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# Writing improper fractions as mixed numbers

CCSS.Math:

Sal rewrite 7/4 as a mixed number. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- What if there is no remainder for the whole number, Is this possible? .-.

Maybe with... 8/2 . How would I solve this into a mixed number?(31 votes)- You know how many times does 2 go into 8 4times right you wouldn’t have a mixed number you would just have 4 wholes(3 votes)

- How can i use this in future coming terms(24 votes)
- Mathematics is very important in life, even if it doesn't seem like.

eg. Video games, food, transportations.

To think about it, almost everything includes mathematics.

For Mix Fraction in specific, they can be found a lot in cooking. You need it to measure how many cups of flour in your favourite cake, or how many cups of rice in your dinner.(17 votes)

- I have one question: sometimes you have to do these kind of things really fast; I was wondering if there was a fast and accurate way to convert fractions and mixed numbers, so you don't have to take that long and do all that stuff and take an hour to do one math problem.(10 votes)
- You can use Sal’s way of doing it, to get it faster, practice it multiple times.(5 votes)

- multiplying mixed numbers and improper fractions(5 votes)
- This is a mixed number… 2 1/2 . This is a improper fraction… 5/2. They're the same number, just in different forms.(6 votes)

- how does 4 go into 7(6 votes)
- what do you mean bruh its like if you have 7 rock's and you gotta get redov em all but too get redav em you have to find seven more rocks and ya find four ov em they cancel out four of the rocks you have 3 lef is basic subtract man I would not say this to ya face but sense ya probly won't see it anyhow If you dont no that well well well nevermind hope that help's cowboy(3 votes)

- does anyone know how to rename as an improper fraction from a mixed number. 😱(7 votes)
- What if you have 0 wholes?(5 votes)
- if you have zero whole's then its not a mixed number(3 votes)

- how do you change fractions to improper fractions(3 votes)
- To change fractions (I assume you mean proper fractions) to improper fractions, take the whole number in the proper fraction and multiply it by the denominator of the fraction, then add that result to the numerator of the fraction and you will get the improper fraction. For example: 5 1/2 is the proper fraction. To convert it to an improper fraction multiply 5 by 2 which gives you 10. Then add 10 to the numerator which is 1. Your answer would end up being 11/2. I hope that helped.(5 votes)

- how do you do this with fractions such as 30/1?(3 votes)
- It is quite easy since the denominator is 1, any numerator with a denominator of 1 is a whole number, except 0/1. Think of it as a pizza, a pizza can come in 12 slices or 8 or ten thousand, (the slices to that pizza must be impossibly thin) but if it only comes in as whole pizza without slices then it would be 1/1, if you ordered two of the same pizzas it would be 2/1, and if you ordered that exact pizza 30 times, the fraction would be 30/1.(0 votes)

- will i need this for collage(3 votes)
- This is basic math. You need this for life in general. After basic math, you will go on to algebra and other higher level math topics. College generally requires that you know basic math and algebra.(4 votes)

## Video transcript

Write 7/4 as a mixed number. So right now it's an
improper fraction. 7 is larger than 4. Let's write it is
a mixed number. So first I'm just going
to show you a fairly straightforward way of doing
it and then we're going to think a little bit about
what it actually means. So to figure out what 7/4
represents as a mixed number, let me write it in
different colors. So this is going to be equal
to-- the easiest way I do it is you say, well, you
divide 4 it 7. If we're dealing with fourths,
4 goes into 7 a total of one time. Let me do this in
another color. 1 times 4 is 4. And then what is
our remainder? 7 minus 4 is 3. So if we wanted to write this
in plain-- well, let me just do the problem, and then
we'll think about what it means in a second. So you see that 4 goes into 7
one time, so you have one whole here, and then how much
do you have left over? Well, you have 3 left
over, and that comes from right over there. That is the remainder when
you divide 4 into 7. 3 left over, but it's 3 of
your 4, or 3/4 left over. So that's the way we just
converted it from an improper fraction to a mixed number. Now, it might seem
a little bit like voodoo what I just did. I divided 4 into 7, it goes
one time, and then the remainder is 3, so
I got 1 and 3/4. But why does that make sense? Why does that actually
makes sense? So let's draw fourths. Let's draw literally 7 fourths
and maybe it'll become clear. So let's do a little
square as a fourth. So let's say I have a square
like that, and that is 1/4. Now, let's think about what
seven of those mean, so let me copy and paste that. Copy and then paste it. So here I have 2 one-fourths,
or you could see I have 2/4. Now I have 3 one-fourths. Now, I have 4 one-fourths. Now this is a whole, right? I have 4 one-fourths. This is a whole. So let me start on
another whole. So now I have 5. Now I have 6 one-fourths, and
now I have 7 one-fourths. Now, what does this look like? So all I did is I rewrote
7/4, or 7 one-fourths. I just kind of drew
it for you. Now, what does this represent? Well, I have 4 fourths
here, so this is 4/4. This right here is 3/4. Notice, 7/4 is 4/4 with
3/4 left over. So let me write it this way. 7/4 is 4/4 with 3/4 left over. Now what is 4/4? 4/4 is one whole. So you have one whole with
3/4 left over, so you end up with 1 and 3/4. So that is the 3/4 part and
that is your one whole. Hopefully that makes sense and
hopefully you understand why it connects. Because you say, well, how
many wholes do you have? When you're dividing the 4 into
the 7 and getting the one, you're essentially saying
how many wholes? So the number of wholes, or you
can imagine, the number of whole pies. And then how many pieces
do we have left over? Well, we have 3 pieces and each
piece is 1/4, so we have 3/4 left over. So we have one whole pie and
three pieces, which are each a fourth left over.