Answer
-$\frac{2}{5}$
Work Step by Step
$\frac{1}{2}$-$\frac{2}{3}$$\div$$\frac{5}{9}$+$\frac{3}{10}$
First change the division to multiplication of the reciprocal of the divisor
$\frac{1}{2}$-$\frac{2}{3}$$\times$$\frac{9}{5}$+$\frac{3}{10}$
Then multiply
$\frac{1}{2}$-$\frac{18}{15}$+$\frac{3}{10}$
Then reduce that product by 3
$\frac{1}{2}$-$\frac{6}{5}$+$\frac{3}{10}$
Then make all of the fractions have a common denominator of 10.
$\frac{1(5)}{2(5)}$-$\frac{6(2)}{5(2)}$+$\frac{3}{10}$
$\frac{5}{10}$-$\frac{12}{10}$+$\frac{3}{10}$
Then subtract
-$\frac{7}{10}$+$\frac{3}{10}$
Then add
-$\frac{4}{10}$
Then reduce by 2.
-$\frac{2}{5}$
