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India
Class VIII

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

However, $$50% of the water in a $$100 L swimming pool is obviously very different to $$50% of the $$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 $$23 of $$60 all we do is multiply the two numbers together, so $$23×60=40 is our answer. We can do the same with percentages as we know how to turn them into fractions with $$100 as the denominator.

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

$$71%×526 can be rewritten as

$$71100×526=71×526100.

Using a calculator we know this equals $$37346100, which is $$1867350 in simplified form.

Sometimes such large messy improper fractions are easier to understand as mixed numbers, so in this case we can evaluate $$1867350 as $$3732350.

Can you see we can easily estimate this to $$37312? So much simpler!

Worked Examples

QUESTION 1

Evaluate $$28% of $$5000.

QUESTION 2

Evaluate $$51.3% of $$240

Express your answer as a decimal.

QUESTION 3

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

 

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