Main content

### Course: Arithmetic (all content) > Unit 5

Lesson 12: Mixed numbers- Writing mixed numbers as improper fractions
- Writing improper fractions as mixed numbers
- Write mixed numbers and improper fractions
- Comparing improper fractions and mixed numbers
- Mixed numbers and improper fractions review
- Compare fractions and mixed numbers
- Mixed number or improper fraction on a number line

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Writing improper fractions as mixed numbers

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 you have a whole number but no remainder, I'm completely stuck on a question for a quiz.(2 votes)
- That's ok. Some improper fractions will convert to whole numbers. For example: 63/7 = 9

Hope this helps.(2 votes)

- Can you explain how to turn an improper fraction to a whole number?(1 vote)
- You would divide. But many improper fraction can't be changed into whole numbers. They get changed into mixed numbers (a whole number with a fraction).

For example: 56/8 = 7 (a whole number because there is no remainder when you do the division.

59/8 = 7 3/8. It isn't a whole number. It is a mixed number.(4 votes)

- 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?(47 votes)- 8 / 2 = 4. So, it is just a whole number rather than a mixed number.

Note: 8 / 2 is still an improper fraction and it can be reduced. So, you would do the division to change it into the 4.

Hope this helps.(26 votes)

- How can i use this in future coming terms(38 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.(40 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.(20 votes)
- If there are mixed fractions and improper fractions I'm wondering if you can put a improper fration to a mixed fration and vis veversa(12 votes)
- Absolutely! For example, you can add 5/6 to 8/2 by making them common denominators (5/6+24/6 = 29/6) I hope this answers your question! :)(11 votes)

- The denominator represents the size of a group, so when a group is filled up (2/2, or 3/3, etc), it creates a whole for the Mixed number. What is left over is the amount that can't make up another whole group, this is the numerator.(9 votes)
- What if you have 0 wholes?(8 votes)
- if u had 0 wholes it wouldn't be a mixed number. It would be simply a fraction or a improper fraction NOT a mixed number right?(3 votes)

- What does the 7 in 7/4 mean?

Also what does the 4 in 7/4s mean?(5 votes)- The 7 in seven fourths represents the amount you are counting. You're counting 4/4 and 3/4, so you're counting 7 of the fourths.

4 represents the amount in every whole.

If you divide two pizzas into four slices each and you eat one slice of one pizza, you have 7/4 slices left. Seven represents the amount you're counting, which is how much is left in this case, and four represents that there are four slices to a whole.(6 votes)

- how do you change fractions to improper fractions(4 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.(6 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.