How do you solve #\frac { - 2} { 3} \div 1\frac { 4} { 5}#?

First, we write them as fractions.
#-2/3-:(4+color(red)(5)*1)/5=-2/3-:9/5#
If we divide fractions, we swap the denominator and the counter.
#-2/3-:9/5=-2/3*5/9=-(2*5)/(3*9)=-10/27#

First, convert the mixed number to an improper fraction:

#1 4/5 = 1 + 4/5 = (5/5 xx 1) + 4/5 = 5/5 + 4/5 = (5 + 4)/5 = 9/5#

Next rewrite the expression as:

#(-2)/3 -: 9/5 => ((-2)/3)/(9/5)#

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)(9)/color(purple)(5)) => (color(red)((-2)) xx color(purple)(5))/(color(blue)(3) xx color(green)(9)) => (-10)/27 => -10/27#

You first change the mixed fraction to an improper fraction, which is #9/5#

Then reciprocate(flip over) The # 9/5# to make it #5/9#.

The final equation before the main calculation must look like this:

# (-2) /3 * 5/9#
multiply. The -2 multiplying the 5 and the 3 multiplying the 9.

The final answer is:

= #-10/27#