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

Lesson 18: Multiplying unit fractions and whole numbers# Multiplying unit fractions and whole numbers

Learn how to multiply a whole number by a fraction, using both visual and computational methods. Multiplying 1/2 by 5 can be understood as adding five 1/2's together, resulting in 5/2. Created by Sal Khan.

## Want to join the conversation?

- If 1/2 x 5 is 5/2 does that mean 5 x 1/2 is the same?(47 votes)
- Yes. When you multiply a fraction or whole number, if the places are interchange, the answers are the same!

#Warning:This doesn't mean the application process is the same!!XD(51 votes)

- 5/6 × 4 is what(15 votes)
- The answer is 20/6, but it is not simplified. You should always simplify fractions if you can. 20/6 can be simplified to 10/3. since 10/3 is an improper fraction, we need to change it to a mixed number. 10 goes inside 3, 3 times and there is one left over. So the answer is 3 1/3. Sorry if this doesn't make sense, I'm only in fifth grade.(42 votes)

- The star (*) is just another way of saying your multiplying so x is also * just with a different shape. =)(22 votes)
- abdullah what are you doing(1 vote)

- how would you multiply 3 1/4 x 6?(8 votes)
- Try converting 3 1/4 to an improper fraction, that should make it a lot easier(19 votes)

- What does it mean by find each product(10 votes)
- This could mean that there's more than 1 multiplication problem present in the question. Which, in this case, you have to find the products of the multiplication given. I hope this helps Eva Medina Whitley!(14 votes)

- how do you do mixed fractions * fractions(10 votes)
- For example ,if they ask you (5 1/2) right?than you just calculate it like this(2 times five,which is 10 ,after that,youplus 1 to 10.)I hope it will help ALIVIA S.(12 votes)

- when adding them together to get 5/2 why are the 1's added but yet the 2's stay as 2 and not 10?(13 votes)
- But I don’t understand? How do you know what fraction to multiply? Do you have divide? Or…(9 votes)
- Always remember this.. It should be repeated any time you are doing fractions. Every Single Class. Numerator is the top number on a fraction. Denominator is bottom number on a fraction. To multiply fractions just multiply the numerator by whatever you want to multiply the fraction by. It's the easiest and quickest way. Sal hinted at it at the end of the video but try this. 4x 1/6. the numerator is 1 (TOP Number) the number you want to multiply it by is 4 so 1x4 is 4. Now add that into the fraction as the new numerator, so the answer would be 4/6 :)(1 vote)

- So, like you did in 1/2x5, do you just replace the numerator (1) with the factor so its 5/2?(6 votes)
- No, because if the numerator is not 1 then it would not work and would be a different number. Ex: 4/5 x 4 = 20/5.(4 votes)

- what is a unit fraction(4 votes)
- a unit fraction Is a fraction that always has 1 as the numerator(4 votes)

## Video transcript

Let's think about how or
what 1/2 times 5 represents. So one way to think about it is
that this could be five 1/2's added together. So you could view this
as 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2, which is the
same thing as 1 plus 1 plus 1 plus 1 plus 1, over 2,
which is equal to 5/2. The other way to
think about this is that you start with 5 things. So let's say, that's 1 thing. Let me copy and paste that
so they all look the same. So then let me paste it. So that's 2 things. That's 3 things. That's 4 things. And that's 5 things. So the other way to think about
it is you start with 5 things, and you take 1/2 of them. So what would be 1/2 of this? Well, let's see. You have 5 things, so you
would get-- 5 divided by 2 would be 2 and 1/2. So you would get this far. Let me make it like this. So you would get this one. You would get this one. And you would get this one. Now, is this the
same thing as 5/2? Well, what happens if we
divide each of these wholes into halves? So let's do that. So if we just multiplied-- so
we just divide each of these into 2. So instead of having 5
wholes, we now have 10 halves. How many of those halves
have we filled in? Well, we have filled
in 1, 2, 3, 4, 5. So this is also equal to 5/2. So far we just did it
thinking about what multiplication actually means. But if you said, well,
how did I compute this? Well, the way you
could think about it, and multiplying
fractions is actually straightforward from
that point of view, is as long as you can express
both of them as fractions, and 5 we already know is
the same thing as 5 ones, so this we can just
multiply times 5/1. So now that I've expressed
both of them as fractions, I can just multiply
the numerator. So 1 times 5 over 2 times 1. And what's that
going to be equal to? Well, 1 times 5 is 5. 2 times 1 is 2. So once again, we get 5/2.