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# Visually adding fractions: 5/6+1/4

CCSS.Math:

## Video transcript

let's see if we can calculate what 5/6 plus 1/4 is and to help us I have a visual representation of 5/6 and a visual representation of 1/4 notice I have this whole this whole whole I guess you could say broke it up into 1 2 3 4 5 6 sections and we've shaded in five of them so this is 5/6 and then down here we have another hole and we have one out of the four equal sections and so this is 1/4 and I want to add them and I encourage you to any point pause the video and see if you could figure it out on your own well whenever we're adding fractions we like to think in terms of fractions that have the same denominator and these clearly don't have the same denominator but in order to rewrite them with a common denominator we just have to think of a common multiple of 6 and 4 and ideally the smallest common multiple of 6 and 4 and the way that I like to do that is I like to take the larger of the 2 which is 6 and then think about its multiples so I could first think about 6 itself 6 is clearly divisible by 6 but it's not perfectly divisible by 4 so now let's multiply by 2 so then we get to 12 12 is divisible by both 6 and 4 so 12 is a good common denominator here it's a the least common multiple of 6 and 4 so we can rewrite both of these fractions as something over 12 so something over 12 plus something plus something over 12 is equal to now there's a bunch of ways to tackle it but what I want to do is I just want to visualize it here on this on this drawing so if I go if I were to go from if I were to go from 6 equal sections to 12 equal sections which is what I'm doing if I'm going from 6 to the nominator 12 in the denominator I'm essentially multiplying each of these sections by or I'm essentially multiplying the number of sections I have by 2 or I'm taking each of these existing sections and I'm turning them into two sections so let's do that let's do that let me see if I can do it pretty neatly so I could do it a little bit neater than that so it'll look like that and whoops let me do this one I want to divide them fairly close to evenly I'm doing it by eye so it's not going to be perfect so then you have that one and then last on but last but not least you have that one there and then notice I had six sections but now I've doubled the number of sections I've turned the six sections into 12 sections by turning each of the original six into two so now I have one two three four five six seven eight nine ten eleven twelve sections so if I have 12 sections now how many of those twelve are now shaded in instead of having five of the six I now have ten of the twelve that are shaded in so I now have ten 12 five six is the same thing as 10 12 another way you could have thought about that to go from 6 to 12 I had to multiply by 2 so then I have to do the same thing in the numerator 5 times 2 is 10 but hopefully you see that those two fractions are equivalent that I didn't say I didn't change how much is shaded in I just took each of the original six and I turned it into two or I multiplied the total number of sections by 2 to get 12 and then instead of having five six I now have ten twelve shaded in now let's do the same thing with the four with the one-fourth right here I've depicted 1/4 but I want to turn this into something over 12 so to turn it over something in 12 to something over 12 each section has to be turned into three sections so let's do that let's turn each section into three sections so that's one two and three so then I have one two and three I have I think you see where this is going one two and three I have one two and three and so notice all I did is I multiplied before I had four equal sections turned each of those four sections into three sections so now I have 12 equal sections and I did that essentially by multiplying the number of sections I had by three so now what fraction is shaded in well now this original that was one out of the four we can now see is three out of the 12 equal sections it's now three out of the 12 equal sections and so what is this going to be well if I have ten twelfths and I'm adding it to three twelfths well how many 12 stew I have I'm gonna have 13 13 12 and you could see it visually over here as well up here in green I have 10 twelfths shaded in each of these boxes are 1/12 let me write that down each of these boxes are 1/12 that's 1/12 this is 1/12 so how many twelfths do I have shaded in I have the 10 front that are shaded in green and then I have an 11 12 a 12 12 and then finally a 13 the 13 12 is one way to think about it