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### Course: Numbers & Operations - The Real & Complex Number Systems 211-217 > Unit 6

Lesson 3: 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?(374 votes)
- 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.(100 votes)

- I still do not get it that much(17 votes)
- 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! 😊😊(57 votes)

- What do you do if the denominator is different from the other one?(18 votes)
- 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.(16 votes)

- At2:20, I have always wondered why cant we simplify the denominators : 6 and 3 instead of the 6 and 2??(5 votes)
- 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.(41 votes)

- I Hate Math so Much(3 votes)
- Is there any easier way with no division? Or just and easier way.(2 votes)
- 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.(3 votes)

- The part at1:24-1:42where 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.(3 votes)
- I'm pretty sure they were just reducing it and that you'd be okay without doing so.(0 votes)

- how do you get to master challeges(2 votes)
- Sometimes you don't have a mastery challenge, and you have to wait.(1 vote)

- what fraction multiplied by 2 over 5 gives 1 over 12(2 votes)
- So do you always multiply the denominators? Because i was told it was the greatest common factor. So is it always like that or not?(1 vote)
- When multiplying fractions, you always multiply the denominator by the other denominator, yes. The greatest common factor part is only for subtraction and addition.(1 vote)

## 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.