How To Add Multiple Fractions

so we're asked to add 3/15 plus7/15, and then simplify the answer. so just the process when youadd fractions is if they already-- well, first of all, ifthey're not mixed numbers, and neither of these are, andif they have the same

How To Add Multiple Fractions, denominator. in this example, thedenominators are already the same. the denominator is 15.

so if you add these twofractions, your sum is going to have the same denominator,15, and your numerator is just going to be the sum of thenumerator, so it's going to be 3 plus 7, or it's goingto be equal to 10/15. now, if we wanted to simplifythis, we'd look for the greatest common factor in boththe 10 and the 15, and as far as i can tell, 5 is the largestnumber that goes into both of them. so divide the 10 by 5 and youdivide the 15 by 5, and you

get-- 10 divided by 5 is 2and 15 divided by 5 is 3. you get 2/3. now, to understand why thisworks, let's draw it out. let's split somethingup into 15 sections. so let me split it upinto 15 sections. let me see how welli can do this. well, actually, even a betterway, an easier way might be to draw circles. so let me do the 15 sections.

so let me draw. so that is one sectionright over there. that is one section and then ifi copy and paste it, that is a second section, and thena third section, fourth section, and then we havea fifth section. let me copy and pastethis whole thing. so that's five sectionsright there. let me copy and thenpaste 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 wholething is like a candy bar or something, and we have now splitit up into 15 sections. now, what is 3/15? well, it's going to be3 of the 15 sections. so 3/15 is going to be one,two, three: 3/15. now, to that, were adding7 of the 1/15 sections, or 7 of the sections.

so we're adding 7of those to it. so that's one, two, three,four, five, six, seven. and you see now, if you take theorange and the blue, you get one, two, three, four, five,six, seven, eight, nine, ten of the sections, or10 of the 15 sections. and then to see why this is thesame thing as 2/3, you can just split this candy bar intothirds, 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 likethis, we have filled out exactly two-- one, two--of the thirds. this is the third third, butthat's not filled in. so 10/15 is the samething as 2/3.