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Dividing a fraction by a whole number

Dividing fractions by whole numbers can be done visually or using multiplication. To find the result of 2/3 divided by 5, divide 2/3 into 5 equal parts, each representing 2/15 of the whole. Alternatively, multiply 2/3 by 1/5, resulting in 2/15 as the final answer.

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  • duskpin ultimate style avatar for user Anabrie
    So... Denominator times whole number = New denominator...
    And the numerator stays the same?

    If this makes sense, please vote up!
    (148 votes)
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  • duskpin tree style avatar for user IzzyKat22
    If anyone is confused, think of it like this:
    1. KEEP: the first number stays the same.
    2. CHANGE: turn division into multiplication
    3. FLIP: All whole numbers have an invisible one and a fraction bar over them. Flip it so the one is on the bottom and your original number is on the top. For fractions, the denominator and the numerator flip
    You just multiply like normal.
    I hope this was helpful.
    (20 votes)
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  • blobby green style avatar for user seedapple1230
    So.. dividing and multiplying fractions are the same?
    (9 votes)
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  • aqualine ultimate style avatar for user Heaven
    Sorry sal, but dosent make sense to me! please help me understand this in an easier way :(
    (5 votes)
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    • mr pink green style avatar for user David Severin
      The idea comes from dividing fractions.
      There are three possibilities, fraction divided by fraction such as (4/5)/(16/15) where you flip the denominator and multiply to get (4/5)(15/16) which will reduce to 3/4.
      The other two have a whole number in numerator or denominator. In this case, you can change whole number to a fraction by dividing by 1.
      Examples: (5)/(20/4) = (5/1)/(20/4) = (5/1)(4/20) = 1
      (20/3)/5=(20/3)/(5/1)=(20/3)(1/5)=4/3.
      Converting a whole number to a fraction by dividing by 1 is important in math in Algebra for slope and other applications.
      (9 votes)
  • duskpin seedling style avatar for user Addi
    5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
    (8 votes)
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  • aqualine ultimate style avatar for user jordanolson1
    why overcomplicate it by making the whole number into a fraction when you can just flip the fraction allowing you to multiply? Or is that not how this works?
    (6 votes)
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  • mr pants purple style avatar for user dilpeeter
    For those who are still confused, let me try explaining.
    Let's use the same numbers, 2/3 divided by 5. We use this method called "keep, change flip" at our school, which is how Sal did it as well. Basically, you keep the 2/3 the same, you change the division sign into a multiplication sign, and turn 5 into the fraction 5/1, but flip it to be 1/5. Then multiply! 2 x 1 is 2, and 5 x 3 is 15, so you get 2/15. Hope that helped!
    (7 votes)
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  • duskpin tree style avatar for user mandar1809.raut
    If Sal had not divided had not divided all the thirds into 5 equal sections at would he have gotten the answer wrong ?
    (7 votes)
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  • starky tree style avatar for user Shiloh
    this is pretty easy for me those who dont understand you are basically multiplying all you have to do is put a 1 on top of the whole number and then multiply hope i helped
    (6 votes)
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  • male robot donald style avatar for user :) (xx)
    My class does "The Flip Method" where you flip the whole number and switch the division sign to a multiplication sign and then just multiply.

    Vote if helpful.
    (4 votes)
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Video transcript

- [Instructor] Let's see if we can figure out what 2/3 divided by five is equal to. Pause this video and see if you can figure this out. Well, there is a couple of ways that we can approach it. We can first do it in a conceptual way, think about it visually. To do that, let me represent 2/3, so let's say that what I'm drawing right over here is a whole. This is a square, and it represents a whole. Now, I can divide into three equal sections. I'm gonna try to hand-draw that. So, this is, that looks pretty good, three equal sections here. Each is 1/3, and we have 2/3, so we are really representing all of this stuff right over here. That is two of my thirds. Now, I wanna divide those 2/3 by five. Well, the way I could do this is I could divide it into five equal sections. But, if I'm doing it, I might as well just divide everything, all the thirds, into five equal sections, so let me do that. So, one, two, three, and then four, and five equal sections. So, what is one of those five equal sections of my original 2/3? Well, this right over here is one of those five equal sections of my original 2/3. Notice I could draw that, I could draw another one here, another one here, another one there, and another one there, and I would have five equal sections that make up those 2/3. But, what does just one of them represent? And if we figure out what this represents of the whole, then we know what 2/3 divided by five is. Well, when I took my thirds and I divided them into five equal sections, I essentially constructed 15ths. How do I know that? Well, I had one, two, three thirds, and then I divided it into one, two, three, four, five sections, so each of these squares right over here is a 15th. You have three times five, and you could count 'em if you like. And, what we have circled off in red is two of these 15ths. We have 1/15 right over here, and then 2/15 right over there. So, this is going to be equal to 2/15. Now, another way that you could think about, and over time this is the way you will approach it, but it's nice to think about it conceptually, when you divide by any number, it's the same thing as multiplying by the reciprocal. So, five is the same thing as five wholes, or 5/1. And so, 2/3 divided by five is the same thing as 2/3 times the reciprocal of five, or the reciprocal of 5/1, which is you just swap the numerator and the denominator, which is 1/5. And so, another way of thinking about this is this is 1/5 of 2/3, which it once again will be this section right over here. The way you could compute this, conceptually, you see that this is 2/15, but you could also say well, I could just multiply it. When I multiply fractions I can just multiply the numerators. Two times one is two. We do that same red color. Two times one is two, and then I could multiply the denominators. Three times five is 15. And, hopefully, what we just drew out may help make sense of why dividing by something is the same thing as multiplying by the reciprocal. Then, when you multiply fractions, it's the same thing as multiplying the numerators to get our new numerator, and then multiplying the denominators to get our new denominator.