Adding fractions

Learn how to add fractions with different denominators with this instructional video.

How do you add fractions with different denominators? For example, 3/4+1/6, but before I show you how to add fractions with different denominators, let's take a closer look at each of these fractions. Here I have two fraction bars, the top fraction bar is divided into four equal pieces, and I have shaded in three of the four pieces. So the top fraction bar is showing 3/4, the bottom fraction bar is divided into six equal parts, and I have shaded in one of those parts, so this fraction bar is showing us 1/6, and you can clearly see that the part labeled 1/6, is quite a bit smaller, than the parts that are labeled 1/4, and that's why we can't add these fraction the way that they are. What we have to do, is to make all the parts the same size, and we do that by finding a common denominator. So let's return to our problem. To add these two fractions together, we need to find a common denominator. A common denominator for this problem would be a multiple of both four and six. And the easiest way to find that number will be to simply multiply the two denominators together. So that would give us 4x6=24. So 24 is a common denominator. Well, 24 is a terrific common denominator, but it's not the least common denominator, there is a smaller number that's a multiple of both four and six, and that would be our least common denominator or L.C.D for short. One way to find the least common denominator is to list the first few multiples of the larger of the two denominators, and in our case that would be the number 6. So some multiples of 6 would be the number 6 and then 12, 18, 24. we can stop there. Now we already know that 24 is a multiple of 4 and 6, but what about the other numbers, are any of these numbers also a multiple of 4 and of 6? Well sure, the number 12. The number 12 is a multiple of 4 and of 6. So that's going to be our least common denominator. So what are we going to do with this least common denominator? Well, we are going to use it to change 3/4 and 1/6 into new fractions whose denominator would be 12. So let's make equivalent fractions, let's start with 3/4. We want to change 3/4 into a new fraction with a denominator of 12. You can see that 12 is three times bigger then 4, so that means that 4 must have been multiplied by 3 in order to give us 12. Whatever you do to the denominator in a fraction, you must also do to the numerator to keep everything equal. So we are going to multiply the numerator by 3 as well. And three time 3 is 9, so that's our new numerator. So 3/4 is the same as 9/12. these are equal fractions. Let's do the same thing to 1/6. We are going to change 1/6 into a new fraction whose denominator is 12. This time 12 is twice as big as 6, so that means we multiplied 6 by 2 to get 12, and whatever we do to the denominator, we have to do to the numerator. So we are going to multiply 1 by 2 as well, and that gives us a numerator of 2. So 1/6 is the same as 2/12. So now we can rewrite the original problem. Instead of 3/4, we are going to write 9/12, and instead of 1/6 we are going to write 2/12. Let's go back to our fraction bars and see what the new fractions look like. We need to change 3/4 into 9/12, so I am going to increase the denominator till I reach 12, and we have 9/12 shaded in. Let's do the same for 1/6, I am going to change the denominator to 12, and 1/6 is the same as 2/12. Now you can see that all of the parts are exactly the same size, so now we can easily add them together. So 9/12+2/12 = 11/12.