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

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

Evaluate

$$-\frac{21}{50}=-0.42$$

Solution Steps

Multiply \frac{7}{2} times \frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{7\times 4}{2\times 15}.

$$\frac{\frac{\left(\frac{2}{3}-\frac{28}{30}\right)\left(\frac{2}{10}+\frac{3}{5}\right)}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Reduce the fraction \frac{28}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{\left(\frac{2}{3}-\frac{14}{15}\right)\left(\frac{2}{10}+\frac{3}{5}\right)}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Least common multiple of 3 and 15 is 15. Convert \frac{2}{3} and \frac{14}{15} to fractions with denominator 15.

$$\frac{\frac{\left(\frac{10}{15}-\frac{14}{15}\right)\left(\frac{2}{10}+\frac{3}{5}\right)}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Since \frac{10}{15} and \frac{14}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{10-14}{15}\left(\frac{2}{10}+\frac{3}{5}\right)}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Subtract 14 from 10 to get -4.

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

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

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

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

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

Add 1 and 3 to get 4.

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

Multiply -\frac{4}{15} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-4\times 4}{15\times 5}.

$$\frac{\frac{\frac{-16}{75}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Fraction \frac{-16}{75} can be rewritten as -\frac{16}{75} by extracting the negative sign.

$$\frac{\frac{-\frac{16}{75}}{\frac{2}{3}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{\frac{-\frac{16}{75}}{\frac{6}{9}+\frac{4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{\frac{-\frac{16}{75}}{\frac{6+4}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Add 6 and 4 to get 10.

$$\frac{\frac{-\frac{16}{75}}{\frac{10}{9}}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Divide -\frac{16}{75} by \frac{10}{9} by multiplying -\frac{16}{75} by the reciprocal of \frac{10}{9}.

$$\frac{-\frac{16}{75}\times \frac{9}{10}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Multiply -\frac{16}{75} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-16\times 9}{75\times 10}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Do the multiplications in the fraction \frac{-16\times 9}{75\times 10}.

$$\frac{\frac{-144}{750}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

Reduce the fraction \frac{-144}{750} to lowest terms by extracting and canceling out 6.

$$\frac{-\frac{24}{125}}{\frac{3}{5}\times \frac{10}{7}-\frac{2}{5}}$$

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

$$\frac{-\frac{24}{125}}{\frac{3\times 10}{5\times 7}-\frac{2}{5}}$$

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

$$\frac{-\frac{24}{125}}{\frac{30}{35}-\frac{2}{5}}$$

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

$$\frac{-\frac{24}{125}}{\frac{6}{7}-\frac{2}{5}}$$

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

$$\frac{-\frac{24}{125}}{\frac{30}{35}-\frac{14}{35}}$$

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

$$\frac{-\frac{24}{125}}{\frac{30-14}{35}}$$

Subtract 14 from 30 to get 16.

$$\frac{-\frac{24}{125}}{\frac{16}{35}}$$

Divide -\frac{24}{125} by \frac{16}{35} by multiplying -\frac{24}{125} by the reciprocal of \frac{16}{35}.

$$-\frac{24}{125}\times \frac{35}{16}$$

Multiply -\frac{24}{125} times \frac{35}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-24\times 35}{125\times 16}$$

Do the multiplications in the fraction \frac{-24\times 35}{125\times 16}.

$$\frac{-840}{2000}$$

Reduce the fraction \frac{-840}{2000} to lowest terms by extracting and canceling out 40.

$$-\frac{21}{50}$$

Factor

$$-\frac{21}{50} = -0.42$$