Solve 2/4+5/9(3/5)-4/3

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

Evaluate

$$\frac{1}{18}\approx 0.055555556$$

Solution Steps

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

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

Multiply \frac{5}{9} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{1}{2}+\frac{1}{3}\left(-\frac{4}{3}\right)$$

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

$$\frac{1}{2}+\frac{1\left(-4\right)}{3\times 3}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{3\times 3}.

$$\frac{1}{2}+\frac{-4}{9}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{1}{2}-\frac{4}{9}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{9}{18}-\frac{8}{18}$$

Since \frac{9}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-8}{18}$$

Subtract 8 from 9 to get 1.

$$\frac{1}{18}$$

Factor

$$\frac{1}{2 \cdot 3 ^ {2}} = 0.05555555555555555$$