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Subtracting mixed numbers with like denominators word problem

Sal solves a word problem involving mixed number subtraction by using a visual model.

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Video transcript

- [Instructor] After a rain storm, Lily measures the depth of several puddles in her backyard. She records her results in a table. So here are three different puddles and she measures the depth in inches. We're 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 one and 1/4 inches deep it's under the swing. How much deeper was that than the puddle on the sidewalk? 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 what we could do is subtract the 2/4 from the one and 1/4. So we could write one and 1/4 minus 2/4 could write it like that, and we could try to subtract the fraction part 2/4 from the fraction part of this mixed number up here from 1/4 but we immediately have a problem 'cause 2/4 is a larger fraction than 1/4, so how do we deal with that? Well the key is to realize that one can be rewritten as a fraction, one and 1/4 is the same thing as one plus 1/4 which is the same thing as another way to write one in terms of fourths is 4/4 so this is 4/4 plus 1/4 which is going to be equal to 5/4. So now you can do this as 5/4, this number is the same thing as 5/4 minus 2/4, let me rewrite it, minus 2/4, minus two over four. And that's pretty straightforward if I have five of something and I subtract two of it, I'm going to have three of that something 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 one and 1/4. At first we could've thought of one and 1/4 as a whole like this and then it's all let me shade it, the whole and that's one and then I would have a fourth of a whole so let me divide this into four sections, so this is one and 1/4. And at first we say well how do we take away 2/4 from just that I only have 1/4 right over here and our key realization is well look, I actually this whole right over here is actually 4/4 I can think of it as 4/4, so I can think of it like this and now I have 5/4, one, two, three, four, five fourths and now I can take away two of the fourths, so I can take away one of the fourths and two of the fourths and what am I left with? Well then I am going to be left with these 3/4 right over there.