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Percentage of a quantity I


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 or when the car dashboard says that the fuel tank is only $20%$20% full. 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.


Finding Percentages of a Quantity

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%$71% of $526$526 $=$= $71%\times526$71%×526 can be rewritten as
  $=$= $\frac{71}{100}\times526$71100×526  
  $=$= $\frac{71\times526}{100}$71×526100 Get out the calculator!
  $=$= $\frac{37346}{100}$37346100 simplify
  $=$= $\frac{18673}{50}$1867350  

Sometimes such large messy improper fractions are easier to understand as mixed number, 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!

Worked Examples


By converting the percentage to a decimal, find $74%$74% of $4600$4600 kilometres.


Evaluate $24%$24% of $272$272. Leave your answer as a fraction.


When tickets to a football match went on sale, $29%$29% of the tickets were purchased in the first hour. If the stadium seats $58000$58000 people, what was the number of seats still available after the first hour?

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