Question

How can I tell if `3/9` is in simplest form?

Answer 1

`3/9=(3xx1)/(3xx3)=3/3xx1/3=1xx1/3=1/3`

Explanation:

The first question to ask is: Is the fraction in simplest form? The way to tell is if there is a factor that will divide into both the numerator and denominator (other than 1).

Let's look at `2/7`. Is there a factor that will divide into both 2 and 7? No - they are both prime and so there is no factor that will divide into both.

What about `4/25`? We can express it as `(2xx2)/(5xx5)` and see that, again, there is no factor that will divide into both.

So now to `3/9`. Is there a factor that will divide into both? We can write the fraction as `3/(3xx3)` and see that 3 is a factor that will divide into both:

`3/9=(3xx1)/(3xx3)=3/3xx1/3=1xx1/3=1/3`