# Proportional or directly proportional

## Directly proportional

We know proportional means comparing two ratios by putting an equals sign in.

And directly means divide them.

Directly proportional is on top of each other or divide.

**Example 1**

if `8` apples cost `£4.00`

a total of `24` apples cost `£12.00`

This is shown by

`8:4=24:12`

or `8/4=24/12`

**Example 2**

The length of a `1kg` rope is `5m`. If the weight of the rope and its length are in proportion what would be the weight of a `15m` rope?

`1kg:5m` | `=` | `xkg:15m` |

`1/5` | `=` | `x/15` |

Multiply both sides by `15` to get `x` on its own.

`(1times15)/5` | `=` | `(xcancel15)/cancel15` |

`x` | `=` | `(1times15)/5` |

`x` | `=` | `15/5` |

`x` | `=` | `3` |

The weight of a `15m` rope is `3kg`.

**Example 3**

`20` pencils cost `£3.16`. How much would

`30` pencils cost?

`20` pencils : `£3.16``=30` pencils `:x`

`20/(3.16)=30/x`

Rearanging the formula

`x=(30times3.16)/20`

`x=(3times3.16)/2`

`x=4.74`

`30` pencils cost `£4.74`.