Solve (2/3-1/2*4/15)-(2/10+frac{3}{5}):(frac{2}{3}+frac{4}{9}):(frac{3}{5}*frac{10}{7}-frac{2}{5})=

$$( \frac { 2 } { 3 } - \frac { 1 } { 2 } \cdot \frac { 4 } { 15 } ) - ( \frac { 2 } { 10 } + \frac { 3 } { 5 } ) : ( \frac { 2 } { 3 } + \frac { 4 } { 9 } ) : ( \frac { 3 } { 5 } \cdot \frac { 10 } { 7 } - \frac { 2 } { 5 } ) =$$

Evaluate

$$-\frac{25}{24}\approx -1.041666667$$

Solution Steps

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

$$\frac{2}{3}-\frac{1\times 4}{2\times 15}-\frac{\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{2}{3}-\frac{4}{30}-\frac{\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{2}{3}-\frac{2}{15}-\frac{\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Least common multiple of 3 and 15 is 15. Convert \frac{2}{3} and \frac{2}{15} to fractions with denominator 15.

$$\frac{10}{15}-\frac{2}{15}-\frac{\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Since \frac{10}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-2}{15}-\frac{\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Subtract 2 from 10 to get 8.

$$\frac{8}{15}-\frac{\frac{\frac{2}{10}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{\frac{1}{5}+\frac{3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{\frac{1+3}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Add 1 and 3 to get 4.

$$\frac{8}{15}-\frac{\frac{\frac{4}{5}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{\frac{4}{5}}{\frac{6}{9}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{\frac{4}{5}}{\frac{6+4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Add 6 and 4 to get 10.

$$\frac{8}{15}-\frac{\frac{\frac{4}{5}}{\frac{10}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{4}{5}\times \frac{9}{10}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{4\times 9}{5\times 10}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{36}{50}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{8}{15}-\frac{\frac{18}{25}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Multiply \frac{3}{5} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{15}-\frac{\frac{18}{25}}{\frac{3\times 10}{5\times 7}-\frac{2}{5}}$$

Do the multiplications in the fraction \frac{3\times 10}{5\times 7}.

$$\frac{8}{15}-\frac{\frac{18}{25}}{\frac{30}{35}-\frac{2}{5}}$$

Reduce the fraction \frac{30}{35} to lowest terms by extracting and canceling out 5.

$$\frac{8}{15}-\frac{\frac{18}{25}}{\frac{6}{7}-\frac{2}{5}}$$

Least common multiple of 7 and 5 is 35. Convert \frac{6}{7} and \frac{2}{5} to fractions with denominator 35.

$$\frac{8}{15}-\frac{\frac{18}{25}}{\frac{30}{35}-\frac{14}{35}}$$

Since \frac{30}{35} and \frac{14}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{15}-\frac{\frac{18}{25}}{\frac{30-14}{35}}$$

Subtract 14 from 30 to get 16.

$$\frac{8}{15}-\frac{\frac{18}{25}}{\frac{16}{35}}$$

Divide \frac{18}{25} by \frac{16}{35} by multiplying \frac{18}{25} by the reciprocal of \frac{16}{35}.

$$\frac{8}{15}-\frac{18}{25}\times \frac{35}{16}$$

Multiply \frac{18}{25} times \frac{35}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{15}-\frac{18\times 35}{25\times 16}$$

Do the multiplications in the fraction \frac{18\times 35}{25\times 16}.

$$\frac{8}{15}-\frac{630}{400}$$

Reduce the fraction \frac{630}{400} to lowest terms by extracting and canceling out 10.

$$\frac{8}{15}-\frac{63}{40}$$

Least common multiple of 15 and 40 is 120. Convert \frac{8}{15} and \frac{63}{40} to fractions with denominator 120.

$$\frac{64}{120}-\frac{189}{120}$$

Since \frac{64}{120} and \frac{189}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-189}{120}$$

Subtract 189 from 64 to get -125.

$$\frac{-125}{120}$$

Reduce the fraction \frac{-125}{120} to lowest terms by extracting and canceling out 5.

$$-\frac{25}{24}$$

Factor

$$-\frac{25}{24} = -1\frac{1}{24} = -1.0416666666666667$$