Class 6 Chapter 6 Integers Math Formulas

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Commutative Property in addition:-

Changing the order of the integers will not affect the addition.

a + b = b + a 

 

For example:-

2 + 4 = 4+ 2 =6

 

Subtraction does not hold the commutative property:-

Subtraction is not commutative for integers.

a – b ≠ b – a

 

For Example:-

23 – (-27) = 50 (-27) – 23 = -50

 

Associative Property for addition:-

After changing the integers while adding in case of more than two integers the result will be same.

a + (b + c) = (a + b) + c

 

For example:-

5 + (3 + 4) = (5 + 3) + 4 = 12

 

Subtraction does not hold the associative property:-

 

For Example:-

7 – (5-3) = 7 – 2 = 5

(7 – 5) -3 = 2 – 3 = -1

5 ≠ (-1)

 

Additive Identity:-

If we add zero to an integer, value will remain same. Zero is an additive identity for integers

a + 0 = 0 + a = a

 

For example:-

5 + 0 = 0 + 5 = 5

 

Additive inverse:-

‘-2’ when added with ‘+2’ gives zero. So ‘+2’ is the additive inverse of ‘-2’.

 

Note:-

  • Multiplication of two positive integers will be positive.
  • Product of two negative integers is a positive integer.
  • Product of a positive and a negative integer is a negative integer.
  • Multiplication holds commutative and associative property.
  • Division of two positive integers will be positive.
  • Division of two negative integers is a positive integer.
  • Division of a positive integer by a negative integer is a negative integer and vice versa.
  • Division does not hold commutative or associative property.
  • Addition, subtraction and multiplication of two integers will always be an integer. This is called the closure property.
  • Division does not hold closure property.

For example:-

As, = 2.5 (Not an integer)