Symbols are frequently used in mathematical writing. The use of symbols makes the writing very short. For example, using symbols, division of 63 by 9 gives us ‘7’ can be written in short as “63 ÷ 9 = 7”. It is also easier to grasp.
Letters can be used like symbols to make our writing short and simple
While adding, subtracting or carrying out other operations on numbers, you must have discovered many properties of the operations.
For example, what properties do you see in sums like (7 + 3), (3 + 7)?
The sum of any two numbers and the sum obtained by reversing the order of the two numbers and the sum obtained by reversing the order of the two numbers is the same.
Now see how much easier and faster it is to write this property using letters.
Let us use a and b to represent any two numbers. Their sum will be ‘a + b’
Changing the order of those numbers will make the addition as ‘b + a’.
Therefore, the rule will be, for all values of ‘a’ and ‘b’
(a + b) = (b + a).
Let us see two more examples
* Multiplying any number by 1 gives the number itself. It the number is replaced by an alphabet ‘a‘, then the above statement can be represented as a × 1 = a.
* Given two unequal numbers, the division of the first by the second is not the same as the division of the second by the first.
In short, if a and b are two different numbers, then (a ÷ b) is not equal to (b ÷ a)
Take the valve of ‘a’ as 6 and the value ‘b’ as 2 and verify the above property by yourself.
Use a letter for “any number” and write the following properties in short.
i. The sum of a number and zero is the number itself
ii. The product of any two numbers and the product obtained after changing the order of those numbers is the same.
iii. The product of a number and zero is zero
iv. Write the following properties in words