## vera_ewing one year ago Did I write this out correctly?

1. vera_ewing

So I wrote: $\frac{ 1 }{ 3 }m~is~n < \frac{ 1 }{ 2 }m$

2. vera_ewing

@jim_thompson5910 Did I write it correctly?

3. jim_thompson5910

the "is" translates to an equals sign you should have this equation $\Large \frac{1}{3}m = \frac{1}{2}m - n$

4. vera_ewing

So how would I solve? Can I just plug in the answer choices? Or is there a faster, more efficient way?

5. jim_thompson5910

|dw:1434502471198:dw|

6. jim_thompson5910

Let's say m was a multiple of 3 that would mean 1/3 times m is some integer |dw:1434502504575:dw|

7. vera_ewing

$\frac{ 1 }{ 3 }m - \frac{ 1 }{ 2 }m = -n$

8. jim_thompson5910

m & n are integers, so the "-n" portion on the RHS is an integer the 1/2 times m portion must also be an integer to form the entire RHS to be an integer

9. jim_thompson5910

|dw:1434502575606:dw|

10. jim_thompson5910

|dw:1434502590368:dw|

11. jim_thompson5910

so m must be a multiple of 2 and 3

12. vera_ewing

Ohhh okay! Thanks for explaining that!

13. jim_thompson5910

np