Fractions and Ratios
Now that you know what fractions are, it is time to learn ratios.
We know that fractions are the parts of a whole, when it is divided into equal parts. So, what are ratios or what is a ratio?
Ratios are fractions, in a sense that they are comparisons of a number of things to another number of things.
When fractions
^{1}/
_{2},
^{5}/
_{3}, and
^{4}/
_{9} are written as ratios, they are written this way: 1:2, 5:3 and 4:9. We read these as: "1 is to 2", "5 is to 3", and "4 is to 9", respectively. These can also be read as "1 for every 2", "5 for every 3", and "4 for every 9", respectively. The phrases that take the place of the ":" between the numbers in a ratio, like "is to" and "for every", can be replaced by other phrases like "in every", "of every" and others depending on the situation.
Unlike fractions, though, when ratios are reversed, they don't always completely lose their meaning. For instance, when we reverse 1:2 or "1 for every 2", we get 2:1 or "2 for every 1". If we use that in an actual comparison, they can still mean the same thing:
"There is 1 orange for every 2 apples in the basket" can mean the same thing as "There are 2 apples for every 1 orange in the basket".
But, if that is a fraction
^{1}/
_{2} does not mean the same thing as its reciprocal
^{2}/
_{1}.
The way you read a ratio can also change the meaning of things, so not all substitutes for the colon (:) in rations are applicable to each ratio and comparison. For example, the phrase "of every" in the comparison "1 of every 2 grapes in the bunch is rotten", cannot be used in 5:3. If we use "of every", it will not make sense: "5 of every 3 grapes in the bunch is rotten". There can never be 5 grapes in 3 grapes, rotten or not!
Let's take a look at some more examples of ratios and comparisons.
In the image above, you have three locks and six keys. If we expressed this as a ratio, it would be 3:6. In faction form, that is
^{3}/
_{6}. This means that there are 3 locks for every 6 keys. The reverse also means the same thing: 6:3, which translates to "for every 6 keys there are 3 locks".
Notice that when we reverse the ratio, we mentioned the keys first and then the locks, which was unlike in the original ratio when the locks were mentioned first and then the keys. This is very important. The original statement compared 3 : 6 = locks : keys, so when we reverse the number to 6 : 3, we also reverse the items being compared, keys : locks.
Still using our example, 3:6, we will simplify our ratio. In fraction form, 3:6 =
^{3}/
_{6} which is equal to
^{1}/
_{2}. So, 3:6 = 1:2. Three locks is to six keys means the same thing as one lock is to two keys.
Now, take a look at the image below. Can you make comparisons from this image and express them into fractions and ratios?
Here are a few examples of fractions and ratios that you can get from the image above:
^{1}/
_{3} or 1:3 -> One-third of the cups is red, or 1 out of 3 cups is red.
^{2}/
_{3} or 2:3 -> Two-thirds of the cups are standing, or 2 out of 3 cups are standing.
^{3}/
_{3} or 3:3 -> Three-thirds of the cups are colored, or 3 out of 3 cups are colored.