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2.03 Percentages of an amount

Lesson

Before diving into further applications of percentages, let's review finding percentages of an amount.

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

 

Practice questions

Question 1

Find $10%$10% of $\$696.60$$696.60, rounded to the nearest five cents.

Question 2

Find $5%$5% of $\$41.70$$41.70, rounded to the nearest 5 cents.

Question 3

Find $1%$1% of $\$14.37$$14.37, rounded to the nearest five cents.

 

Other percentages of quantities

Once we know $10%$10%, $5%$5% or $1%$1% of a value, we can use these to build other percentages of amounts.

For example, if we know $10%$10% of $70$70 is $7$7, then we can find $20%$20%:

$10%$10% of $70$70 $=$= $7$7  
$\therefore20%$20% $=$= $14$14

Multiply both sides by $2$2.

If we know  $1%$1% of $250$250 is $2.5$2.5, then we can find $3%$3%:  

$1%$1% of $250$250 $=$= $2.5$2.5  
$\therefore3%$3% $=$= $7.5$7.5

Multiply both sides by $3$3.

In general, we can find percentage of an amount by using multiplication and turning the percentage into a fraction with $100$100 as the denominator or writing the percentage as a decimal.

 

Worked example

Example 1

Find $12%$12% of $70$70.

Think: Write $12%$12% as a fraction with a denominator of $100$100 and use multiplication.

Do:

$12%$12% of $70$70 $=$= $12%\times70$12%×70

Remember in maths, "of" means "multiplied by".

  $=$= $\frac{12}{100}\times70$12100×70

$%$% is the same as a fraction out of $100$100.

  $=$= $\frac{840}{100}$840100  
  $=$= $8.4$8.4

Simplify.

 

Using the calculator

Using the calculator we can find a percentage of an amount by using multiplication and one of the following:

  • Use the percentage button if your calculator has one
  • Using the fraction or division button to rewrite the percentage as a fraction with a denominator of $100$100
  • Rewrite the percentage as a decimal

Let's look at a few different ways below.

 

Worked example

Example 2

Find $7%$7% of $58$58, using your calculator.

Method 1. Use the percentage button on your calculator.

Method 2.  Using the fraction or division button to rewrite the percentage as a fraction with a denominator of $100$100.

Method 3. Convert the percentage to a decimal. $7%=0.07$7%=0.07, as percent means per $100$100, divide by $100$100 by moving the decimal point two places to the left.

 

Practice questions

Question 4

A town receives $14%$14% of its water supply from the runoff of melted snow. The city has a yearly water supply of $27000000$27000000 megalitres.

  1. Find $1%$1% of the yearly water supply.

  2. Hence find the number of megalitres that comes from melted snow each year.

Question 5

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

Question 6

Sally is paid $7%$7% on the first $\$2600$$2600 of goods sold and $1%$1% on any value thereafter. Goods to the value of $\$15400$$15400 are sold.

  1. Calculate the commission earned on the first $\$2600$$2600 of goods sold.

  2. Calculate the commission earned on the amount of goods sold in excess of $\$2600$$2600.

  3. What is the total commission earned?

Outcomes

1.1.3.1

calculate a percentage of a given amount

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