Question

How do you simplify `3 2/5 div 3 1/2`?

Answer 1

See the entire simplification process below:

Explanation:

First, convert the compound fractions to improper fractions:

`((3 xx 5/5) + 2/5) -: ((3 xx 2/2) + 1/2) ->`

`(15/5 + 2/5) -: (6/2 + 1/2) ->`

`17/5 -: 7/2`

We can now rewrite this expression as:

`(17/5)/(7/2)`

We can now use this rule for dividing fractions:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

Substituting and calculating gives:

`(color(red)(17)/color(blue)(5))/(color(green)(7)/color(purple)(2)) = (color(red)(17) xx color(purple)(2))/(color(blue)(5) xx color(green)(7)) = 34/35`