# Difference between Ratio and Percentage

In this video, I’m going to talk about ratios and percentages. Now, a ratio is a way to compare two different quantities to one another. For instance, let’s take marbles. If we have 20 red marbles and 25 blue marbles, we can say that the ratio of red marbles to blue marbles is 20:25.

This is what ratio notation looks like. You have a number that represents the first quantity, then the colon, and then a number that represents the second quantity. This right here is not a proper ratio, because you can reduce it to a smaller number representation of the same idea.

Any time you have two numbers in a ratio that can both be divided by the same number, it’s not yet in a proper ratio format. 20 and 25 can both be divided by 5. If we divide 20 by 5, we get 4, and if we divide 25 by 5, we get 5. The true ratio of red marbles to blue marbles is 4:5.

That’s kind of how ratios work. Percentages are also a way to compare two different things, but, generally, these are used to compare a part of something to the whole. Let’s say that in this bag of marbles we also had 5 white marbles. That means that the total number of marbles in the bag is 20 plus 25 plus 5 (50).

50 marbles in the bag as a whole. There are 20 red marbles, so we might wonder, “What is the percentage of red marbles in the bag?” Generally, the way you want to approach this is you want to create a fraction, then convert it to a percentage. If we have 20 red marbles, that’ll be our numerator. We said we had 50 marbles in the bag as a whole. That will be our denominator. 20 red marbles, 50 total. This is our fraction of red marbles to total marbles: \(\frac{20}{50}\).

In order to make this a percentage, we’ll have to multiply the top and bottom by 2 to get the denominator equal to 100.

Multiply this by \(\frac{2}{2}\), and that’ll give us \(\frac{40}{100}\).

Now, a percentage is just another way to represent a fraction where the denominator is 100. If we say 40%, that’s the same as saying 40 one-hundredths. The percentage of red marbles in the bag is going to be 40%.

This is how you write a percent: You write a number and then this symbol (%), and that denotes 40 hundredths, 40% of the whole.

That is how you can use ratios and percentages for simple things.