Properties of Integers

Chapter 1 Class 7 Integers
Concept wise
 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

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 .

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.