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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.

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  • winston baby style avatar for user Hobbs Conor
    If you have to add a fraction by a whole number can we just add the number and not turn it into a fraction?
    (21 votes)
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    • aqualine ultimate style avatar for user Caden Cummins
      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.
      (5 votes)
  • female robot grace style avatar for user Nadia Chibani
    i stil dont get how 2/3 times 6 is equal to 4
    (7 votes)
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    • duskpin ultimate style avatar for user Chloe Atallah
      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.
      (9 votes)
  • starky sapling style avatar for user 2029makanapreston-brown
    Im just suprised how smart u guys are
    (10 votes)
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  • old spice man green style avatar for user SantiagoF
    What if the whole number is a one
    (6 votes)
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  • male robot donald style avatar for user 01robotboy
    Is there another way to do this?
    (3 votes)
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    • leaf red style avatar for user Cavan P
      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
      (9 votes)
  • duskpin ultimate style avatar for user Lilgatornator
    What if you're multiplying a whole number by a fraction? Is it the same approach?
    (5 votes)
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  • starky sapling style avatar for user Michaelr.Renaud
    He is demonstrating another method of finding the fraction of the whole number he used. If 6/6 = 6 then 2/3 = 4/6. Therefore, 2/3 or 4/6 of 6 equals 4 because 4 is 2 out of every 3 in 6. Also, if 3 x 2 = 6, then 2 x 2 = 4 and 2/3 = 4 out of the whole 6
    (5 votes)
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  • aqualine ultimate style avatar for user FKZ
    I still don't understand the process because I thought of it as actually multiplying 2/3 x 6 and that completely through me off
    (6 votes)
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  • male robot johnny style avatar for user TTVimaGod
    How do you simplify fraction and how do you do a fraction number line
    (4 votes)
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  • duskpin tree style avatar for user Alessio Pirazzini
    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.
    (4 votes)
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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.