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### Course: Arithmetic>Unit 10

Lesson 6: Multiplying fractions and whole numbers

# Multiplying fractions and whole numbers

Multiplying fractions is about combining parts of a whole. When you multiply two fractions together, you're taking a part of a part. When you multiply a fraction by a whole number, you're taking multiple copies of that fraction. In both cases, the result is a new fraction that represents a different part of a whole. Created by Sal Khan.

## Want to join the conversation?

• If you have to add a fraction by a whole number can we just add the number and not turn it into a fraction?
• Yes. This will create what math likes to call a 'mixed number', at least, when you're adding.
Take this example:
You order two large pepperoni pizzas for a big party you're throwing with your friends. They eat a few slices, and you're left with only two thirds for one pizza. However, the other pizza is still whole.
We can solve this problem by creating a mixed number, which is made by simply adding a whole number and a fraction together, like so: one and two thirds. You can also express it as 1 2/3 or 1+2/3.
Hope this helped.
• i stil dont get how 2/3 times 6 is equal to 4
• Whenever you have a series of mulitplications and divisons they are meant to be done left to right. In this case, 2/3 = 0.666.... repeating. 0.6666... x 6 = 3.9999....6. The reason for this number is that the 0.666 is meant to be endless. The more 6s you would add, the closer the result would be to 4.
Another way to do this, which is more precise, would be to treat the numbers as fractions, 2/3 x 6/1. In this case, 2x6 = 12, then 12/3 = 4. We cannot do 2/(3x6) because that would be the same as multiplying by 1/6, not 6/1.
• Is there another way to do this?
• The easiest way to think about multiplying fractions by whole numbers is to multiply the numerator of the fraction by your integer and then bring over the deonominator.

3/4 * 8 can be thought of as (3*8)/4, or 24/4, or 6.
1/2 * 7 is (1*7)/2, or 7/2
6/23 * 3 is(6*3)/23, or 12/23
• At , why did he multiply the whole number with a numerator even though we learned to multiply with the denominator can someone describe me please?
• This is because sal has 6 2/3, but he wants to add them together, not find a equivalent fraction. You would use the denominator when trying to find an equivalent fraction.
• The way he showed it is for people that do not know to use multiplication. I can see how people can get confused on this.
• how do you figure out if a question is right or wrong
• 🥺can you explain it in a easier way please you made this more difficult🥺
• Basically, 2/3 x 6 , we got it as 12/3, so if we simply it (divide) using the denominator 3 (12 divided by 3) we get 4 in the end

PS: Put your question in an answer to this question so that I can reply to your question, I will still check the regular comments though. Also, if this was commented at least four months ago, your question will probably not be answered.
• is math easy?
(1 vote)
• Adding 2/3 together 3 times is one way to do it. But you could also multiply 6/1 by 2/3. Right? Because 6 over 1 is six ones so its 6 wholes.

## Video transcript

Let's think a little bit about what it means to multiply 2/3 times 6. One way to think about it is to literally take six 2/3 and add them together. This is six 2/3 right over here. And if we wanted to actually compute this, this would be equal to-- well, we're going to take these six 2's and add them together. So we could view it as 2 times 6 over 3. 2 times 6 over 3, which is the same thing, of course, as 2, 4, 6, 8, 10, 12, 12/3. And what is 12/3 equal to? Well, we could rewrite 12 as-- so this is equal to-- we could rewrite 12 as 3 plus 3 plus 3 plus 3 over the yellow 3. Let me do it like this so I don't have to keep switching colors. This is going to be the same thing as 3/3 plus 3/3 plus 3/3 plus 3/3. And each of these are obviously a whole. Each of these equal 1. That's 1 and that's 1, so this is going to be equal to 4. So that's one way to conceptualize 2/3 times 6. Another way to think of it is as 2/3 of 6. So let's think about that. Let me draw a number line here. And I'm going to draw the number line up to 6. So what I care about is the section of the number line that goes to 6. So that looks pretty good. So this is 1, 2, 3, 4, 5, and 6. So if we want to take 2/3 of 6, we can think of this whole section of the number line between 0 and 6 as the whole. And then we want to take 2/3 of that. So how do we do that? Well, we divide it into thirds, to three equals sections. So that's one equal section, two equal sections, and three equal sections. And we want two of those thirds. So we want 1/3 and 2/3. Now where does that get us? That gets us to 4. So we get, obviously, to the same answer. We would be in a tough situation if somehow we got two different answers. Either way, 2/3 times 6 or 6 times 2/3, either way, that is going to be equal to 4. But there are two different ways of viewing this. This first way is literally viewing it as 2/3 six times. And this way is we're taking a fraction of the number 6. We're going 2/3 of the way to 6, which would get us to 4.