Question

How do you simplify `\frac { - \frac { 2} { 3} } { 2\frac { 2} { 3} }`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the denominator as:

`2 2/3 = 2 + 2/3 = (3/3 xx 2) + 2/3 = 6/3 + 2/3 = (6 + 2)/3 = 8/3`

Next, we can rewrite the expression as:

`((-2)/3)/(8/3)`

Now, we can 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)(-2)/color(blue)(3))/(color(green)(8)/color(purple)(3)) = (color(red)(-2) xx color(purple)(3))/(color(blue)(3) xx color(green)(8)) => (color(green)(cancel(color(red)(-2)))color(red)(-1) xx color(blue)(cancel(color(purple)(3))))/(color(purple)(cancel(color(blue)(3))) xx color(red)(cancel(color(green)(8)))color(green)(4)) => -1/4`