Percentages and fractions are part of our every day lives, but did you know you can write percentages as 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!
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!
You know that we can have improper fractions, which are fractions that are more than a whole, so does that mean we can have 'improper' percentages as well? Of course! Things such as $104%$104%, $560%$560% or even $1000000%$1000000% are all more than a whole, which is $100%$100%, and they all exist!
If we took one pizza as one whole, then here we have $275%$275%, as we have $2$2 whole pizzas plus $75%$75%of a third pizza.
But what does something like $104%$104% mean?
Well if we convert it into fractions we'll get $\frac{104}{100}=\frac{26}{25}$104100=2625
which is $1\frac{1}{25}$1125 as a mixed number, and we know this means $1$1 whole plus $\frac{1}{25}$125!
We can then just as easily compare percentages more than $100%$100% with fractions.
Express $5%$5% as a simplified fraction
Think about how to get rid of that decimal point in the without changing the answer
Do:
$\frac{5%}{100%}$5%100% | $=$= | $\frac{5}{100}$5100 | |
$=$= | $\frac{1}{20}$120 |
Question: What is $12\frac{4}{5}$1245 $%$% as a fraction?
Think about changing the mixed number 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 |
Percentage → Fraction: divide by $100%$100%
Express $784%$784% as a fraction. Give your answer as a simplified mixed number.
Express $0.67%$0.67% as a fraction in simplest form.