In this video, we're looking at what fractions are and how we can simplify them. So when we talk about fractions, we're really just talking about parts of a whole number, like one half or three quarters. And we write them as a numerator, which is at the top, over a denominator at the bottom. For example, if we had a pizza. split it into four parts, and then gave somebody three of them, they would have three fourths, or three quarters of the pizza, and we'd be left with one quarter.
So the number on top tells you how many pieces you have, and the number on the bottom tells you how many pieces there are in one whole. When you're asked to simplify a fraction, you basically need to make the numerator and denominator as small as possible, and to do this we divide them both by the same number. For example if we had 12 over 18, both of these numbers are divisible by 6, so we can divide them by 6 and get 2 as our new numerator and 3 as our new denominator, so 2 thirds is our simplified If you didn't know that both of them were divisible by 6 though, you could have divided them both by a smaller number like 2 to get 6 over 9, and then divided them both by 3 to get 2 over 3. You basically just keep on dividing them until you can't go any smaller. The key point to remember when you're simplifying fractions is you have to divide both the numerator and the denominator by the same number.
For example, we divided both by 2 to get 6 over 9, and then both by 3 to get 2 thirds. Because of this, all of these fractions are equivalent to each other. We can see this more clearly if we represent each of the fractions as a ring.
12 over 18 means that our ring has been split into 18 sections, and we only have 12 of them. 6 over 9 means that the ring is split into 9 sections, and we have 6 of them. And 2 over 3 means that it's been split into 3 sections, and we have 2 of them.
As you can see, even though each ring has been split into a different number of sections, exactly the same amount of each ring has been shaded. And this is what we mean when we say that they're all equivalent. Let's have a go at these two questions.
In this first one, we need to simplify the fraction 4 over 12. The quick way to do this would be to divide top and bottom by 4, which gives us 1 over 3 straight away. However, you could also have done it by dividing by 2 first to get 2 over 6, and then by 2 again to get 1 over 3. Either way, you end up with the same correct answer. For this second one, we need to simplify 20 over 25, and there's actually only one number that goes into both of these, which is 5. So we have to divide top and bottom by 5, which gives us 4 over 5, or 4 fifths, as our simplified version. Anyway, that's everything for this video, so hope you found it useful, and we'll see you soon!