Percentages

NZ Level 5

Percentage of a Quantity

Lesson

Percentages are used for a variety of things, usually when we want to describe how much of something there is.

For example, perhaps you only want $50%$50% of the juice in your cup, when the car dashboard says that the fuel tank is only $20%$20% full or when your phone battery has $78%$78% life left.

However, $50%$50% of the water in a $100$100 L swimming pool is obviously very different to $50%$50% of the $2$2 L milk in your fridge. Let's take a look at how we can figure out how much there ACTUALLY is when we hear about percentages.

We already know how to find a fraction of a quantity through multiplication. For example, we know to find $\frac{2}{3}$23 of $60$60 all we do is multiply the two numbers together, so $\frac{2}{3}\times60=40$23×60=40 is our answer. We can do the same with percentages as we know how to turn them into fractions with $100$100 as the denominator.

For example, we want to find what $71%$71% of $526$526 is, so let's **multiply them together**.

$71%\times526$71%×526 can be rewritten as

$\frac{71}{100}\times526=\frac{71\times526}{100}$71100×526=71×526100.

Using a calculator we know this equals $\frac{37346}{100}$37346100, which is $\frac{18673}{50}$1867350 in simplified form.

Sometimes such large messy improper fractions are easier to understand as mixed numbers, so in this case we can evaluate $\frac{18673}{50}$1867350 as $373\frac{23}{50}$3732350.

Can you see we can easily estimate this to $373\frac{1}{2}$37312? So much simpler!

Evaluate $28%$28% of $5000$5000.

Evaluate $51.3%$51.3% of $240$240

Express your answer as a decimal.

Lisa scored $70%$70% on her Maths exam, which was marked out of $140$140. What was Lisa's actual mark out of $140$140?

Understand operations on fractions, decimals, percentages, and integers