Before diving into further applications of percentages, let's review finding percentages of an amount from our lesson in Chapter 2.
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 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 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
Solve: 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
Solve: 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.
Find $1%$1% of the yearly water supply.
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$$15400 are sold.
Calculate the commission earned on the first $\$2600$$2600 of goods sold.
Calculate the commission earned on the amount of goods sold in excess of $\$2600$$2600.
What is the total commission earned?