Solve (5/9-1/3:3/2)+1/2*frac{5}{3}

$$( \frac { 5 } { 9 } - \frac { 1 } { 3 } : \frac { 3 } { 2 } ) + \frac { 1 } { 2 } \cdot \frac { 5 } { 3 }$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Divide \frac{1}{3} by \frac{3}{2} by multiplying \frac{1}{3} by the reciprocal of \frac{3}{2}.

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

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

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

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

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

Since \frac{5}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 5 to get 3.

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

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

$$\frac{1}{3}+\frac{1}{2}\times \frac{5}{3}$$

Multiply \frac{1}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{1\times 5}{2\times 3}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 3}.

$$\frac{1}{3}+\frac{5}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{2}{6}+\frac{5}{6}$$

Since \frac{2}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{2+5}{6}$$

Add 2 and 5 to get 7.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$