4.01 Introduction to ratios
Part to part ratios
A ratio compares the relationship between two values. It tells us how much there is of one thing compared to another. We write ratios in the form a:b which is read as "a to b".
Consider the following image:
If we want to describe the relationship between the number of blue dots and the number of green dots, we could say that there is 1 blue dot for every 3 green dots. We could also express this as a ratio, which we would write as 1:3.
A "part to part" relationship is similar to what we saw in the dot example above. It is comparing one part to another part.
The order that the words are written correspond to the order of the values in the ratio, so it is important that we don't mix them around.
Examples
Example 1
Write 15 oranges to 76 oranges as a ratio.
A ratio compares the relationship between two values. We write ratios in the form a:b which is read as "a to b".
Part to whole ratios
We can also describe a "part to whole relationship" with ratios. For example, if we wanted to describe the ratio of green dots to all the dots in the above image, we could write it as 3 : 4, because there are 3 green dots and 4 dots in total.
A part to whole ratio is a ratio that shows the ratio of one component compared to the whole or the total quantity.
Examples
Example 2
Consider the following diagram:
Write the ratio of the shaded region of trees to the total number of trees.
A part to whole ratio is a ratio that shows the ratio of one component compared to the whole or the total quantity.
Ratios as fractions
We can also express ratios as fractions. To convert a part to whole ratio to a fraction, simply rewrite the ratio as a fraction. The left side of the ratio is the numerator, and the right side is the denominator. For example:
| \displaystyle 2:3 | \displaystyle = | \displaystyle \dfrac{2}{3} |
A part to part ratio can be changed into a fraction by first being converted into a part to whole ratio. The denominator will be equal the sum of both parts of a part to part ratio.
For example, if we wanted to write the ratio of green dots to total dots as a fraction, we first need to find the total number of dots to use as the denominator.
We can see that there are 3 green dots out of a total of 4 dots. Our ratio is 3:4, and as a fraction, \dfrac{3}{4}.
Examples
Example 3
In a fruit basket, there are 3 apples and 2 oranges.
Represent the ratio of the apples to the fruits in the basket as a fraction.
To convert a part-to-whole ratio to a fraction, simply rewrite the ratio as a fraction. The left side of the ratio is the numerator, and the right side is the denominator.