Use less than,

greater than, or equal to compare the two fractions

21/28, or 21 over 28, and 6/9, or 6 over 9. So there’s a bunch

of ways to do this. The easiest way is if they

had the same denominator, you could just compare

the numerators. Unlucky for us, we do not

have the same denominator. So what we could do is we

can find a common denominator for both of them and convert

both of these fractions to have the same denominator

and then compare the numerators. Or even more simply, we could

simplify them first and then try to do it. So let me do that

last one, because I have a feeling that’ll be

the fastest way to do it. So 21/28– you can see that

they are both divisible by 7. So let’s divide

both the numerator and the denominator by 7. So we could divide 21 by 7. And we can divide– so let

me make the numerator– and we can divide

the denominator by 7. We’re doing the same

thing to the numerator and the denominator,

so we’re not going to change the

value of the fraction. So 21 divided by 7 is 3,

and 28 divided by 7 is 4. So 21/28 is the exact

same fraction as 3/4. 3/4 is the simplified

version of it. Let’s do the same thing for 6/9. 6 and 9 are both divisible by 3. So let’s divide

them both by 3 so we can simplify this fraction. So let’s divide

both of them by 3. 6 divided by 3 is 2,

and 9 divided by 3 is 3. So 21/28 is 3/4. They’re the exact same fraction,

just written a different way. This is the more

simplified version. And 6/9 is the exact

same fraction as 2/3. So we really can

compare 3/4 and 2/3. So this is really

comparing 3/4 and 2/3. And the real benefit of

doing this is now this is much easier to find a common

denominator for than 28 and 9. Then we would have to

multiply big numbers. Here we could do

fairly small numbers. The common denominator

of 3/4 and 2/3 is going to be the least

common multiple of 4 and 3. And 4 and 3 don’t share any

prime factors with each other. So their least common

multiple is really just going to be the

product of the two. So we can write 3/4

as something over 12. And we can write 2/3

as something over 12. And I got the 12 by

multiplying 3 times 4. They have no common factors. Another way you could

think about it is 4, if you do a prime

factorization, is 2 times 2. And 3– it’s already

a prime number, so you can’t prime

factorize it any more. So what you want to do

is think of a number that has all of the

prime factors of 4 and 3. So it needs one 2,

another 2, and a 3. Well, 2 times 2 times 3 is 12. And either way you

think about it, that’s how you would get

the least common multiple or the common

denominator for 4 and 3. Well, to get from 4 to 12,

you’ve got to multiply by 3. So we’re multiplying the

denominator by 3 to get to 12. So we also have to multiply

the numerator by 3. So 3 times 3 is 9. Over here, to get

from 3 to 12, we have to multiply the

denominator by 4. So we also have to multiply

the numerator by 4. So we get 8. And so now when we

compare the fractions, it’s pretty straightforward. 21/28 is the exact

same thing as 9/12, and 6/9 is the exact

same thing as 8/12. So which of these is

a greater quantity? Well, clearly, we have the

same denominator right now. We have 9/12 is clearly

greater than 8/12. So 9/12 is clearly

greater than 8/12. Or if you go back

and you realize that 9/12 is the exact

same thing as 21/28, we could say 21/28 is definitely

greater than– and 8/12 is the same thing as 6/9– is

definitely greater than 6/9. And we are done. Another way we could

have done it– we didn’t necessarily

have to simplify that. And let me show you

that just for fun. So if we were doing it

with– if we didn’t think to simplify our

two numbers first. I’m trying to find a

color I haven’t used yet. So 21/28 and 6/9. So we could just find

a least common multiple in the traditional way

without simplifying first. So what’s the prime

factorization of 28? It’s 2 times 14. And 14 is 2 times 7. That’s its prime factorization. Prime factorization

of 9 is 3 times 3. So the least common

multiple of 28 and 9 have to contain a 2,

a 2, a 7, a 3 and a 3. Or essentially, it’s

going to be 28 times 9. So let’s over here

multiply 28 times 9. There’s a couple of

ways you could do it. You could multiply

in your head 28 times 10, which would be 280,

and then subtract 28 from that, which would be what? 252. Or we could just multiply

it out if that confuses you. So let’s just do the second way. 9 times 8 is 72. 9 times 2 is 18. 18 plus 7 is 25. So we get 252. So I’m saying the

common denominator here is going to be 252. Least common

multiple of 28 and 9. Well, to go from 28 to 252,

we had to multiply it by 9. We had to multiply 28 times 9. So we’re multiplying 28 times 9. So we also have to multiply

the numerator times 9. So what is 21 times 9? That’s easier to

do in your head. 20 times 9 is 180. And then 1 times 9 is 9. So this is going to be 189. To go from 9 to 252, we

had to multiply by 28. So we also have to multiply

the numerator by 28 if we don’t want to change

the value of the fraction. So 6 times 28– 6

times 20 is 120. 6 times 8 is 48. So we get 168. Let me write that

out just to make sure I didn’t make a mistake. So 28 times 6– 8 times 6 is 48. 2 times 6 is 12, plus 4 is 16. So right, 168. So now we have a common

denominator here. And so we can really just

compare the numerators. And 189 is clearly

greater than 168. So 189/252 is clearly

greater than 168/252. Or that’s the same

thing as saying 21/28, because that’s what

this is over here. The left-hand side is

21/28, is clearly greater than the right-hand side,

which is really 6/9.

it;;;really taught me more about……fractions…

but ..Sal I wanted understand more about ELECTRONICS,,,,,,can u record videos about them please…….

me too i did not know a thing about this

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Fffff

Hhhhhhhh

This shit sucks ass !

Can you please do a video on simplifiying BIG fractions not small ones like 2/4 , 3/6 , and 4/8 come on pleaseeeee

very helpful for my kid

good I like your video

da frick I want from us

I dont get it somehow…

boi im a grumpy cat for cring out loud

This was so helpful thank you