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In a previous video, we learned all about factoring whole numbers. And now we're going to learn how factoring can help us when working with fractions. We're going to learn how to simplify fractions. Simplifying a fraction means re-writing the fraction using the smallest top and bottom numbers we can without changing the value of the fraction. To help us understand what simplifying a fraction really means, let s take a look at the simplest fraction I can think of: 1 over 2Now this is already as simple as it can possibly be. So, let s go the other way and complicate it by dividing our rectangle here up into more parts. The amount of our rectangle that s shaded is still the same, but now the numbers for our fraction are 3 over 6. The numbers are bigger because our rectangle is now divided into more parts. The fraction we have now (3 over 6) is equivalent to our original fraction (1 over 2)That means they have the same value. They represent the same amount. So what if someone gives you the fraction 3 over 6. (Like three-sixths of a candy bar)Well we know from our picture, that means they're really giving you one-half. But how can we show that using math and not pictures? Well, that's where factoring comes in! Let s take our complicated fraction (3 over 6) and factor both the top and bottom numbers. Now the bottom number (6) can be factored into 2 3. The top number (3) is a prime number. Its only factors are 1 and itself, so we can write that as 1 3. There we have re-written our fraction using factoring, and now it kinda looks like two fractions being multiplied together: (1 over 2) times (3 over 3)Of course, 3 over 3 is what I like to call a whole fraction since its value is equal to 1. Now here's the interesting part... Since 3 over 3 equals 1, and multiplying by 1 has no effect on a number, we can just get rid of that 3 over 3. Basically, the 3 on the top and the 3 on the bottom cancel each other out. And once they re gone, we're left with the fraction: 1 over 2. So that means that the fraction 3 over 6 simplifies to 1 over 2. Another way of thinking about it is that we retrying to find any whole fractions that are hiding in the fraction we are trying to simplify. And if we find any, we can just get rid of them and the fraction we're left with is simpler than what we started with. Now that we know the basics, let s learn the procedure for simplifying fractions. First: Replace the top and bottom numbers of the fraction with their prime factors. Next: Look to see if any of the factors are the same on the top and bottom. If they are, we call them common factors because they re something that both the top and bottom have in common. If you find a pair of common factors, you can cancel them out. Just draw a line through them like this. And Last: Once all the common factors have been canceled, you need to re-multiply any factors that are left over on the top or bottom. This makes sure that you end up with only one number on the top and bottom of your...
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