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### Course: Arithmetic>Unit 15

Lesson 5: Dividing fractions by fractions

# 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!
• Can you give a couple of examples that you worked and and got incorrect? Maybe this will help where you are going wrong.
• fractions before was so easy 😭
• so are you just fliping the numarator and denominator is that what it basicaly is for reciprocal?
• Yeah, pretty much.But this concept only applies if the integer is 1.
• 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.
• Yes and no is orange but the pineapples are eating the maybes so we cant drink bricks anymore
• but we can drink bricks if we draw the sky triangle with a bucket of green
• so does it just mean that the group is just the reciprocal to get how many groups are there?
• 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.
• You lost me at
• I followed the video until - . 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?

At - , 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.