Adding fractions with like denominators

So we're asked to add 3/15 plus 7/15, and then simplify the answer. So just the process when you add fractions is if they already-- well, first of all, if they're not mixed numbers, and neither of these are, and if they have the same denominator. In this example, the denominators are already the same. The denominator is 15. So if you add these two fractions, your sum is going to have the same denominator, 15, and your numerator is just going to be the sum of the numerator, so it's going to be 3 plus 7, or it's going to be equal to 10/15. Now, if we wanted to simplify this, we'd look for the greatest common factor in both the 10 and the 15, and as far as I can tell, 5 is the largest number that goes into both of them. So divide the 10 by 5 and you divide the 15 by 5, and you get-- 10 divided by 5 is 2 and 15 divided by 5 is 3. You get 2/3. Now, to understand why this works, let's draw it out. Let's split something up into 15 sections. So let me split it up into 15 sections. Let me see how well I can do this. Well, actually, even a better way, an easier way might be to draw circles. So let me do the 15 sections. So let me draw. So that is one section right over there. That is one section and then if I copy and paste it, that is a second section, and then a third section, fourth section, and then we have a fifth section. Let me copy and paste this whole thing. So that's five sections right there. Let me copy and then paste that. So that is 10 sections, and then let me do it one more time. So that is 15 sections. So you can imagine this whole thing is like a candy bar or something, and we have now split it up into 15 sections. Now, what is 3/15? Well, it's going to be 3 of the 15 sections. So 3/15 is going to be one, two, three: 3/15. Now, to that, were adding 7 of the 1/15 sections, or 7 of the sections. So we're adding 7 of those to it. So that's one, two, three, four, five, six, seven. And you see now, if you take the orange and the blue, you get one, two, three, four, five, six, seven, eight, nine, ten of the sections, or 10 of the 15 sections. And then to see why this is the same thing as 2/3, you can just split this candy bar into thirds, so each third would have five sections in it. So let's do that. One, two, three, four, five, so that is 1/3 right there. One, two, three, four, five, that is another third right there. And notice, when you do it like this, we have filled out exactly two-- one, two-- of the thirds. This is the third third, but that's not filled in. So 10/15 is the same thing as 2/3.