Question

How do you simplify `1/5 div 3/5`?

Answer 1

The simplified answer is `1/3`.

Explanation:

You can use this nifty property when diving by fractions:

`a/b div color(red)c/color(blue)d qquad => qquad a/b xx color(blue)d/color(red)c`

Just flip the fraction, and change it to multiplication. Here's this property applied to our problem:

`color(white)=1/5 div color(red)3/color(blue)5`

`=1/5xxcolor(blue)5/color(red)3`

`=(1xxcolor(blue)5)/(5xxcolor(red)3)`

`=(1xxcolor(red)cancelcolor(blue)5)/(color(red)cancelcolor(black)5xxcolor(red)3)`

`=1/color(red)3`

That's the most simplified it gets. Hope this helped!