USE OF LETTERS AND FORMULAE

1.USE OF LETTERS:

We can  represent numbers in problems not only by figures but also by letters. For instance we use the letter x to denote any statement or element in a given problem.

example

; Find the total cost of 25 pens at Rs 2 per pen.

The total cost =the number of pens x the cost per pen

                      = 25x 2=50 rupees.

we thus represent numbers by letters that stand for any value we assign to them,we pass from Arithmetic to Algebra.

Find the total cost of x copies of a book at Rs.y per copy

The total cost=the number of copies x the cost per copy

                      = x multiplied by y

                      = xy rupees

Note the product x multiplied by y is written in Algebra as xy, where the sign x is being omitted.

Such problems are enough to show how letters are used in Algebra to represent numbers.Moreover it will be noticed that the methods to work out the problems are the same as those used in Arithmetic.

Thus we conclude that Arithmethic and Algebra are closely allied to each other and therefore they are science of numbers and not seperate subjects.

The use of letters in Algebra gives a wider scope and hence Algebra is called " Generalised Arithmetic".

Now we can make general statements leading to formulae.