Ratio and proportion are two very closely linked topics.
Proportion is used to show parts of a whole and ratios are used to compare two (or more) amounts.
Converting fractions into ratios is slightly easier if you look at it the other way round first.
Example 1: I have red and green beads in the ratio of 7: 3. What fraction of the beads are red?
Firstly, we need to know how many parts there are in total. If I have a ratio of 7:3, this means there are 10 parts in total, (Just add them together)
If 7 of these parts are red, the fraction of red balls is 7/10
So how do we do this the other way round.
Example 2: Write 3/4 as a ratio.
3/4 means 'three out of four'. If we wrote this as a ratio, we are looking for 4 parts in total and one of the numbers in the ratio must be 3.
The only way we can do this is if the ratio is 3:1
Is it always this easy?
Unfortunatly no, there is one exception. This exception is if we use a fraction doesn't represent part of a whole.
Example 3: James has 3/5 as many marbles as John. Write the total number of marbles as a simplified ratio.
We know that James has 3/5 of a marble for each one that John has. We could write this as ...
But we know that we can't have a fraction in a ratio so I multiply both sides by 5. This gives me 3:5
Give me some algebra!
Situation 1: A fraction of a whole.
|=||a: b - a|
Situation 2: Fraction used as a rlationship between two variables