Solve {2/3div3/4-(4/9-1/3)}*frac{3}{5}

$$\{ \frac { 2 } { 3 } \div \frac { 3 } { 4 } - ( \frac { 4 } { 9 } - \frac { 1 } { 3 } ) \} \times \frac { 3 } { 5 }$$

Evaluate

$$\frac{7}{15}\approx 0.466666667$$

Solution Steps

Divide \frac{2}{3} by \frac{3}{4} by multiplying \frac{2}{3} by the reciprocal of \frac{3}{4}.

$$\left(\frac{2}{3}\times \frac{4}{3}-\left(\frac{4}{9}-\frac{1}{3}\right)\right)\times \frac{3}{5}$$

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

$$\left(\frac{2\times 4}{3\times 3}-\left(\frac{4}{9}-\frac{1}{3}\right)\right)\times \frac{3}{5}$$

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

$$\left(\frac{8}{9}-\left(\frac{4}{9}-\frac{1}{3}\right)\right)\times \frac{3}{5}$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{1}{3} to fractions with denominator 9.

$$\left(\frac{8}{9}-\left(\frac{4}{9}-\frac{3}{9}\right)\right)\times \frac{3}{5}$$

Since \frac{4}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8}{9}-\frac{4-3}{9}\right)\times \frac{3}{5}$$

Subtract 3 from 4 to get 1.

$$\left(\frac{8}{9}-\frac{1}{9}\right)\times \frac{3}{5}$$

Since \frac{8}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-1}{9}\times \frac{3}{5}$$

Subtract 1 from 8 to get 7.

$$\frac{7}{9}\times \frac{3}{5}$$

Multiply \frac{7}{9} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{9\times 5}$$

Do the multiplications in the fraction \frac{7\times 3}{9\times 5}.

$$\frac{21}{45}$$

Reduce the fraction \frac{21}{45} to lowest terms by extracting and canceling out 3.

$$\frac{7}{15}$$

Factor

$$\frac{7}{3 \cdot 5} = 0.4666666666666667$$