Middle Years

# 4.03 Percentage of a quantity

Lesson

### Calculating 10%, 5% and 1% of a quantity without calculator

Some of the easiest key values to start with when finding percentages are $10%$10%, $5%$5% and $1%$1% of the amount.

$10%$10% as a fraction is $\frac{10}{100}=\frac{1}{10}$10100=110, so $10%$10% is the same as $1$1 tenth.  This is good news, it means we can find $10%$10% of any amount by finding $1$1 tenth, or by dividing the amount by $10$10.

Here are some examples

$10%$10% of $56$56 is $5.6$5.6

$10%$10% of $230$230 is $23$23

$10%$10% of $1.5$1.5 is $0.15$0.15.

#### Practice question

Find $10%$10% of $\$16.20$$16.20, rounded to the nearest 5 cents. The next easiest one to find is 1%1%. In the same way that 10%10% is \frac{10}{100}=\frac{1}{10}10100=110, 1%1% is \frac{1}{100}1100. So to find 1%1% of something we divide the amount by 100100 Here are a few more examples 1%1% of 256256 is 2.562.56 1%1% of 12001200 is 1212. 1%1% of 4.74.7 is 0.0470.047. #### Practice question ##### Question 2 Find 1%1% of \66.20$$66.20, rounded to the nearest 5 cents.

To find $5%$5%, start by first finding $10%$10% and then halve it.

Here are some more examples

$5%$5% of $200$200$10%$10% is $20$20, so $5%$5% is $10$10.

$5%$5% of $240$240.  Well $10%$10% is $24$24, so $5%$5% is $12$12.

$5%$5% of $36$36$10%$10% of $36$36 is $3.6$3.6, so $5%$5% is $1.8$1.8

#### Practice question

##### Question 3

Find $5%$5% of $\$466.11466.11, rounded to the nearest five cents.

Remember!

To find:

$10%$10% of an amount, divide the amount by $10$10.

$1%$1% of an amount, divide the amount by $100$100

$5%$5% of an amount, find $10%$10% and then halve it.

### And then we build

Once we know $10%$10%, $5%$5% or $1%$1% of a value, we can also find multiples of those.

For example, if we know $10%$10% of $70$70 is $7$7, then we can find $20%$20%$2\times10%=20%$2×10%=20%, so $20%$20% would be $2\times7=14$2×7=14.

If we know  $1%$1% of $250$250 is $2.5$2.5, then we can find $3%$3%$3\times1%=3%$3×1%=3% so $3%$3% would be $3\times2.5=7.5$3×2.5=7.5

#### Practice question

##### Question 4

We want to find $45%$45% of $5$5 hours.

1. How many minutes are there in $5$5 hours?

2. What is $10%$10% of $300$300 minutes?

3. What is $5%$5% of $300$300 minutes?

4. Hence find $45%$45% of $300$300 minutes.

### Calculating percentages of quantities using a calculator

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 remember in maths, "of" means "multiplied by" $=$= $\frac{71}{100}\times526$71100​×526 a % is the same as a fraction out of $100$100, enter it into the calculator $=$= $373.46$373.46

#### Worked example

To find $7%$7% of $58$58, we could type:

However, if you find it easier, you can also convert the percentage to a decimal or fraction and enter it in the calculator that way. For example, the question above could be entered as:

Another way to use a calculator for percentages is to use the fraction form.  Remember that per cent means per one hundred.

#### Practice questions

##### Question 5

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

##### Question 6

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

##### Question 7

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?