Two part ratios

When you hear the word ratio you must try to remember the words "to every"

If something is $1$ to $5$ ratio you must read this as $1$ to every $5$

A ratio shows how two numbers compare.

$x$ to every $y$

To help you remember ratio is "to every" see below

A ratio is 2 numbers to say how many numbers in another

Raise a toe (ratio) to every (to every) one.

Ratio $=$ to every

There are several ways mathematicians express ratios

$5:1$ ratio $=5$ to every $1$

$5/1$ ratio $=5$ to every $1$

$5$ to $1$ ratio $=5$ to every $1$

Example 1

A train has been built at a ratio of $1:12.5$ . If the model train is $35cm$ tall how tall is the real thing?

if a scale is 1:12.5 then for every 1 there is 12.5

The ratio is $1$ to every $12.5$

so $1cm$ to every $12.5cm$

If $1=12.5$

then $35=x$

(treat this like all calculations in our percentages section)

Put a divide sign between them

$1/35=12.5/x$

rearranging

$x=(12.5times35)/1$

$x=437.5cm$

Answer:

The real train is $437.5cm$ tall.

Example 2

To make biscuits you need $350\ grams$ of wheat. This makes 22 biscuits. How many grams of wheat do you need to make 30 biscuits?

So the ratio is $22$ biscuits to every $350\ grams$ wheat.

$22=350$

Work out $1$ biscuit

$1=x$

(treat this like all the calculations in our percentages section).

Put a divide sign between them

$22/1=350/x$

rearrange

$x=(350times1)/22$

$x=15.9\ grams$ of wheat.

so the ratio is

$1$ biscuit to every $15.9\ grams$ of wheat

Now we can work out 30 biscuits.

$1=15.9$

$30=x$

(treat this like all the calculations in our percentages section).

Put a divide sign between them.

$1/30=15.9/x$

rearranging

$x=(15.9times30)/1$

$x=477\ grams$

Answer:

$477\ grams$ make $30$ biscuits.