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CCSS Math: 4.NF.A.1

Let's think about what
fraction of this grid is actually shaded in pink. So the first thing we
want to think about is how many equal
sections do we have here? Well, this is a 1, 2,
3, 4, 5 by 1, 2, 3 grid. So there's 15 sections here. You could also count it-- 1,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. So there are 15
equal sections here. And how many of
those equal sections are actually shaded in
this kind of pinkish color? Well, We have 1, 2, 3, 4, 5, 6. So it's 6/15 is shaded in. But I want to
simplify this more. I have a feeling that there's
some equivalent fractions that represent the exact
same thing as 6/15. And to get a sense of that, let
me redraw this a little bit, where I still shade in
six of these rectangles, but I'll shade them a
little bit in one chunk. So let me throw in another
grid right over here, and let me attempt to
shade in the rectangles as fast as possible. So that is 1-- 1 rectangle. I'll even make my
thing even bigger. All right, 1 rectangle,
2 rectangles, 3 rectangles-- halfway
there-- 4 rectangles, 5 rectangles shaded in and
now 6 rectangles shaded in. So this right over
here, what I just did, this is still 6
rectangles of the 15 rectangles are shaded in. So this is still 6/15. These are representing
the same thing. But how can I simplify
this even more? Well, when you look
at it numerically, you see that both 6 and
15 are divisible by 3. In fact, their greatest
common factor is 3. So what happens if we divide the
numerator and denominator by 3? If we do the same thing to the
numerator and the denominator, we're not going to be changing
the value of the fraction. So let's divide
the numerator by 3 and divide the denominator by 3. And what do we get? We get 2 over 5. Now how does this make sense
in the context of this diagram right here? Well, we started off
with 6 shaded in. You divide by 3, you
have 2 shaded in. So you're essentially saying,
hey, let's group these into sections of 3. So let's say that this right
over here is one section of 3. This is one section
of 3 right over here. So that's one section of 3. And then this is another
section of 3 right over here. And so you have
two sections of 3. And actually let me color
it in a little bit better. So you have two sections of 3. And if you were to combine
them, it looks just like this. Notice this is covering
the exact same area as your 6 smaller ones did. And then how many equal
sections of this size do you have on
this entire thing? Well, you have 5 equal sections. Because this is one section
of 3 right over here, this is another section of 3. And then this is
another section of 3. So notice, you're covering
the exact same area of the original thing. You're covering 2 out
of the 5 equal sections. So 2/5 and 6/15 are
equivalent fractions. So if you want to say
what fraction of this is covered in the simplest
form, you would say 2/5.