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### Course: Arithmetic>Unit 15

Lesson 1: Fractions as division

# Creating a fraction through division

In this video, we'll learn about the relationship between division and multiplication using fractions. Watch how dividing by a number is the same as multiplying by its reciprocal. Then watch as Sal practices this concept using a fun, everyday example. Created by Sal Khan.

## Want to join the conversation?

• No matter how many times fractions are explained to me I can't get it to click in my head.
So when you are dividing a number by a number smaller than itself, does the product represent how many sections of the whole you have?
How does changing the division sign to a times sign, and flipping the fraction express the same thing?
• I feel you I can never understand fractions as decimals.
• is the 3/4 equation always like that? Please explain.
• 3/4 really just means 3 divided by 4. Just like 1/4 means one divided by four. I like to use money as an example. If you have a one dollar bill and give it to your sister for "quarters" you get back four quarters. Another way to write that is 4/4 or four fourths of a dollar. If you reduce 4/4 to lowest terms by dividing the top and the bottom by four you get 1/1 which is just 1 - one dollar. Did that help?
• I love fraction and my teacher says to leave the first faction alone here is and example 2/6 divided by 1/6 so the multiplication is 2/6 times 6/1.
• 2 equal groups, WHAT THAT LOOKS SO UNEVEN
• Wouldn't it be 3/6 not 3/2?
• i know that this is an old question and you probably got the hang of it by now, but just in case someone else has the same problem - it is 3/6 of a whole, which is 3 bars, but a single bar represents one whole. so 3/2 here means that we have 3 halves of a bar of soap.
• You could also say he has 1.5 bars of soap, right?
• wait so 1/2 can mean 1 divided by 2? why am i just now learning that?
• Yes it is indeed true that 1/2 is 1 divided by 2 (or 2 into 1). In general, the fraction a/b means a divided by b (or b into a). Every fraction is really the result of a division problem! This is an important concept to understand about fractions.

Have a blessed, wonderful day!
• does the video show u a easy way to divide ur fractions
• Not so sure… but I do have an easy way to divide your fractions! it’s called KCF Keep Change Flip. You keep the fraction on the left hand side, change the division sign to multiplication, and then flip the number to your right hand side for example: 5/6 ➗ 7/10 would change in to 5/6 ✖️10/7. Then you solve from there. Hope this helped

-Hopper
• if you have 5/14-6/28 how is that possible? p.s that is one thing I learned. please explain.
(1 vote)
• first turn 5/14 into 10/28 by multiplying 5 and 14 by 2. then you will get 10/28. after that you should subtract 6/28 from 10/28 and get 4/28. finally you simplify 4/28 by dividing it by 4 and you get the answer 1/7
• is the 3/4 equation always like that? Please explain.
if you have 5/14-6/28 how is that possible? p.s that is one thing I learned. please explain.

## Video transcript

My wife and I have recently purchased an assortment pack of soap, and we both want to experience all 3 bars. And we are not willing to share soap with each other. So we have a little bit of a conundrum. How do we share these 3 bars of soap so that we each get to experience all of the smells? So this might be a nice rose smell. This might be some type of ivory smell. I don't even know if that's a legitimate smell. This might be some type of sandalwood, which is always very nice. And my wife has an idea. She says, look I'm going to take these 3 bars, so we're starting with 3 bars of soap. And I'm going to divide it into 2 equal groups. And I said, how are you going to do that? And she says, well, I'm just going to take out some type of carving saw or carving knife, or who knows what it is, and I'm just going to cut it right down the middle, so right down this. This is my wife cutting the soap right over here with her saw. So she's cutting the soap right over here. So she has divided the soap into 2 equal groups. So she's taken 3 bars, and she's divided into 2 equal groups. So the interesting question here is, how many bars of soap do we each have now? And I encourage you to pause the video and think about that for a second. How many bars of soap do we each have now? Well, let's just visualize my share. Let's say I take this bottom half right over here. So this is Sal's share of the soap. Let me write this out. So this is Sal's share. My wife took this top half. Well, what do I have? Well, I have 1/2, I have another 1/2, and I have another 1/2 of a bar. So I have 3/2 bars of soap. Or you could say that I have 3 times 1/2 bars of soap. Notice, something very interesting happened here. 3 divided by 2 is equal to 3 times 1/2. And we could make it even more interesting, because we know 2 is the exact same thing as 2/1. So 3 divided by 2/1 is equal to 3 times 1/2. Notice we went from a division to a multiplication, and we took the reciprocal. And that makes complete sense. We have 3/2 bars now. But what's 3 times 1/2? Well, 3 times 1/2 is equal to 3/2. So just doing this little simple, smelly soap example, we've got a very interesting result. 3 divided by 2 is the same thing as 3 times 1/2, which is the same thing as 3/2.