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# Converting mixed numbers to improper fractions

Video transcript

Write 5 and 1/4 as
an improper fraction. So just as a reminder,
an improper fraction is one where the
numerator is greater than or equal to
the denominator. So improper fraction means that
the numerator-- and actually, I should say the absolute
value of the numerator-- is greater than or equal
to the absolute value of the denominator. I could have just shortened
it, but you get the idea. The numerator is greater
than or equal to-- or the absolute value
of the numerator is greater than or equal
to the absolute value of the denominator. In this situation right
here, it's a mixed number. We have it as a combination
of 5, which is just a whole number, and 1/4,
which is a proper fraction, because the numerator is
less than the denominator. The absolute value
of the numerator is less than the absolute
value of the denominator. So to write it as an
improper fraction-- and I'll show you kind of the
methodology for doing it-- and then we'll talk a
little bit about why that methodology works. So 5 and 1/4, the methodology
is pretty straightforward. You say, OK, 5,
the whole number 5, that is the same
thing as 20 over 4. And so 20 over 4 plus
1 over 4 is 21 over 4. Or another way to think about
it is, 5 times 4 is 20, plus 1 is 21. 21 over 4. So that's the methodology. Pretty straightforward. And I'm going to
draw it out so it makes a little bit more sense. So once again, you
take the mixed number, or you take the whole
part of the mixed number, you multiply it times the
denominator, you get 20. And then you add that 20
to 1, you get 21 over 4. And now it's an
improper fraction. The absolute value
of our numerator is greater than the absolute
value of our denominator. Now I do want to show
you why this works. So to see why this
works, let's think about what 5 and 1/4 means. It means we have 5 wholes. So let's say that
this is a whole. So that's 1 whole. And let me copy and
paste it five times. So that's 2, that's 3,
that's 4, and then that is 5. So we have five wholes. So that's this stuff
that I've drawn in green. That's 5 holes right there. And then we have 1/4. So I'll do 1/4 of a whole. And just to be clear that
it's part of a whole, I could have drawn the
whole in a dotted line, to say that we don't have that
whole, we have only 1/4 of it. And that's that 1/4. So this is 5 and 1/4. So to write it as an
improper fraction, you can really view this
5 as some fraction over 4. And to think of it that
way, divide each of these into fourths. Or this is one way
to think about it. So this right over here is
4/4, this is another 4/4, this is another 4/4-- I should
have copied and pasted this-- this is another 4/4,
and this is another 4/4. So now how many
fourths do we have? How many fourths? We have 4/4 here, 4/4 here, 4/4
here, 4/4 here, and 4/4 here. So just what we have in green. We have 20 fourths. That's what we have in
green, right over here. That is the same thing as 5. Each of these are 4/4, so you
could view this as 5 times 4/4, right? 4/4 is 1. 5 times 4/4 is 20 over 4. That's what we have
right over here. And now we can add
it to that 1/4. And you will get 21. We have the same denominator. So we can just add
the numerators. 21 over 4. So that's the conceptual
understanding of why it works. But when you see
any mixed number, it's a pretty
straightforward process. Multiply the 5
times 4, you get 20. 20 plus 1 is equal to 21 over 4. And actually, let me
just write that out. Just so you get clear
on what I'm doing. So 5 and 1/4, that
is the same thing-- that's equal to 5
times 4 plus 1, over 4. And this is why.