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## 4th grade (Eureka Math/EngageNY)

### Unit 5: Lesson 6

Topic F: Addition and subtraction of fractions by decomposition- Intro to adding mixed numbers
- Intro to subtracting mixed numbers
- Add and subtract mixed numbers (no regrouping)
- Add and subtract mixed numbers (with regrouping)
- Fraction word problem: lizard
- Subtracting mixed numbers with like denominators word problem
- Add and subtract mixed numbers word problems (like denominators)

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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.

## 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.