UK Secondary (7-11)
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Fractions and Percentages II

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.


$\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


$\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


$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


$\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


Express the fraction $\frac{9}{22}$922 as a percentage, writing your answer with two decimal places.


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

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