Solve [(z/3-1/2*4/15)-(2/10+frac{3}{5}):(frac{2}{3}+frac{4}{9})]

$$[ ( \frac { z } { 3 } - \frac { 1 } { 2 } \cdot \frac { 4 } { 15 } ) - ( \frac { 2 } { 10 } + \frac { 3 } { 5 } ) : ( \frac { 2 } { 3 } + \frac { 4 } { 9 } ) ]$$

Evaluate

$$\frac{z}{3}-\frac{64}{75}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{z}{3}-\frac{1\times 4}{2\times 15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 15}.

$$\frac{z}{3}-\frac{4}{30}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{z}{3}-\frac{2}{15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 15 is 15. Multiply \frac{z}{3} times \frac{5}{5}.

$$\frac{5z}{15}-\frac{2}{15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Since \frac{5z}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5z-2}{15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{5z-2}{15}-\frac{\frac{1}{5}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Since \frac{1}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{5z-2}{15}-\frac{\frac{1+3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Add 1 and 3 to get 4.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{6}{9}+\frac{4}{9}}$$

Since \frac{6}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{6+4}{9}}$$

Add 6 and 4 to get 10.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{10}{9}}$$

Divide \frac{4}{5} by \frac{10}{9} by multiplying \frac{4}{5} by the reciprocal of \frac{10}{9}.

$$\frac{5z-2}{15}-\frac{4}{5}\times \frac{9}{10}$$

Multiply \frac{4}{5} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5z-2}{15}-\frac{4\times 9}{5\times 10}$$

Do the multiplications in the fraction \frac{4\times 9}{5\times 10}.

$$\frac{5z-2}{15}-\frac{36}{50}$$

Reduce the fraction \frac{36}{50} to lowest terms by extracting and canceling out 2.

$$\frac{5z-2}{15}-\frac{18}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 25 is 75. Multiply \frac{5z-2}{15} times \frac{5}{5}. Multiply \frac{18}{25} times \frac{3}{3}.

$$\frac{5\left(5z-2\right)}{75}-\frac{18\times 3}{75}$$

Since \frac{5\left(5z-2\right)}{75} and \frac{18\times 3}{75} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(5z-2\right)-18\times 3}{75}$$

Do the multiplications in 5\left(5z-2\right)-18\times 3.

$$\frac{25z-10-54}{75}$$

Combine like terms in 25z-10-54.

$$\frac{25z-64}{75}$$

Expand

$$\frac{z}{3}-\frac{64}{75}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{z}{3}-\frac{1\times 4}{2\times 15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 15}.

$$\frac{z}{3}-\frac{4}{30}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{z}{3}-\frac{2}{15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 15 is 15. Multiply \frac{z}{3} times \frac{5}{5}.

$$\frac{5z}{15}-\frac{2}{15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Since \frac{5z}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5z-2}{15}-\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{5z-2}{15}-\frac{\frac{1}{5}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Since \frac{1}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{5z-2}{15}-\frac{\frac{1+3}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Add 1 and 3 to get 4.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{2}{3}+\frac{4}{9}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{6}{9}+\frac{4}{9}}$$

Since \frac{6}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{6+4}{9}}$$

Add 6 and 4 to get 10.

$$\frac{5z-2}{15}-\frac{\frac{4}{5}}{\frac{10}{9}}$$

Divide \frac{4}{5} by \frac{10}{9} by multiplying \frac{4}{5} by the reciprocal of \frac{10}{9}.

$$\frac{5z-2}{15}-\frac{4}{5}\times \frac{9}{10}$$

Multiply \frac{4}{5} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5z-2}{15}-\frac{4\times 9}{5\times 10}$$

Do the multiplications in the fraction \frac{4\times 9}{5\times 10}.

$$\frac{5z-2}{15}-\frac{36}{50}$$

Reduce the fraction \frac{36}{50} to lowest terms by extracting and canceling out 2.

$$\frac{5z-2}{15}-\frac{18}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 25 is 75. Multiply \frac{5z-2}{15} times \frac{5}{5}. Multiply \frac{18}{25} times \frac{3}{3}.

$$\frac{5\left(5z-2\right)}{75}-\frac{18\times 3}{75}$$

Since \frac{5\left(5z-2\right)}{75} and \frac{18\times 3}{75} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(5z-2\right)-18\times 3}{75}$$

Do the multiplications in 5\left(5z-2\right)-18\times 3.

$$\frac{25z-10-54}{75}$$

Combine like terms in 25z-10-54.

$$\frac{25z-64}{75}$$