 24

 

R.H.S

(a × b) × c

= (2 × 3) × 4

= 6 × 4

= 24

 

∴ a × (b × c) = 24

Since

 a × (b × c) = (a × b) × c

 

∴ Multiplication is associative.

Division

 

(a ÷ b) ÷ c = a ÷ (b ÷ c)

Take a = 2, b = 3 & c = 4

 

L.H.S

(a ÷ b) ÷ c

= (2÷3) ÷4

= (2/3)÷4

= 2/3×1/4

= 1/6

 

R.H.S

a ÷ (b ÷ c)

= 2÷(3÷4)

= 2÷(3/4)

= 2×4/3

= 8/3

 

(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)

Since

(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)

 

∴ Division is not associative.

  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.