Numeracy, Maths and Statistics - Academic Skills Kit

Percentages (animal science)

ContentsToggle Main Menu 1 Definition 2 Basic calculations and background2.1 Worked Example 12.2 Solution 3 More complex calculations3.1 Worked Example 23.2 Solution 4 Ratios 5 Simplifying Ratios5.1 Worked Example 35.2 Solution5.3 Worked Example 45.4 Solution 6 Test yourself 7 External links 8 See also

This is a subject-specific page for Animal Science students.

Definition

A percentage is a proportion of an amount, group or set. Another way to think of this is as a fraction out of 100. So if you had an 80% success rate at a task, this would mean that for every 100 attempts, 80 of them would be a success.

Basic calculations and background

Converting Fractions to Percentages

To convert fractions to percentages divide the numerator (number on the top) by the denominator (number on the bottom) and multiply by 100 this will give you the fraction as a percentage.

For example $\frac{5}{8}$ can be expressed as a percentage by $5\div8\times100 =62.5$%.

Worked Example 1

There is a group of 56 dogs. 36% of these dogs are Spaniels, 16% are Border Collies, 10 of the dogs are Lakeland terriers, and 17 of the dogs are Newfoundlands.

a) How many of the 56 dogs are Spaniels?

b) How many are Border Collies?

c) What percentage of the 56 dogs are Lakeland terriers (to 3 s.f.)? *

d) What percentage are Newfoundlands (to 3 s.f.)?

* (“3 s.f” means “rounded to three significant figures”: include just the first three digits of a number. For example, to 3 s.f $1.032 = 1.03$).

Solution

a): 36% of the dogs are Spaniels.

$56\times0.36 = 20.16 $, so 20 are Spaniels.

b): 16% of the dogs are Border collies.

$56\times0.16 = 8.96$, so 9 are Border Collies.

c): 10 of the dogs are Lakeland terriers.

As a percentage, this is $10 \div 56 \times 100 = 17.9\%$.

d): 17 dogs are Newfoundlands.

So as a percentage this is $17\div 56 \times 100 = 30.4$%.

More complex calculations

Percentage difference

This is calculating the difference between two amounts and displaying the difference as a percentage of the average of the two numbers.

To calculate this we use the formula:

\begin{equation} \frac{\text{(difference of the values)}}{\text{(mean of the values)}}\times100 = \text{ Percentage difference}. \end{equation}

See Worked Example 2 .

Calculating percentage changes

You calculate a percentage change when the amount of something you have changes. Use this method when you know the original value, the new value and you want to calculate the change as a proportion of the original amount.

(you may have come across this in your animal behaviour module, as percentage improvement in inter-observer reliability)

Percentage increase:

If the amount increases then we use the formula:

\begin{equation} \frac{\text{(new value} - \text{original value)}}{\text{original value}}\times100 = \text{ Percentage increase}. \end{equation}

Percentage decrease:

If the amount decreases then we manipulate the above formula to stop it being negative by reversing the top of the fraction:

\begin{equation} \frac{\text{(original value} - \text{new value )}}{\text{original value}}\times100 = \text {Percentage decrease}. \end{equation}

Using percentage change to calculate new amounts:

This method is used when you know the percentage change and the original amount and you want to calculate how much you now have. To do this use the formula:

\begin{equation} \frac{\text{(new percentage)}}{100}\times\text{(original value)} = \text{New amount}. \end{equation}

For instance, suppose you had a poor lambing season and only had 80% of last year's total of 90 lambs. To calculate how many you had this year, substitute $80%$ as the “new percentage” and $90$ as the “original value” in the formula. That is, you have $90 \div 100 \times 80 = 72$ lambs this year.

Suppose you already had 70 cattle and your cattle numbers increased by 10%. You can calculate the new total using the formula $70 \div 100 \times 110 = 77$ cattle.

Note: This is equivalent to $70 \times 1.10 =77$. This is because percentages are a fraction out of 100 and multiplying by 1.10 is the same as dividing by 100 and multiplying by 110.

Worked Example 2

Leo and Sandy are both young Tom cats. They were let out to hunt one night. Leo caught 5 mice and Sandy caught 7.

a) What is the mean number of mice caught by the two cats, and what is the percentage difference between them?

b) How many mice did Leo catch, as a percentage of Sandy's figure?

Solution

a)

Firstly to calculate the mean of the two figures, we add the numbers and divide by 2: $(7+5)\div2 = 6$.

The difference between the two values is $7 - 5 = 2$.

The percentage difference is the difference divided by the mean multiplied by 100.

The percentage difference is $2 \div 6 \times 100 = 33.3\%$.

b)

Leo caught 5 mice and Sandy caught 7.

As a fraction, Leo caught $\frac{5}{7}$ as many mice as Sandy.

As a percentage, Sandy caught $5 \div 7 \times 100 = 71.43\%$ of what Leo caught.

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 3

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 4

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