How to Simplify Fractions | Math with Mr. J

In this video, I'm going to cover how to simplify a fraction, also known as writing a fraction in its lowest terms. Now in this video, I'll go through two examples, which should be helpful for anyone looking for a quick review or refresher. If simplifying fractions is new to you or you need more examples, I have a part 2 where I go through a couple more. That link is down in the description. So no matter where you're at as far as simplifying fractions, hopefully between these two videos, we can get it down. Let's jump into our examples, starting with number one, where we have four eighths. So when it comes to simplifying fractions, we are looking to get the smallest numbers in value that we possibly can for our numerator and denominator. We do this by finding common factors between our numerator and denominator, numbers that we can divide both our numerator and denominator by. Once the only common factor is one, we are in simplest form. So for number one here, I'm going to write out the factors for both four and eight, and then we'll go from there. Now you do want to get to the point where you do not need to write out the factors when simplifying, but again for this one, I will. We'll start with four. So let's come down here. So when it comes to factors, we need to think all of the numbers that we can multiply together to equal four, or all of the numbers that four is divisible by. You can also think of it as all of the numbers that go into four, so to speak. So we can start our factor list with one, and then the number itself, four, because we know that one times four equals four. Or you can think of it as one and four go into four. So you can always start with one and the number itself. So let's think if there are any other factors. Well, we know two times two equals four, or we can think of it as two goes into four. So two is a factor. And those are all of the factors of four. One, two, and four. Now let's list our factors of eight. So we can start with one, and then eight. I'll leave a gap in there so we can fill in any other factors. Well, we know two times four equals eight, or we can think two and four go into eight. We can divide eight by two and four. So let's put two and four. And those are all of the factors of eight. One, two, four, and eight. So we want to use the greatest common factor between four and eight here. That way we can simplify in one step. So the greatest common factor is four here. So let's divide both our numerator and denominator by four in order to break this fraction down and get it into simplest form. And remember, if you divide both your numerator and denominator by the same number, we are going to get an equivalent fraction. So we are not changing the value of the fraction when we simplify. Four divided by four is one. Eight divided by four is two. So we have one half. Now the only common factor between one and two is one. So this is, in simplest form, and we are done. So four-eighths in simplest form is one-half. Now I do want to show you another path that we can take in order to simplify this fraction. So let me rewrite four-eighths here. Now another common factor is two. So what happens if we divide both four and eight by two? So let's do this. Divide by two. Divide by two. Four divided by two is two. Eight divided by two is four. So we get two-fourths, which is different than one-half. But we still have a common factor of two. So we can divide by two again, and we get two divided by two is one. Four divided by two is two. So we get one-half that way as well. So something to keep in mind. There can be different paths to get to the simplest form of a fraction. Now if you use the greatest common factor between your numerator and denominator, you will simplify in one step. If you use a factor that is less than the greatest common factor, it will take more than one step. Let's move on to number two, where we have six-fifteenths. Let's write out the factors for six and fifteenth. So we need to think all the numbers that we can multiply. Let's start with six. All the numbers we can multiply to equal six, or all of the numbers we can divide six by. All of the numbers that go into six, so to speak. So always start with one and the number itself. Put a gap in between, and your spacing and ability to think of factors will get better the more you do. So let's think if there are any other factors of six. Well, we know two times three equals six. So two and three are factors of six, and those are the factors of six. One, two, three, and six. So let's list the factors of 15. So we have one, and then the number itself, 15. What other factors of 15 are there? Well, three and five. Three times five equals 15, or we can think that 15 is divisible by both three and five. We are able to divide 15 by both three and five, and it works out without a remainder. So let's look for any common factors. Well, one is a common factor, but we want something greater than one. We have a greatest common factor of three. So let's divide our numerator and denominator by three. Six divided by three is two. Fifteen divided by three is five. Now the only common factor between two and five is one, so we are done. We are simplified. Six fifteenths in simplest form is two fifths. Now one more thing I do want to mention is that a fraction can already be in simplest form. So for example, if you have the fraction of three fourths and you are looking to simplify, that is already in simplest form. The only common factor between three and four is one, so that would be in simplest form as is. So something else to keep in mind. So there you have it. There's how you simplify a fraction. I hope that helped. Thanks so much for watching. Until next time, peace.