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# Adding fractions with like denominators

CCSS.Math:

## Video transcript

so we're asked to add three 15 s plus 7 15 s 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 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 over 15 now if we wanted to simplify this we 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 so you 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 draw let's 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 well 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 so let me copy and then let me paste it that is a second section and then third section fourth 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 so let me copy and then paste that so that is ten sections and then let me do it one more time so that is 15 section 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 315 well it's going to be 3 of the 15 sections so 315 so it's going to be 1 two three three fifteen now to that we're adding seven of the 115th sections or seven of the sections so we're adding seven of those to it so that's one two three four five six seven and you see now if you take the orange in 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 1/2 of the thirds this is the third third but that's not filled in so 10 15 is the same thing as 2/3