Ratios
What is a Ratio?
A ratio is just a way of describing how two or more numbers compare to each other.
Say you own 2 cats and 1 dog - then you'd say you have a ratio of 2:1 cats to dogs - in other words, you have 2 times as many cats as dogs.
Lets try another example, say you have 10 tropical fish - 6 are green and 4 are red.
Then a ratio to describe the number of green fish to red fish would be 6:4. You could simplify this ratio to 3:2 - by simply dividing both sides of the ratio by the common factor of 2. In which case, you could say that for every 2 red fish you have 3 green fish.
Lets try some examples ...
There are some golf balls in a bag
16 of the balls are white
6 of the balls are orange
Write down the ratio of the number of orange balls to white balls in its simplest form
First we write down the ratio - there are 6 orange balls & 16 white so the ratio is:
6:16
Now, simplifying ratios is just the same as simplifying fractions - we find a number which divides into both sides of the ratio (just in the same way as we find a number which divides into both the numerator & denominator for fractions).
A number which divides into both 6 & 16 is 2 - so we divide both sides of the ratio by 2 and get:
3:8 ... and that's our answer!
Lets try another example ...
Three friends share $240 in the ratio 6:4:2
Mr Big receives the largest share - how much does Mr Big receive?
Well, we know that the money is split 6:4:2 between 3 people - so the money is split like this:
- someone receives 6 equal shares of the money
- someone receives 4 equal shares of the money
- someone receives 2 equal shares of the money
So, in total there are 6 + 4 + 2 equal shares, or 12 equal shares of the money.
Each equal share is calculated as $240 divided by 12 - which equals $20
The largest share paid out is 6 equal shares, so Mr Big receives 6 x $20 or $120!
and finally, one more example about ratios ...
A website sells CDs & DVDs.
In one week the number of CDs sold and the number of DVDs sold were in the ratio 4:7
The total number of CDs & DVDs sold in the week was 253
How many CDs were sold?
Well, we know that the ratio of CDs to DVDs sold is 4:7 so the total number of equal shares is 4 + 7 which is 11
So, each equal share is 253 divided by 11 - which equals 23
So, there were 23 x 4 or 92 CDs sold & 23 x 7 or 161 DVDs sold!