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

Lesson 21: Multiplying fractions

# 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.

## Want to join the conversation?

• Is there another way to put answers in simplest form another way then the ones shown in the video?
• Yes. Lets say we have a question saying 5/3 x 10/5. You can simplify the two fives so it can become 1/3 x 10. This is easier to make it into simplest form.
• I still do not get it that much
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).

• What do you do if the denominator is different from the other one?
• Well, when multiplying fractions it doesn't matter if the denominators are different. You simply just multiply the two denominators to get your answer and the same for the numerators.
• At , I have always wondered why cant we simplify the denominators : 6 and 3 instead of the 6 and 2??
• 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.
• 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.
• I'm pretty sure they were just reducing it and that you'd be okay without doing so.
(1 vote)
• Is there any easier way with no division? Or just and easier way.
• 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.
• 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.
• 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. :)
• Am I allowed to convert the denominator to be even to six??
to get 5/6*4/6 = 20/30
• It has to be a number that equals 6 when you multiply it or when you divide it.