Fractions and Percentages
Woo! We've come a long way from first learning about fractions and percentages and how to convert between different representations of the two. Do you think you can remember them all? Remember the main rule that will allow us to do the conversions:
Fraction → Percentage: multiply by $100%$100%
Percentage → Fraction: divide by $100%$100%
Are you ready to tackle some of the following challenges? Let's go!
Example - tricky decimal points
Question 1
Express $5.8%$5.8% as a simplified fraction
Think about how to get rid of that decimal point in the without changing the answer.
Do:
| $\frac{5.8%}{100%}$5.8%100% | $=$= | $\frac{5.8}{100}$5.8100 | |
| $=$= | $\frac{58}{1000}$581000 | multiplying top and bottom by $10$10 | |
| $=$= | $\frac{29}{500}$29500 |
Example - more than a whole
Question 2
Convert $\frac{16}{3}$163 into a percentage
Remember that you can have percentages more than $100$100
Do:
| $\frac{16}{3}\times100%$163×100% | $=$= | $\frac{1600%}{3}$1600%3 |
| $=$= | $533\frac{1}{3}$53313 $%$% |
Example - mixed fractions
Question 3
Question: What is $12\frac{4}{5}$1245 $%$% as a fraction?
Think about changing the mixed fraction into something simpler first
Do
| $12\frac{4}{5}$1245 $%$% | $=$= | $\frac{64%}{5}$64%5 | turn to improper fraction |
| $=$= | $\frac{64%}{5}\div100%$64%5÷100% | to change to fraction $[/]$[/] $100%$100% | |
| $=$= | $\frac{64}{5}\div100$645÷100 | $%$%signs cancel out | |
| $=$= | $\frac{64}{5}\times\frac{1}{100}$645×1100 | change to multiplication of reciprocal | |
| $=$= | $\frac{64}{500}$64500 | evaluate | |
| $=$= | $\frac{16}{25}$1625 | simplify |
Example - back to decimals
Question 4
Express $\frac{4}{13}$413 as a percentage, rounded to $2$2 decimal places
Think about whether you need to round up or round down
Do
| $\frac{4}{13}\times100%$413×100% | $=$= | $\frac{400%}{13}$400%13 | multiply numerators |
| $=$= | $30.7692$30.7692 ... $%$% | evaluate | |
| $=$= | $30.77%$30.77% | round to $2$2 decimal places |
Have you ever...
...thought about when people might use percentages and when people might use fractions?
See if you can list some different places where they would use one or the other!
More Worked Examples
QUESTION 5
Express the fraction $\frac{9}{22}$922 as a percentage, rounding your answer to two decimal places.
QUESTION 6
Convert the mixed number $2\frac{16}{25}$21625 to a percentage.