Solve (2/5+4/9-2/3)*5/2-frac{3}{5}

$$( \frac { 2 } { 5 } + \frac { 4 } { 9 } - \frac { 2 } { 3 } ) \cdot \frac { 5 } { 2 } - \frac { 3 } { 5 }$$

Evaluate

$$-\frac{7}{45}\approx -0.155555556$$

Solution Steps

Least common multiple of 5 and 9 is 45. Convert \frac{2}{5} and \frac{4}{9} to fractions with denominator 45.

$$\left(\frac{18}{45}+\frac{20}{45}-\frac{2}{3}\right)\times \frac{5}{2}-\frac{3}{5}$$

Since \frac{18}{45} and \frac{20}{45} have the same denominator, add them by adding their numerators.

$$\left(\frac{18+20}{45}-\frac{2}{3}\right)\times \frac{5}{2}-\frac{3}{5}$$

Add 18 and 20 to get 38.

$$\left(\frac{38}{45}-\frac{2}{3}\right)\times \frac{5}{2}-\frac{3}{5}$$

Least common multiple of 45 and 3 is 45. Convert \frac{38}{45} and \frac{2}{3} to fractions with denominator 45.

$$\left(\frac{38}{45}-\frac{30}{45}\right)\times \frac{5}{2}-\frac{3}{5}$$

Since \frac{38}{45} and \frac{30}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{38-30}{45}\times \frac{5}{2}-\frac{3}{5}$$

Subtract 30 from 38 to get 8.

$$\frac{8}{45}\times \frac{5}{2}-\frac{3}{5}$$

Multiply \frac{8}{45} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 5}{45\times 2}-\frac{3}{5}$$

Do the multiplications in the fraction \frac{8\times 5}{45\times 2}.

$$\frac{40}{90}-\frac{3}{5}$$

Reduce the fraction \frac{40}{90} to lowest terms by extracting and canceling out 10.

$$\frac{4}{9}-\frac{3}{5}$$

Least common multiple of 9 and 5 is 45. Convert \frac{4}{9} and \frac{3}{5} to fractions with denominator 45.

$$\frac{20}{45}-\frac{27}{45}$$

Since \frac{20}{45} and \frac{27}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-27}{45}$$

Subtract 27 from 20 to get -7.

$$-\frac{7}{45}$$

Factor

$$-\frac{7}{45} = -0.15555555555555556$$