# Introduction to Equations, Variables and Formulas

#### Back to Maths Grade 9/10

## Introduction

This is a Maths tutorial aimed at Grade 9/10 students, discussing what equations, variables and formulas are. The video tutorial is still to come.

## What are Equations?

An equation is a shorthand way of describing two things as being equal. For example, the below equation tells us that one metric kilo of apples is equivalent in mass to 2.2 imperial pounds of apples.

### 1 kilogram of apples = 2.2 pounds of apples

The above equation can be rewritten using variables.

## What are variables?

A variable is a symbol used to represent a number, either in an equation or in text. These symbols are usually letters of an alphabet; most commonly from either the English (e.g. *a*, *b*, *c*) or Greek (e.g. *alpha* (α), *beta* (β), *gamma* (γ)) alphabets. For example, G is the symbol used to represent the gravitational constant (6.67408 × 10^{-11} m^{3}/kg^{1}·s^{2}). Similarly, the small letter g is used to represent acceleration due to gravity.

## Unknown vs Known Variables

Variables can be classified as being either known or unknown. Other terms are real and apparent; and bound and unbound respectively.

Known, Real, Bound Variables

A known, real or bound variable is one where the value is a set number which does not change; this is also known as a *constant* number. G, the gravitational constant is a constant number, and thus can be called a known, real or bound variable.

Unknown, Apparent, Unbound Variables

An unknown, apparent or unbound variable is one which can change i.e. it is *not* constant. Acceleration due to gravity varies depending on the masses of the different bodies involved. For example, the value of g is approximately six times greater on earth than it is on the moon.

This variability in g makes it an apparent variable, but only until the subjects involved (e.g. earth, moon, pluto etc.) are defined - then it becomes a known variable. This is important: variables can switch between being known or unknown.

## What are Formulas?

Formulas are a special type of equation that includes multiple unknown variables. At the beginning of this tutorial we said that the first equation (*1 kilogram of apples = 2.2 pounds of apples*) could be rewritten using variables. Below is one way of doing this. Have a look at it and decide if you think it can be classified as a formula or not.

### y = 2.2 x

where:

~ y is mass (of anything, including apples) in kilograms; and

~ x is mass (of anything, including apples) in pounds.

*So what did you think? Can it be classified as a formula?*

If you answered yes, then you're correct. In this equation, 2.2 is a known variable and BOTH *y* and *x* are unknown variables. Two unknown variables in an equation makes it a formula.

In this tutorial we've learned what equations, variables and formulae^{#} are. The next tutorial will discuss why formulae are useful.

^{#}NB: The words *formulae* and *formulas* are both the plural of formula.