Understanding Ratios: Calculation & Writing 📊

In this video we discuss what a ratio is and how to calculate a ratio. We go through a few examples and show the different ways ratios can be written.

Transcript/notes
What is a ratio

A ratio is a comparison. It is a fraction used to compare 2 quantities. It compares 1 number to another number, such as hours to pay, miles to gallons and even one brand of shampoo to another brand of shampoo.

It is typically written as a fraction, such as a over b, but can be written as a colon b or a to b. And all of these are pronounced the same “a to b”.

As an example let’s say that a burger joint has 4 different cheeses you can get on a burger, American cheese, pepper jack cheese, swiss cheese and blue cheese. On a given day, they sell 40 burgers with American cheese, 60 with pepper jack, 25 with swiss and 15 with blue cheese.

If we want to find the ratio of blue cheese to pepper jack, we take the first number mentioned, in this case blue cheese and put that on top, so 15 on top in the numerator, and the second number pepper jack, which is 60, on the bottom in the denominator. And this fraction can be reduced to 1 over 4.
Always reduce if possible, as smaller numbers are easier to work with and easier to comprehend.

And ratios allow us to make projections. For instance, if it took me 40 minutes to hike a 1 mile trail, so, 40 to 1, and I am going to hike a 3 mile trail tomorrow, based on the 40 to 1 ratio, I should expect it to take me 120 minutes to hike the 3 mile trail. Because 3 miles is 3 times as long as 1 mile, so, it should take me 3 times the amount of time, so, 3 times 40, which equals 120 minutes.

One note, if a ratio is measuring the same thing, such as time, money or distance, they must be in the same units. As an example, if I said 10 hours to 2 days, we would not write this ratio as 10 to 2, because we are comparing the same thing, time, in different units. So, we would convert 2 days to hours, which is 48 hours, and we would have a ratio of 10 to 48, which can be reduced to 5 to 24.

Here are a couple of more examples on the screen for you of some ratios.

Timestamps
0:00 What is a ratio?
0:10 How to write a ratio
0:21 Example of a ratio
1:12 Ratios allow projections
1:38 Ratios and units of measure