Numeracy, Maths and Statistics - Academic Skills Kit

Ratios (Animal Science)

ContentsToggle Main Menu 1 Ratios 2 Simplifying Ratios 3 Worked Example 1 4 Worked Example 2 5 Test yourself 6 External links 7 See also

Ratios

A ratio is the numeric relationship between two different quantities. A ratio is usually displayed using a colon ' : '.

For example, Beth has 5 horses and Simon has 7. The ratio of Beth's Horses to Simon's is 5:7.

Converting ratios into fractions:

\begin{equation} \text{To convert the ratio A : B : C into fractions:} \frac{\text{A}}{\text{(A+B+C)}} , \frac{\text{B}}{\text{(A+B+C)}} , \frac {\text{C}}{\text{(A+B+C)}}. \end{equation}

So for the above example there are 12 horses in total and five of those are Beth's, so to display this as a fraction of the total it is $\frac{5}{12}$. Similarly $\frac{7}{12}$ of the Horses are Simon's.

Or, equivalently as a percentage: $5 \div 12 \times 100 = 41.67\%$ are Beth's and $7 \div 12 \times 100 = 58.33\%$ are Simon's.

Simplifying Ratios

If you are given a ratio such as $20:40:120$, this can be simplified!

First you must find the greatest common divisor of the numbers (the biggest number that divides all of the numbers). In this case it is $20$, so divide each of the numbers by the greatest common divisor and the ratio is now simplified to $1:2:6$.

Worked Example 1

Worked Example - Ratios

You are making feed for a flock of 100 ewes. You need silage, barley and soyabean meal at a ratio of $5:2:1$. In one day you need $81.25$kg of silage. How many kilograms of barley and soyabean seal do you require?

(This is an example similar to what you may come across in the stage 2 animal feed module, or if you were to work as a nutritionist in a feed mill or laboratory.)

Solution

We know that for every $5$kg of silage we need $2$kg of barley and $1$kg of soyabean meal.

Note we cannot simplify this ratio further: no number bigger than 1 divides all three numbers.

The ewe's feed is made up of $5+2+1 = 8$ parts; each part is one eighth of the feed, with $\frac {5}{8}$ of the feed being silage.

The $81.25$kg of silage is $5$ parts of the entire ewe's feed, so divide this number by $5$ to get the weight of an eighth of the total feed.

$81.25 \div 5 = 16.25 \text{kg}$.

Each one-eighth part is $16.25$kg. Soyabean meal constitutes one part, i.e. $16.25$kg, and barley constitutes two parts, i.e. multiplying by two gives us the amount of barley we need: $32.5$kg.

To conclude, we need 32.5kg of barley and 16.25kg of soyabean meal.

Worked Example 2

Worked Example - Ratios

Jamie has to dose his calf with Metacam at a dose rate of 2.5mg /100kg. His calf weighs 59kg. How much Metacam should he administrate?

Solution

His dose rate is 2.5mg per 100kg. This calf weighs 59kg.

Work out how many mg of Metacam should be administered per kg by $2.5\text{mg}\div100\text{kg} = 0.025$mg per kg.

This calf weighs 59kg, so to establish the amount of Metacam to administer multiply by 59:

$0.025\text{mg} \times 59 = 1.475$mg.

Jamie should administer 1.475mg of Metacam to the calf.

Test yourself

Try our Numbas test on percentages and ratios.

External links

Proportions at Math is Fun

Percentage practice worksheet

Percentage difference at Math is Fun