In this video, we’re going to talk about ratios and percentages. Now, a ratio is a way to compare two different quantities to one another.

So, for instance, let’s take: If we have 20 red, and 25 blue, we can say that the ratio of red to blue is 20:25.

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The transcript is provided for your convenience

And so, this is what ratio notation looks like. You have a number that represents the first quantity, and a colon, and then a number that represents the second quantity.

And so, this right here is not a proper ratio, because you can reduce it to a smaller number representation of the same idea. So, 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.

So, 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. So, the true ratio of red to blue is 4:5.

So, 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.

So, let’s say that in this bag we also add 5 white. So, that means that the total number of in the bag is 20 plus 25 plus 5, or 50.

So, 50 in the bag is a whole, and there are 20 red, so we might wonder, what is the percentage of red in the bag? Generally, the way you want to approach this is you want to create a fraction, and then convert it to a percentage.

So, if we have 20 red, that’ll be our numerator, and we said we had 50 in the bag as a whole, so that will be our denominator. So, 20 red, 50 total.

So, this is our fraction of red total. In order to make this a percentage, we’ll have to multiply top and bottom by 2 to get the denominator equal to 100. So, multiply this by 2/2, and that’ll give us 40/100.

Now, a percentage is just another way to represent a fraction where the denominator is 100, so if we say 40%, that’s the same as saying 40/100. So, the percentage of red 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% of the whole. And so, that is how you can use ratios and percentages for simple things.

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The next lesson: Calculation of a Percentage