Middle Years

# 4.04 One amount as a percentage of another

Lesson

### Determining the percentage

What if we know there is a rainwater tank with a capacity of $50$50 kL but it only has $24$24 kL of water in it? Knowing the percentage of water in the tank has more meaning for most people than knowing how many kL of water there is.

What would the fraction of water in the tank be? Remember that in a fraction the numerator represents how much there is and the denominator represents the total capacity. So here the fraction is $\frac{24}{50}$2450.

To find what percentage of water is in the tank then we multiply it by $100%$100%

 $\frac{24}{50}\times100%$2450​×100% $=$= $48%$48%

### Different units

If the amounts we are using are different units, then we must do some unit conversion first, before finding fractions or percentages.

#### Worked example

What percentage $65$65 cm is of $3$3 m? (Give your answer to $2$2 decimal places)

Let's convert both to centimetres. $65$65 cm is already in centimetres, and $3$3 m is $3\times100$3×100 cm $=300$=300 cm.

Then find the percentage:

 $\frac{65}{300}\times100%$65300​×100% $=$= $21.67%$21.67%

### Complementary parts

Complementary parts are in general two thing that come together to make a whole. In this case we are talking about two percentages that sum to $100%$100%. For example:

$\text{amount with water}+\text{empty amount}=\text{full tank}$amount with water+empty amount=full tank

Remember that $100%$100% represents a total amount or a whole quantity. So if our tank is $42%$42%full, we find the percentage that is empty by evaluating $100-42$10042. This means $58%$58% of the tank is empty.

#### Practice questions

##### Question 1

When Bart looked at the bill from the mechanic, the total cost of repairs was $\$800$$800. \640$$640 of this was for labour and the rest was for replacement of parts.

1. What percentage of the cost of repairs was for labour?

2. What percentage of the cost of repairs was for replacement of parts?

##### Question 2

Ben is going to purchase some sports gear on layby. This involves paying some money as a deposit, and paying the remainder later. The price of the gear is $\$6565.

1. If he needs to pay $25%$25% deposit, how much is this? As we are dealing with dollars and cents, give your answer to two decimal places.

2. What is the remaining balance on the layby purchase? Give your answer to two decimal places.

##### Question 3

What percentage is $134$134 L of $536$536 L?

##### Question 4

What percentage is $385$385 metres of $4$4 km?