## anonymous one year ago Will Medal Answer ASAP!!!!! 1: What is the GCF of the numerator and denominator in the following fraction? 21m^2n/28mn^2 7m^2n^2 7mn 21m^3n^3 mn

1. anonymous

so whats the question?

2. anonymous

im putting it up right now!

3. anonymous

alrighty then.

4. anonymous

@paki

5. anonymous

@geny55 @Photon336

6. Photon336

So this is what we have right @jessie13 $\frac{ 21m ^{2}n }{ 28mn ^{2} }$

7. Photon336

so greatest common factor, is the largest number that can go into both the numerator and denominator

8. anonymous

1 dont get it!

9. Photon336

Let's break this up into two parts

10. Photon336

$\frac{ 21 }{ 28 } * (\frac{ m ^{2}n }{ mn ^{2} })$

11. Photon336

do you know how to subtract powers?

12. Photon336

whenever we divide exponents we subtract the exponents. so we will do that first $\frac{ m ^{2}n}{ mn ^{2} } = Numerator[ m ^{2}-m ^{1} = m] denominator [n ^{1}-n ^{2}] = n ^{-1}$ we simplify the variables first. $\frac{ m }{ n }$

13. Photon336

@jessie13 so now this is what we have we need to find the greatest common factor so it has to be the largest number that goes into both 21 and 28 $\frac{ 21 }{ 28 } *(\frac{ m }{ n })$

14. anonymous

wait the gcf is 7

15. Photon336

@jessie13 yep :) here's why. and that's why I told you to do it that way yeah so |dw:1444067072198:dw|

16. Photon336

let me rewrite this

17. anonymous

k

18. Photon336

$\frac{ 3 m}{ 4 n} * *\frac{ 7 mn}{ 7 mn } = \frac{ 21 }{ 28 } \frac{ m*m = m ^{2}n }{n*n = n ^{2}m }$

19. Photon336

$(7mn) = GCF$ because if we multiply this by 3m/4n we get what we started with @jessie13 look at this tell me if this makes sense to you

20. anonymous

okay!

21. anonymous

ya it makes more sense thanks!

22. Photon336

can you show me why this makes sense @jessie13 ?