Can the following terms cancel?

[Krack]

Hello there.

Please have a look at the equation below.



Can the two mu's (u's) in the following expression cancel? If no, can someone please explain why?

Thank you.

 

[BigBeachBanana]

To answer your question:
[math]\frac{2*3}{11*5+3*7}=\frac{6}{55+21}=\frac{6}{76}[/math]By your logic:
[math]\frac{2*\sout{3}}{11*5+\sout{3}*7}=\frac{2}{55+7}=\frac{2}{62}\neq \frac{6}{76}[/math]

 

[Krack]

Thanks for your reply.

Can you please tell me what material I need to study to understand why they can't cancel.

Is it because of addition?

Thanks.

 

[BigBeachBanana]

Thanks for your reply.

Can you please tell me what material I need to study to understand why they can't cancel.

Is it because of addition?

Thanks.

You can only reduce fractions when both numerator and denominator are composed of multiplication only.
Consider another example: [math]\frac{3}{3(3+5)}=\frac{3}{3(8)}=\frac{3}{24}=\frac{1}{8}[/math]Notice that 3(3+5) is multiplication, so you can cancel:
[math]\frac{\sout{3}}{\underbrace{\sout{3}(3+5)}_{multiplication}}=\frac{1}{8}[/math]

 

[Dr.Peterson]

Thanks for your reply.

Can you please tell me what material I need to study to understand why they can't cancel.

Is it because of addition?

Thanks.

The way I've often stated it to students, you can only cancel common factors of the entire numerator and denominator. You can't cancel a factor that is in only one term.

Why? Because canceling means something like this:
[math]\frac{2(x+y)}{2z}=\frac{2}{2}\cdot\frac{x+y}{z}=1\cdot\frac{x+y}{z}=\frac{x+y}{z}[/math]You can't do that with, say,
[math]\frac{2x+y}{2z}[/math]where 2 is not a factor of the entire numerator.

 

[blamocur]

The way I've often stated it to students, you can only cancel common factors of the entire numerator and denominator. You can't cancel a factor that is in only one term.

Why? Because canceling means something like this:
[math]\frac{2(x+y)}{2z}=\frac{2}{2}\cdot\frac{x+y}{z}=1\cdot\frac{x+y}{z}=\frac{x+y}{z}[/math]You can't do that with, say,
[math]\frac{2x+y}{2z}[/math]where 2 is not a factor of the entire numerator.

I would add a suggestion: pick some numbers and plug them in into the original and the "cancelled" fractions and see which cancelling preserves the value of the fraction.

 

[Harry_the_cat]

Krack:
Which one is correct?

\(\displaystyle \frac{ab}{c+ad} = \frac{b}{c+d}\)

OR

\(\displaystyle \frac{ab}{ac+ad} = \frac{ab}{a(c+d)}=\frac{b}{c+d}\)

They can't both be correct.