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Subtracting mixed numbers with like denominators

Thuyết minh video

after a rainstorm Lily measures the depth of several puddles in her backyard Shira chords her results in a table so here are three different puddles and she measured measures the depth in inches and then were asked how much deeper was the puddle under the swing than the puddle on the sidewalk so pause this video and see if you can figure that out so they say how much deeper was the puddle under the swing so that's this one right over here it's 1 in 1/4 inches deep it's under the swing how much deeper was that then the puddle on the sidewalk let me do that in a different color the puddle on the sidewalk and we see here the puddle on the sidewalk is 2/4 inches deep so we could do is subtract the 2/4 from the 1 and 1/4 so we could write 1 and 1/4 minus 2/4 we could write it like that and we could try to subtract the fraction part 2 4 it's from the fraction part of this mixed number up here from the 1/4 but we immediately have a problem because to force is a larger fraction than 1/4 so how do we deal with that well the key is to realize that 1 can be re-written as a fraction 1 and 1/4 is the same thing as 1 and 1/4 is the same thing as 1 plus 1/4 which is the same thing as another way to write 1 in terms of fourths is 4/4 so this is 4/4 plus 1/4 plus 1/4 which is going to be equal to 5/4 so now you can view this as 5/4 this number is the same thing as 5/4 - 2/4 let me rewrite it - 2/4 minus 2 over 4 and that's pretty straightforward if I have 5 of something and I subtract two of it I'm gonna have 3 of that some thing in this case I'm talking about 3/4 so this is going to be 3/4 so how much deeper was the puddle under the swing than the puddle on the sidewalk well 3/4 of an inch and just another way that you could have visualized this is look I'm going to subtract 2/4 from 1 and 1/4 at first we could have thought of 1 and 1/4 as a whole like this and then so let me see it shaded the hole and that's one and then I would have a fourth of a hole so let me divide this into four equal sections so this is 1 and 1/4 and at first we said well how do we take away two forts from just that I only have 1/4 right over here and our key realization is well look I actually this hole right over here is actually 4/4 I could think of it as four forts so I could think of it like this and now I have five four it's one two three four five forts and now I could take away two of the fourths so I could take away one of the forts and two of the fourths and what am I left with well then I'm going to be left with these three forts right over there