Lesson

Percentages and fractions are part of our everyday lives, but did you know you can write percentages and fractions, and fractions as percentages? For example, you probably know that $50%$50% is the same as a half, or $\frac{1}{2}$12, but WHY?

Every percentage can be thought of as a fraction with a denominator of $100$100. In fact, that's what the percent sign means! Doesn't it look like a strange mixed up little $100$100, or even a fraction with a $0$0 on top and and a $0$0 on bottom? Even cooler is the fact that the word *percent *actually comes from *per centum*, which is Latin for *per one hundred*! For example, $3%$3% would mean $3$3 per $100$100, which is a fancy way of saying $3$3 out of $100$100. This is why we can write it as the fraction $\frac{3}{100}$3100, which is ALSO like saying $3$3 out of $100$100.

So to convert any percentage to a fraction all you have to do is to take the number in front of the percent sign and put it as the numerator of a fraction with a denominator of $100$100, or in other words, **divide by $100$100.**

But how did we go from $50%$50% to $\frac{1}{2}$12? Well, using what we just learnt, $50%=\frac{50}{100}$50%=50100. Can you see that we can simplify this fraction by dividing top and bottom by $50$50? $50\div50=1$50÷50=1, and $100\div50=2$100÷50=2, so $\frac{50}{100}=\frac{1}{2}$50100=12, voila!

Getting back is a little more difficult but we just have to remember that all percentages are fractions with $100$100 as the denominator. For example, to find $\frac{4}{5}$45 as a percentage, we're really just finding $\frac{4}{5}$45ths of $100%$100% - which is one whole - and we know to find a certain fraction of another we just **multiply them together**. $\frac{4}{5}\times100%=\frac{4\times100%}{5}$45×100%=4×100%5 = $\frac{400%}{5}=80%$400%5=80%.

$33\frac{1}{3}$3313% and $66\frac{2}{3}$6623% are special percentages, can you guess what they'll be as fractions? Try and put $\frac{1}{3}$13 and $\frac{2}{3}$23 into your calculator and seeing what decimal it becomes! Now try putting those percentages in! That's right, all four values turn into one of two **recurring decimals** $0.3333$0.3333... and $0.6666$0.6666... So it's important to remember that $33\frac{1}{3}$3313% = $\frac{1}{3}$13 and $66\frac{2}{3}$6623% = $\frac{2}{3}$23, and later you'll learn why that's so when you encounter these strange decimals.

On sale now!

You might have seen percentages in a lot of shops and markets when there're special sales and deals. Have a look at the picture below and try converting them into fractions!

Convert $90%$90% into a fraction. Give the fraction in simplest form.

Convert $\frac{5}{10}$510 into a percentage.

A student survey found that $\frac{1}{5}$15 of students play Saturday sport, and that $\frac{3}{5}$35 of students play Sunday sport.

What percentage of students play a weekend sport?

What percentage of students do not play weekend sport?