Solve {[(1/2*4/3)+5/9]-9/5}=

$$\{ [ ( \frac { 1 } { 2 } \cdot \frac { 4 } { 3 } ) + \frac { 5 } { 9 } ] - \frac { 9 } { 5 } \} =$$

Evaluate

$$-\frac{26}{45}\approx -0.577777778$$

Solution Steps

Multiply \frac{1}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{2\times 3}+\frac{5}{9}-\frac{9}{5}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 3}.

$$\frac{4}{6}+\frac{5}{9}-\frac{9}{5}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{5}{9}-\frac{9}{5}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{5}{9} to fractions with denominator 9.

$$\frac{6}{9}+\frac{5}{9}-\frac{9}{5}$$

Since \frac{6}{9} and \frac{5}{9} have the same denominator, add them by adding their numerators.

$$\frac{6+5}{9}-\frac{9}{5}$$

Add 6 and 5 to get 11.

$$\frac{11}{9}-\frac{9}{5}$$

Least common multiple of 9 and 5 is 45. Convert \frac{11}{9} and \frac{9}{5} to fractions with denominator 45.

$$\frac{55}{45}-\frac{81}{45}$$

Since \frac{55}{45} and \frac{81}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-81}{45}$$

Subtract 81 from 55 to get -26.

$$-\frac{26}{45}$$

Factor

$$-\frac{26}{45} = -0.5777777777777777$$