Solve (3-15/8*4/9-1/2)-2/3:frac{8}{15}]:[(frac{10}{7}*frac{14}{25}-frac{3}{5})*frac{10}{3}+frac{4}{9}]}*(3-frac{13}{8})

$$( 3 - \frac { 15 } { 8 } \times \frac { 4 } { 9 } - \frac { 1 } { 2 } ) - \frac { 2 } { 3 } : \frac { 8 } { 15 } ] : [ ( \frac { 10 } { 7 } \times \frac { 14 } { 25 } - \frac { 3 } { 5 } ) \times \frac { 10 } { 3 } + \frac { 4 } { 9 } ] \} \times ( 3 - \frac { 13 } { 8 } )$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

Multiply \frac{15}{8} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$3-\frac{15\times 4}{8\times 9}-\frac{1}{2}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Do the multiplications in the fraction \frac{15\times 4}{8\times 9}.

$$3-\frac{60}{72}-\frac{1}{2}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Reduce the fraction \frac{60}{72} to lowest terms by extracting and canceling out 12.

$$3-\frac{5}{6}-\frac{1}{2}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{18}{6}-\frac{5}{6}-\frac{1}{2}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Since \frac{18}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-5}{6}-\frac{1}{2}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Subtract 5 from 18 to get 13.

$$\frac{13}{6}-\frac{1}{2}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Least common multiple of 6 and 2 is 6. Convert \frac{13}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{13}{6}-\frac{3}{6}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Since \frac{13}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-3}{6}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Subtract 3 from 13 to get 10.

$$\frac{10}{6}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}-\frac{\frac{2}{3}}{\frac{8}{15}}$$

Divide \frac{2}{3} by \frac{8}{15} by multiplying \frac{2}{3} by the reciprocal of \frac{8}{15}.

$$\frac{5}{3}-\frac{2}{3}\times \frac{15}{8}$$

Multiply \frac{2}{3} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{3}-\frac{2\times 15}{3\times 8}$$

Do the multiplications in the fraction \frac{2\times 15}{3\times 8}.

$$\frac{5}{3}-\frac{30}{24}$$

Reduce the fraction \frac{30}{24} to lowest terms by extracting and canceling out 6.

$$\frac{5}{3}-\frac{5}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{20}{12}-\frac{15}{12}$$

Since \frac{20}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-15}{12}$$

Subtract 15 from 20 to get 5.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$