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?

Thinkabout 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, writing your answer with two decimal places.

QUESTION 6

Convert the mixed number $2\frac{16}{25}$21625 to a percentage.