All right. This is Fifth Grade Module Three Lesson Four.
We're going to be adding fractions using the area model.
Only now we're going to end up with improper fractions, so to speak,
or fractions that are between one and two.
And we're going to be asked to convert that to a mixed number whenever necessary, or whenever possible.
All right, so we're going to continue drawing those pictures using the area model to get our answers.
So, we're going to start with, and I'm going to go pretty fast because this is Lesson 4,
meaning we, in Lesson 3 we already did this pretty slowly and carefully and clearly.
So this time I'm going to go a little bit faster.
And we're going to start with two identical area models
that are still not identical. You know, you would think I would know how to do this by now, but, no.
So here is three fourths, one, two, three-fourths.
And then here is two-thirds. One-third and two-thirds.
So we've got three-fourths here, and we've got two-thirds here.
And just like in the previous video, we're gonna cut each of the fourths into thirds,
and each of the thirds into fourths.
So I'm going to use my red pen, and I'm going to cut each of the fourths into thirds,
and I'm gonna cut each of the thirds into fourths.
And that means three-fourths suddenly becomes one, two, three, four, five, six, seven, eight, nine. Nine-twelfths.
And each of the third, the two-thirds, becomes one, two, three, four, five, six, seven, eight, becomes eight-twelfths.
So we end up with nine-twelfths plus eight-twelfths.
And when we add those together we get seventeen-twelfths.
And we know that 12/12 equals 1 whole.
So that would be 12/12 plus an extra 5/12.
So that means we have one whole and 5/12 left over.
Now, kind of a cool thing you could do is, you could like imagine getting scissors,
and let's take this piece right here, and move it right here.
And let's take this piece right here, and move it right here.
And let's take this piece, and move it right here.
So that, right now, makes one whole, right here.
And then,
these guys are gone,
leaving just these 5 pieces right here.
So here's your one whole, and then here's your 5/12 left over.
So that's a visual way to show that the answer really is one whole with 5/12 left over.
So we're going to do another practice. And we've got 5/6 + 1/2.
So I'm gonna try and draw two identical rectangles.
And I'm going to cut the first one into 6ths, and shade in 5/6. One, two, three, four, five 6ths.
There's my five-sixths.
And I'm going to cut this one in half. Whew! That's not so bad.
That's pretty quick.
There's one-half.
All right. And then, I'm going to cut each of the sixths in half.
And I'm going to cut each of the halfs into sixths.
So, instead of 5 sixths, we end up with one, two, three, four, five, six, seven, eight, nine, ten. So we end up with 10/12.
And instead of 1/2, we end up with one, two, three, four, five, six. We end up with 6/12.
So our problem becomes 10/12 + 6/12, that's equal to 16/12.
That's definitely more than one whole, so we could change that to 12/12 + 4/12.
So that equals 1 and 4/12.
Now our 5th graders probably know that 1 and 4/12, because 4/12 can be written as 1 x 4, and 3 x 4
So we now know that 1 and 4/12 is equal to 1 and 1/3.
So either one of these answers would be appropriate.
Or, heck, we could leave it as 16/12, if we want to.
Last problem for this slide, uh, this video.
Mr. Sinofsky used 5/8 of a tank of gas to visit relatives over the weekend,
and another half a tank commuting to work the next week.
He then took another weekend trip and used a 1/4 tank of gas.
How many tanks of gas did Mr. Sinofsky use altogether?
So, if I were to draw a tape diagram, it doesn't say we have to, but I'm going to.
And I'm not gonna try and make these sizes relative and appropriate.
I'm just going to say that first he used 5/8.
Then he used a half.
Then he used a quarter.
All right, so I'm not worried about making these proportional,
I'm just trying to represent the entire thing, represent the problem,
and now we're supposed to add.
And, so, we are going to do, this is essentially two problems in one.
Although, I think some students would be able to see that 1/2 + 1/4,
like if you imagine a clock, 1/2 + 1/4,
1/2 + 1/4 is equal to 3/4, so really this becomes a problem where we're doing 5/8 + 3/4.
All right, and so, I'm going to scroll down a little bit, and now we're going to solve that problem, 5/8 + 3/4.
So, draw two boxes, cut this one into 5/8. So I'm going start with cutting it into fourths.
And each fourth I cut into halfs. So now I'm going to shade in 5 of those eighths.
One, two, three, four, five. There's my 5/8.
And I'm going to cut this into 3/4, you cut that into fourths, I mean.
And then you shade in 3 of those fourths. All right.
So here we have 5/8. Here we have 3/4.
Now the way they have us doing it in Engage-NY now,
we're not finding the least common denominator.
What we're doing is we are just using that cutting method,
which means we're gonna get a big common denominator, which is 32.
At this point, that's not particularly the most effective, or efficient way of doing it.
Although, we're going to stick with it right now.
If you want to talk about a different way that you could have cut this up, you're welcome to.
But right now, I'm just going to stick with the plan here.
And I'm gonna cut the eighths into fourths, and the fourths into eighths.
And then 5/8 becomes, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve,
thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty.
So each of them, each fifth, I mean each eighth gets cut into four more pieces.
so you get 20/32, and over here, each of the fourths,
one, two, three, four, five, six, seven, eight, gets cut into 8 pieces.
So that means we're going to have 24/32.
So now our problem becomes 20/32 + 24/32,
adding that together you get 44/32.
And that, we're going to have 32/32 + 12/32,
And so that equals one whole and 12/32. So that's the answer.
We could that 44/32 is the answer, and then we could even simplify it even further
and say take that one and 12/32, and we know that 12/32 can be written as,
let's see, we could write that as 4 x 3, and 4 x 8, so that equals one and three-eighths.
So we have the answer 1 and 3/8, 1 and 12/32, or we have the answer 44/32.
And so that is Fifth Grade Module 3 Lesson 4, we're adding fractions using the area model,
to find answers that are between 1 and 2, which required us to convert that number to a mixed number.