# Why are Formulas Useful?

#### Back to Maths Grade 9/10

## Introduction

This is a Maths tutorial aimed at Grade 9/10 students, discussing why formulas are useful. What equations, formulas and variables are was discussed in the last tutorial. The video tutorial is still to come.

## Why are Formulas useful?

Formulas are useful because they allow us to *describe patterns or observations*. For example, we've learned that we can calculate the area of a square or rectangle by counting the number of square units in the shape.

But we can also do it by multiplying the shape's width by its height.

This pattern can be conveyed using the below formula.

### area of a square or rectangle = h x w

Where

~ h represents height; and

~ w represents width.^{#}

^{#}Both height and width are unknown variables.

You can see how this simple formula can help us to easily calculate the area of a square or rectangle. The more variables (known and unknown) there are in a formula, the more useful they can be - you just need to make sure you remember the variables in the right order.

## Why else are Formulas useful?

Formulas allow us not only to make statements about patterns we've observed, but also allow us to accurately predict things that we haven't (yet) observed. For example, we may not personally have measured the force of gravity on a 1000 kg mass at the surface of earth, but using the formula above, we can easily predict that it would be 9,820 N (see below).

F_{gravity} |
= | G x (^{m1•m2}/_{r2}) |
---|---|---|

F_{gravity} |
= | 6.674×10^{−11} m^{3}/_{kg⋅s2} x (^{m1•m2}/_{r2}) |

F_{gravity} |
= | 6.674×10^{−11} m^{3}/_{kg⋅s2} x (^{1000kg x 5.97237×1024kg}/_{(6.371 x 106m)2}) |

F_{gravity} |
= | 6.674×10^{−11} m^{3}/_{kg⋅s2} x (^{5.97237×1027kg}/_{40.589641 x 1012m2}) |

F_{gravity} |
= | 6.674×10^{−11} m^{3}/_{kg⋅s2} x (^{5.97237×1015kg}/_{40.589641m2}) |

F_{gravity} |
= | 6.674 m^{3}/_{kg⋅s2} x (^{5.97237×104kg}/_{40.589641m2}) |

F_{gravity} |
= | 6.674 m^{3}/_{kg⋅s2} x 1,471.402 kg/_{m2} |

F_{gravity} |
= | 9,820 m/_{s2} or 9,820 N |

So far we've seen how formulas are useful for remembering universally known patterns and using them to predict things we haven't observed. In the the next tutorial we will learn how to create a simple formula and use it to predict things in everyday life, with a practical example.