Question

How do you write the fraction `20/35` in simplest form?

Answer 1

`4/7`

Explanation:

When writing a fraction in it's simplest form, this means simplifying it. You do this by finding a common number that goes into both the numerator and the denominator (top and bottom number) and divide the numerator and denominator by that number. You can find this number by finding the factors of the numerator and denominator.

Factors of 20:

`20 -> 20xx1, 10xx2 or 5xx4`

Factors of 35:

`35 -> 35xx1 or 7xx5`

As you can see the highest common factor in both `20` and `35` is `5`, therefore we divide the numerator and denominator by `5` respectively.

`20/5=4` therefore the numerator changes from `20 -> 4`

`35/5=7` therefore the denominator changes from `35 -> 7`

`therefore` `20/35 -> 4/7`

Answer 2

Remove common factors.

Explanation:

`20/35 = (5*4)/(5*7) = (cancel(5)*4)/(cancel(5)*7) = 4/7`

You can also think of it this way:

`20/35 = (color(red)(5)*4)/(color(red)(5)*7) = color(red)(5/5) * 4/7 = color(red)(1) * 4/7 = 4/7`