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# Equivalent fraction and whole number multiplication problems

Video transcript

So we have here, it says 2 times
4/3 is equal to 8 times blank. And what I encourage you to do
is pause the video right now and try to think about what
should go in this blank. So I'm assuming
you've given your try. Now, let's think through this. So 2 times 4/3, we can literally
view that as the same thing as-- if we rewrite the 4/3, this
is the same thing as 2 times-- instead of writing
4/3 like this, I'm literally going to
write it as four 1/3's. And I know it sounds like I just
said the same thing over again. But I'm literally going to write
1/3 four times-- 1/3 plus 1/3 plus 1/3 plus 1/3. If you call each of
these 1/3, you literally have four of them. This is four 1/3's. 2 times 4/3 is the same thing as
2 times, literally, four 1/3's. Now, what would this be? Well, this is going to be equal
to-- let me just copy and paste this-- is going to
be this two times. So copy, and then
let me paste it. So that's one group of
those 1/3's, of those four 1/3's, or one group of
one of these four 1/3's. And then, we'll
have another one. And then, we'll
have another one. And we're going to
add them together. That's literally 2 times 4/3. So let's add these together. Now what do we have? Well, we have a bunch of 1/3's. And we need to count them up. We have one, two, three, four,
five, six , seven, eight 1/3's. This is literally
equal to-- and we could, just to make it
clear what I've just done, we could ignore the
parentheses and just add up all of these things together. So that might make it
a little bit clearer. So let me do that just to
make it clear that I literally take-- I've taken eight 1/3's
and I'm adding them together, which is the exact
same thing as 8/3. So let me clear that, and let me
clear that, let me clear that. And so this is literally, or
this is clearly, or hopefully clearly, equal to 8 times 1/3. I have 8 1/3's there. So going back to the
original question, what is this equal to? 2 times 4/3 is the same
thing as 8 times 1/3. And we've already seen
that 8 times 1/3, well, that's literally 8/3. So we could also write
it like this-- 8 over 3. Let me do that 3 in that
other color-- 8 over 3.