A ratio compares values.
A ratio says how much of one thing there is compared to another thing.
In the above image there are 3 blue squares to 1 yellow square
Ratios can be expressed using:
: to separate the value for example 3 : 1
Instead of the : you can use the word "to" for example 3 to 1
You can write it like a fraction i.e `3/1`
Ratio can be scaled up or increased
How many squares are blue and how many are yellow in the below image?
6 : 2
3 : 1
The ratio here is also 3 blue squares to 1 yellow square even though there are more squares.
When scaling ratios up or down the trick is always to multiply or divide the number by the same value.
4 : 5 is the same as
4 x 2 : 5 x 2
This equals 8 : 10
Ratios are used in Recipes
For example to make pancakes you can use 3 cups of flour and 2 cups of milk.
If you need pancakes for more people you will need 4 times the quantity so you multiply the number by 4.
3 x 4 : 2 x 4
This equals 12 : 8
This ratio is still the same!
Part to Part and Part to Whole Ratios
The examples given in the previous pages have been part to part i.e comparing one part to another part.
A Ratio can also show a part comapred to the whole lot
For Example: There are 5 students, 2 are boys and 3 are girls.
Part to Part
The ratio of boys to girls is 2:3 or 2/3
The ratio of girls to boys is 3:2 or 3/2
Part to Whole
The Ratio of boys to all the students is 2:5 or 2/5.
The Ratio of girls to all the students is 3:5 or 3/5.
Try it yourself
What is the ratio of:
- Oranges to Bananas
- Bananas to Oranges
- Oranges to Total number of fruits
- Bananas to Total number of fruis
Ratio as a percentage
A percent is a ratio whose second term is 100.
Percent means parts per hundred.
The word comes from the Latin phrase per centum, which means per hundred.
In maths the symbol % is used for percent.
Look at the table below:
Ratio as a Decimal
Write the ratio as a fraction.
As stated earlier, ratios are typically written with a colon.
In our example, the ratio of boys to girls is 2:3.
The ratio can be converted to a fraction by replacing the colon with a fraction bar.
For example, 2:3 can be written as 2/3.
Divide the numerator (top number) by the denominator (bottom number) in your fraction.
In our example, if you divide 2/3, you get .666666
If necessary, round the decimal.
If your decimal goes on for several places, as our example does, you will need to round it.
Sometimes, you may be asked to round to a certain number of places.
If not, round to two decimal places. So, we would round our number to 0.67
Express your answer as a ratio.
So, the ratio of boys to girls in the class is 0.67.
- Ratio_img1 by elimu used under CC_BY-SA
- Ratio_img2 by elimu used under CC_BY-SA
- pancakes by Unknown used under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
- boysgirls by Unknown used under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
- fruits by elimu used under CC_BY-SA
- Ratio_img6 by elimu used under CC_BY-SA
- Ratio_img7 by elimu used under CC_BY-SA
All work unless implicitly stated is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.