Question

How do you simplify `\frac { 2} { 3} \div 1\frac { 3} { 5}`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the mixed number as an improper fraction:

`1 3/5 = 1 + 3/5 = (5/5 xx 1) + 3/5 = 5/5 + 3/5 = (5 + 3)/5 = 8/5`

Next, we can rewrite the expression as;

`(2/3)/(8/5)`

We can now use this rule for dividing fractions to evaluate the expression:

`(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)(2)/color(blue)(3))/(color(green)(8)/color(purple)(5)) = (color(red)(2) xx color(purple)(5))/(color(blue)(3) xx color(green)(8)) = (cancel(color(red)(2)) xx color(purple)(5))/(color(blue)(3) xx cancel(color(green)(8))color(green)(4)) = 5/12`