formulae

You will learn:

• What is a formula?
• Framing a formula.
• Changing the subject of a formula.
• Making substitution in a formula.

Introduction

A formula is a mathematical statement of equality which shows the relationship between two or more quantities by means of mathematical symbols. Or in other words we can say a mathematical relationship or rule expressed using symbols.

Let us try to frame formulas.

Framing a formula

Mathematical statement: The Area of rectangle (A) is equal to the product of its length(l) and width(w).
Formula: A = l × W 

Mathematical statement: Father's age is 5 times the age of his son. What is the age of father one years ago, if the present age of father is x years and son is y years.
Formula:  x − 1 = 5( y − 1)

Mathematical statement: The arithmetic mean M of three quantities a, b and c is equal to their sum divided by number of quantities.
Formula: M = (a + b + c) ∕ 3

Changing the subject of a formula

In formula u = v − at, u is expressed in terms of variables v, a and t. Here u is the subject of the formula. Each formula can be written to make another variable as the subject of the formula. This formula can also be written as v = u + at. Here subject of formula is v.
Lets take another example: change the subject of the below formula for c
\(E = mc^2\) -> \(c = \sqrt {\frac{E}{m}}\)

Substitution in a formula

Substitution in a formula involves finding the value of the subject by substituting the other variables in the formula with the given values. Examples:

• If A = l × W (Area of a rectangle), where l is 10 and W is 5. Find A.

Answer: A = 10 × 5 = 50

• x = y + 10, find x when y is 20.

Answer: x = 20 + 10 = 30