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Multiplying 2 fractions: 5/6 x 2/3

When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. After putting the two results together as a new fraction, you may need to simplify the fraction in order to express it in its lowest terms. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • male robot johnny style avatar for user AlexanderB464
    Is there another way to put answers in simplest form another way then the ones shown in the video?
    (373 votes)
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  • blobby green style avatar for user addalyn.velotta
    I still do not get it that much
    (17 votes)
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    • duskpin ultimate style avatar for user 🐧 MrPenguin2 🐧
      Addalyn, say you had to solve 6/10 * 3/6,
      What would you do? well you would fist look at you numbers then you would put the numerator with the other numerator and the denominator with the other denominator.
      (Sounds confusing,right?), so it would look something like this:
      6/10 * 3/6 = 6*3(numerators)/10*6(denominators), so 6*3 is 18 so 18 is your numerator(for the answer), 10*6 = 60 so 60 is your denominator(for your answer). so the answer is 18/60, well that's a big number so lets simplify it, so you need to find a LCM(Least Common Multiple) witch is 6 so it would look like this 18(/)6/60(/)6= 3/10.

      (* is times((/) is division)
      If you still don't understand maybe watch the vidio a few time(then you start to understand).

      Hope this answers your question! 😊😊
      (58 votes)
  • starky seed style avatar for user 🎷 Lylly 🎷
    What do you do if the denominator is different from the other one?
    (18 votes)
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  • aqualine ultimate style avatar for user Pringles
    At , I have always wondered why cant we simplify the denominators : 6 and 3 instead of the 6 and 2??
    (6 votes)
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    • mr pink red style avatar for user MadFish
      If you multiply or divide top and bottom of any fraction by the same number, you do not change the value of the fraction. If you modify only top or only bottom you are changing the value of the fraction.
      Here are examples.
      Let's say I have fraction 1/2. That's half.
      I can multiply top and bottom by 2. (1*2)/(2*2) = 2/4. Now I made 2 quarters. Guess what? 2 quarters is one half. 1/2=2/4. This two fractions look different, but they represent the same value.

      Take a pizza, divide it into 12 equal slices, take 3 slices. How much of pizza did you get? 3/12. I can divide top and bottom by 3. (3/3)/(12/3) = 1/4. Take a look at the 3 slices you got. You have a quarter of a pizza. So 3/12 = 1/4

      In the video the fraction was (5 * 2) / (6 * 3). We can divide top and bottom by 2 and the value will not change. (5 * 2 / 2) / (6 * 3 / 2). 2 / 2 = 1 and 6 / 2 = 3. You'll get (5 * 1) / (3 * 3). That is what you've seen in the video.
      Let's compare (5 * 2) / (6 * 3) = 10/18. Divide top and bottom by 2 you'll get 5/9. (5 * 1) / (3 * 3) = 5/9. The same!! If you take 2 pizzas and divide one into 18 equal slices and than take 10 slices, the other divide into 9 slices and take 5 of them, you'll get the same amount of pizza.
      Let's take original fraction (5 * 2) / (6 * 3) and try to divide only the bottom part (5 * 2) / (6 / 3 * 3 / 3) = (5 * 2) / (3 * 1) = 10/3 That is totally different value. That fraction means 3 whole pizzas and one third of fourth pizza. This does not equal to our original fraction.
      Lengthy explanation, but I hope it is helpful.
      (42 votes)
  • blobby green style avatar for user johncena1388
    The part at - where you divide the 2 by 1 and 6 by 3 without multiplying is confusing. I really don't understand how you did that part. It's quicker but I don't know why you divided like that. I'll stick to the first multiplying one.
    (5 votes)
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  • aqualine ultimate style avatar for user Lindt Xu
    Is there any easier way with no division? Or just and easier way.
    (3 votes)
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    • stelly blue style avatar for user Kim Seidel
      There are really 2 steps to multiply fractions.
      -- Multiply numerator to numerator; and denominator to denominator.
      -- Completely reduce the fraction.

      Reducing the fraction is required. This is the part that involves division. So, you can't get around it.
      Ways to make this easier:
      1) Know your multiplication tables from 1 thru at least 12. Memorize them.
      2) Learn the divisibility tests (you can search for the video on this topic).

      These enable you to more quickly identify common factors that need to be divided out to reduce the fraction.

      Hope this helps.
      (4 votes)
  • starky sapling style avatar for user Italy
    Which way, for Multiplying Fractions, would you recommend using? I've seen that you mentioned more than one, but I don't really see a difference.

    I'm trying to understand this concept, Fractions aren't my strong suit.
    (3 votes)
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    • male robot donald style avatar for user Aneesh
      Really, it’s just what suits you. I personally like to use the standard way (Just multiplying the numerators and then the denominators, as mentioned in this video.) But, if you are more of a visual person and see stuff better visually, use the mode method. Hope this helps. :)
      (2 votes)
  • leafers seed style avatar for user Kelsey Wayne
    Am I allowed to convert the denominator to be even to six??
    to get 5/6*4/6 = 20/30
    (3 votes)
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  • blobby green style avatar for user benjamingarci86
    do you always have to simplify?
    (4 votes)
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  • duskpin ultimate style avatar for user worldwideviola
    Is the decimal between the numbers a multiplication sign?
    (3 votes)
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Video transcript

We're asked to multiply 5/6 times 2/3 and then simplify our answer. So let's just multiply these two numbers. So we have 5/6 times 2/3. Now when you're multiplying fractions, it's actually a pretty straightforward process. The new numerator, or the numerator of the product, is just the product of the two numerators, or your new top number is a product of the other two top numbers. So the numerator in our product is just 5 times 2. So it's equal to 5 times 2 over 6 times 3, which is equal to-- 5 times 2 is 10 and 6 times 3 is 18, so it's equal to 10/18. And you could view this as either 2/3 of 5/6 or 5/6 of 2/3, depending on how you want to think about it. And this is the right answer. It is 10/18, but when you look at these two numbers, you immediately or you might immediately see that they share some common factors. They're both divisible by 2, so if we want it in lowest terms, we want to divide them both by 2. So divide 10 by 2, divide 18 by 2, and you get 10 divided by 2 is 5, 18 divided by 2 is 9. Now, you could have essentially done this step earlier on. You could've done it actually before we did the multiplication. You could've done it over here. You could've said, well, I have a 2 in the numerator and I have something divisible by 2 into the denominator, so let me divide the numerator by 2, and this becomes a 1. Let me divide the denominator by 2, and this becomes a 3. And then you have 5 times 1 is 5, and 3 times 3 is 9. So it's really the same thing we did right here. We just did it before we actually took the product. You could actually do it right here. So if you did it right over here, you'd say, well, look, 6 times 3 is eventually going to be the denominator. 5 times 2 is eventually going to be the numerator. So let's divide the numerator by 2, so this will become a 1. Let's divide the denominator by 2. This is divisible by 2, so that'll become a 3. And it'll become 5 times 1 is 5 and 3 times 3 is 9. So either way you do it, it'll work. If you do it this way, you get to see the things factored out a little bit more, so it's usually easier to recognize what's divisible by what, or you could do it at the end and put things in lowest terms.