Important Formulas: Basic Geometrical Ideas | Mathematics (Maths) Class 6 PDF Download

If a, b, c, etc. are whole numbers, then
(1) a + b is a whole number. [Closure property of addition]
(2) a × b is a whole number. [Closure property of multiplication]
(3) (a − b) may or may not be a whole number.
(4) a + b may or may not be a whole number
(5) a + b = b + a
(6) a × b = b × a
(7) a − b is not equal to b − a if a and b are unequal.
(8) a + b is not equal to b + a if a and b are unequal.
(9) a + b = b + a if and only if a = b.
(10) (a + b) + c = a + (b + c) [Associativity of addition].
(11) a × (b × c) = (a × b) × c [Associativity of Multiplication].
(12) a × (b + c) = a × b + a × c [Distributive of multiplication over addition].
(13) a × (b − c) = a × b – a × c, if b > c [Distributive of multiplication over Subtraction].
(14) a + 0 = a = 0 + a [Existence of multiplicative identity].
(15) a × 0 = 0 = 0 × a ]Existence of multiplication identity]
(16) a × 1 = a = 1 × a
(17) a + 1 = a.
(18) In general (a – b ) – c ≠a – (b – c).
(19) In general (a + b ) + c ≠a + (b + c).
(20) If a is dividend, b(≠0) divisor, q quotient and r remainder, then a = bq + r.
[Division algorithm]