Mammoth Memory

Proportional or directly proportional

Directly proportional

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

And directly means divide them.

Direct proportions means to divide both numbers in the ratio

Directly proportional is on top of each other or divide.

Directly is divide to put both numbers above each other  

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` `=` `3kg`

 

Example 3

`20` pencils cost `£3.15`. How much would

`30` pencils cost?

 

`20` pencils cost `£3.15``=30` pencils `:x`

    `20/(£3.15)=30/x`

Rearanging the formula

`x=(30times£3.15)/20`

`x=(3times£3.15)/2`

`x=£4.72`

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