Using Letters

Mathematical symbols simplify expressions and make writing concise. For example, instead of writing "Division of 75 by 15 gives us 5," we use the symbolised form:
75 ÷ 15 = 5
Similarly, letters (variables) can be used to generalise mathematical properties.
1. Commutative Property of Addition
The sum of two numbers remains the same regardless of their order:
(a + b) = (b + a) for all values of a and b
Example: 9 + 4 = 4 + 9

2. Multiplicative Identity
Any number multiplied by 1 remains unchanged:
a × 1 = a
1 × a = a
Example: 7 × 1 = 7
                1 × 7 = 7

3. Non-Commutativity of Division
The order of division affects the result:
(a ÷ b) ≠ (b ÷ a) for a ≠ b
Example: 8 ÷ 4 = 2, but 4 ÷ 8 = 0.5