When solving we only multiply the numerator is by the LMC when simplifying we multiply the numerator and the denominator by the LMC

Answer 1

So, let's use a couple of simpl examples.

1/6 + 3x/12 = 16/24

The LCM is 24, right? We then apply it by multiplying the numerator by the LCM divided by the denominator. 24/6 = 4. 4(1) = 4, to start, so we have...

4/24 + 6x/24 = 16/24

In order to solve for x, we don't need the denominators anymore. We could keep them but they just get in the way.

4 + 6x = 16

6x = 12

x = 2

Now, if we want to check...

1/6 + 3(2)/12 = 16/24

1/6 + 6/12 = 16/24

4/24 + 12/24 = 16/24

16/24 = 16/24

Now, to the 2nd part. When simplyfying, we divide the numerator and the denominator by the GCF of both. Let's use our 16/24 from above.

The GCF of 16 and 24 is 8. We divide both 16 and 24 by 8, we end up with 2/3, right?

So, if this was a T/F question, perhaps I over-explained that the answer is false.