Question

How do you evaluate `-\frac{18\times z}{207\times z}`?

Answer 1

`-2/23`

Explanation:

By evaluating or I assume simplifying the fraction, we can first cancel out the `z` since `z/z=1`

`(-18*z)/(207*z)= -18/207`

Remember you can only do this since the `z` is multiplied to both the numerator and denominator. If it was added to the numerator and denominator, then we could not do this since canceling out `z` is really just dividing it by itself, and we can only do this without distribution to multiplied/divided terms.

Now we simplify `-18/207`

We know 18 is divisible by 9 but what about 207? The divisibility rule for 9 is that if the sum of the digits is divisible by 9, then the number is divisible by 9.

The digits in 207 are 2, 0, and 7.

`2+0+7=9` and 9 is divisible by 9.

This means 207 is divisible by 9. So:

`-18/207=(-18/9)/(207/9)=-2/23`

Simplified, the fraction is `-2/23`

I hope this helps you out!