Question

How do you divide `\frac { 3} { 4} \div 3\frac { 3} { 5}`?

Answer 1

See a solution process below:

Explanation:

First, convert the term on the right from a mixed number to an improper fraction:

`3/4 -: 3 3/5 => 3/4 -: (3 + 3/5) => 3/4 -: ([5/5 xx 3] + 3/5) =>`

`3/4 -: (15/5 + 3/5) => 3/4 -: (15 + 3)/5 =>`

`3/4 -: 18/5`

Next, rewrite the expression as:

`(3/4)/(18/5)`

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))`

`(color(red)(3)/color(blue)(4))/(color(green)(18)/color(purple)(5)) = (color(red)(3) xx color(purple)(5))/(color(blue)(4) xx color(green)(18)) = (cancel(color(red)(3)) xx color(purple)(5))/(color(blue)(4) xx cancel(color(green)(18))6) = 5/24`