Question

How do you simplify `\frac { 78} { 182}`?

Answer 1

`78/182=3/7`

Explanation:

Given:

`78/182`

We can find the greatest common factor (GCF) of two numbers like this:

• Divide the larger number by the smaller to give a quotient and remainder.

• If the remainder is `0` then the smaller number is the GCF.

• Otherwise repeat with the smaller number and the remainder.

So in our example, given `182` and `78`...

`182/78 = 2" "` with remainder `26`

`78/26 = 3" "` with remainder `0`

So the GCF of `182` and `78` is `26` and:

`78/182 = (color(red)(cancel(color(black)(26)))*3)/(color(red)(cancel(color(black)(26)))*7) = 3/7`