Mammoth Memory

Ratios in the form `1:n` or `n:1`

If you are ever asked to express a ratio in the form `1:n` or `n:1` just treat it like a directly proportional ratio.

 

Example 1

Express `6:10` in the form `1:n`

So the ratio is

`6:10`

and we need to work out

`1:n`

(see our section on percentages for full explanation)

`6:10`

`1:n`

Now put a divide sign in

`6/1=10/n`

Rearranging the formula

`n=(10times1)/6`

`n=10/6`

simplifying the fraction

`n=5/3`

So the ratio in the form `1:n` is

`1:5/3`

 

 

Example 2

The ratio of girls to boys in a school is:

`800` boys to `1200` girls

What is the ratio in the form `n:1`?

So the ratio is

`800:1200`

and we need to work out

`n:1`

(see our section on percentages for full explanation)

`800:1200`

    `n:1`

Now put a divide sign in

`800/n=1200/1`

Rearranging the formula

`(800times1)/1200=n`  or

`n=(800times1)/1200`

`n=800/1200`

simplifying the fraction

`n=(8cancel00)/(12cancel00)`

`n=8/12`

simplify the fraction further

`n=4/6`

simplify the fraction further

`n=2/3`

This will not simplify any further so the answer is

`2/3:1`

 

Example 3

A chief is cooking a meal for many and she knows that she has to buy `3` carrots to `8` parsnips. She also knows that the ratio of parsnips to broccoli is `6` parsnips to `1` broccoli. Write out the ratio in the form `A:B:C`

The ratio is     `3` carrots `:8` parsnips and

`6` parsnips `:1` broccoli

Line these up we would have

`3` carrots `:8` parsnips and `6` parsnips `:1` broccoli

We need to make the second ratio have 8 parsnips i.e. the same as the first ratio.

Therefore

`6` parsnips `:1`

and we need to work out 

`8` parsnips `:n`

(see our section on percentages for full explanation)

`6:1`

`8:n`

Now put a divide sign in

`6/8=1/n`

rearranging the formula

`n=(1times8)/6`

`n=8/6`

Simplify the fraction

`n=4/3`

So the new ratio is

`8` parsnips `:4/3` broccoli

So the full ratio is

`3` carrots `:8` parsnips and `8` parsnips `:4/3` broccoli

Which is the same as

`3` carrots `:8` parsnips `:4/3` broccoli

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