Percent composition involving the same units
In mathematics we not only sometimes need to find percentages of things, but also need to express amounts of things in percentages. For example we know there is a rainwater tank has $24$24L of water in it but can hold $50$50L, how do we know what percentage is full?
Back to Fractions
The key here is look at a situation carefully, gather all the relevant information and extract the correct fraction that we can use to convert into a percentage. Let's go back to our rainwater tank example. What do you think the fraction would be if we wanted to find how full the tank was?
Remember that in a fraction the numerator represents how much there is and the denominator represents the total capacity. So here our fraction must be $\frac{24}{50}$2450!
Another way this question might be asked without the tank is: what percentage is $24$24 of $50$50? To work out this question we would ALSO need the fraction $\frac{24}{50}$2450.
Then to convert it into a percentage it is as easy as multiplying it by $100%$100%:
| $\frac{24}{50}\times100%$2450×100% | $=$= | $\frac{12}{25}\times100%$1225×100% | simplify the fraction |
| $=$= | $\frac{12\times100}{25}$12×10025 $%$% | write as one fraction | |
| $=$= | $\frac{12\times4\times25}{25}$12×4×2525 $%$% | split up the $100$100, so I can cancel out common factors | |
| $=$= | $12\times4%$12×4% | cancel the $25$25's | |
| $=$= | $48%$48% | evaluate! |
Worked Examples
Question 1
What percentage is $99$99 of $110$110?
Question 2
What percentage is $134$134 L of $536$536 L?
Question 3
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.
What percentage of the cost of repairs was for labour?
What percentage of the cost of repairs was for replacement of parts?