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### Course: Arithmetic > Unit 15

Lesson 5: Dividing fractions by fractions- Understanding division of fractions
- Dividing a fraction by a whole number
- Divide fractions by whole numbers
- Meaning of the reciprocal
- Dividing a whole number by a fraction
- Dividing a whole number by a fraction with reciprocal
- Divide whole numbers by fractions
- Dividing fractions: 2/5 ÷ 7/3
- Dividing fractions: 3/5 ÷ 1/2
- Dividing fractions

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# Dividing a whole number by a fraction with reciprocal

Dividing by a fraction involves finding the reciprocal and multiplying. For example, when dividing 8 by 7/5, first find the reciprocal of 7/5, which is 5/7. Then, multiply 8 by 5/7, resulting in 40/7 or 5 5/7. This method simplifies fraction division and enhances understanding. Created by Sal Khan.

## Want to join the conversation?

- This is so frustrating.

I don’t get it at all.

When I think I got it and I try to do it, it ends up the wrong way!(10 votes)- Can you give a couple of examples that you worked and and got incorrect? Maybe this will help where you are going wrong.(10 votes)

- fractions before was so easy 😭(6 votes)
- so are you just fliping the numarator and denominator is that what it basicaly is for reciprocal?(5 votes)
- Yeah, pretty much.But this concept only applies if the integer is 1.(0 votes)

- Hey, there Academy! I took a quiz recently and unfortunately, I didn't do too well. I found the quiz to be a bit confusing and the explanation provided was not very helpful. Do you happen to know who created the quiz? I would love to provide some feedback to help make it better next time. Also, it seems like there should be a quick video saying here was your mistake, and here is why you might have got it wrong now let me help you understand this so you can achieve your expectations.(4 votes)
- Yes and no is orange but the pineapples are eating the maybes so we cant drink bricks anymore(3 votes)
- but we can drink bricks if we draw the sky triangle with a bucket of green(2 votes)

- so does it just mean that the group is just the reciprocal to get how many groups are there?(2 votes)
- Yes, you are correct! The number of groups can be determined by taking the reciprocal of the fraction you're using.

To clarify further, let's use the example of dividing 6 cookies into groups of 2/3 again:

1. To find the number of groups, we can take the reciprocal of 2/3. The reciprocal of a fraction is obtained by swapping the numerator and denominator.

The reciprocal of 2/3 is 3/2.

2. Now, we can divide the total number of cookies (6) by the reciprocal (3/2) to find the number of groups.

6 ÷ (3/2) = 6 * (2/3) = 12/3 = 4.

So, in this case, we would have 4 groups of 2/3.

Taking the reciprocal allows us to convert the division problem into a multiplication problem, making it easier to find the number of groups. By multiplying the total quantity by the reciprocal, we can determine how many groups of the desired fraction can be formed.

This concept applies not only to cookies but can also be used with other objects or numbers when dealing with fractions. By understanding the reciprocal relationship, we can easily determine the number of groups or sets based on a given fraction.(3 votes)

- You lost me at0:50(3 votes)
- I followed the video until2:10-2:28. I have no idea what's happening. Is 8 divided by 7/5 connected to the first problem? Also, why are we solving 8 divided by 7/5? How is 5/7 8 times?

At2:30-2:47, you showed us an equation to solve 8 divided by 7/5 but did 8 times 5/7 instead. Why do we change 7/5 to 5/7 if it's a different problem? And why do we use multiplication to solve 8 divided by 7/5?

EDIT: So I figure it out. For how many 7/5 go into 1, since 7/5 is LARGER than 1. (which is 5/5) So you just count the shaded blue which is 5, and add the 7 to the denominator making it 5/7. Since 7/7 equals 1 which is the same as (7/5), 7/5 is smaller than 7/5 and 5/5 is the same as 7/5.

On 8 divided by 7/5. You just follow this equation. 8 times (x) 7, giving you 56, then just add the 7 to the denominator. Your answer would be 56/7.(3 votes) - am i the only one that thinks of the word spectacle when someone says reciprocal(3 votes)

## Video transcript

- [Instructor] In this video,
we're gonna do an example that gives us a little bit of practice to think about what does it
mean to divide by a fraction? So if we wanna figure out what eight divided by 7/5 is, but we're gonna break
it down into two steps. First of all, we're gonna
use these visuals here to think about how many
groups of 7/5 are in one. Or another way of thinking about it is how these 7/5 are in a whole? So pause this video, and just
think about this first part. All right, so let's look at 7/5. 7/5 is everything from
here, all the way to there. And then one is this. So how many 7/5 are in one? Well, you can see that one, which is the same thing
as 5/5, is less than 7/5. So it's actually going
to be a fraction of a 7/5 that is one, or that is in one. And you can see what that fraction is. One is what fraction of 7/5. Well, if you look at the fifths, 7/5 is of course seven of
them, and a whole is 5/5, so five of the 7/5 make a whole. So the answer right over here is 5/7. 5/7 of a 7/5 is equal to one. You can also see this right over here. If you take each of these to be a fifth, each of these to be a fifth, then this whole bar is equal to 7/5. And the blue part is equal to one. So how many 7/5 are in the blue part? Well, we can see it's
5/7 of the whole bar. Once again, 5/7 of the whole bar. So we can also think about this as one divided by 7/5. This is another way of saying
how many 7/5 are in one, or how many groups of 7/5 are in one? And this is equal to 5/7, which we've learned in other videos is the reciprocal of 7/5. The numerator and the
denominator is swapped. So now what is eight
divided by 7/5 going to be? Well, if one divided by 7/5 is 5/7, or if you have 5/7 of a 7/5, of a 7/5 in one, I know the oral language
gets a little bit confusing. Well, you're going to have
eight times that many in eight. So this is going to be the same thing as eight times, we could do it this way, eight times one, divided by 7/5. Or you could just view this as eight times the reciprocal of 7/5,
which is five over seven. And we've learned how
to multiply this before. Eight times 5/7 is going to be equal to 40/7, and we're done. You could obviously also
write that as a mixed number if you like, this would be
the same thing as 5 5/7. So the big picture is when we think about how many of a fraction are in one, that's the same thing as saying, what's one divided by that fraction? As you see visually here, you essentially get the
reciprocal of that fraction. And so if you take any
other number other than one divided by that fraction, you're essentially just gonna multiply it by that reciprocal, because
it's that number times one. So when you divide by that fraction, it's that number times the reciprocal.