Solve [3/6*(3/4-5/2)-5/14:(frac{3}{2}+1)]*[frac{2}{5}*(frac{1}{3}-frac{1}{5})*-5]

$$[ \frac { 3 } { 6 } \cdot ( \frac { 3 } { 4 } - \frac { 5 } { 2 } ) - \frac { 5 } { 14 } : ( \frac { 3 } { 2 } + 1 ) ] \cdot [ \frac { 2 } { 5 } \cdot ( \frac { 1 } { 3 } - \frac { 1 } { 5 } ) \cdot - 5 ]$$

Evaluate

$$\frac{19}{70}\approx 0.271428571$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\left(\frac{1}{2}\left(\frac{3}{4}-\frac{5}{2}\right)-\frac{\frac{5}{14}}{\frac{3}{2}+1}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{5}{2} to fractions with denominator 4.

$$\left(\frac{1}{2}\left(\frac{3}{4}-\frac{10}{4}\right)-\frac{\frac{5}{14}}{\frac{3}{2}+1}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Since \frac{3}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{1}{2}\times \frac{3-10}{4}-\frac{\frac{5}{14}}{\frac{3}{2}+1}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Subtract 10 from 3 to get -7.

$$\left(\frac{1}{2}\left(-\frac{7}{4}\right)-\frac{\frac{5}{14}}{\frac{3}{2}+1}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Multiply \frac{1}{2} times -\frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{1\left(-7\right)}{2\times 4}-\frac{\frac{5}{14}}{\frac{3}{2}+1}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Do the multiplications in the fraction \frac{1\left(-7\right)}{2\times 4}.

$$\left(\frac{-7}{8}-\frac{\frac{5}{14}}{\frac{3}{2}+1}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Fraction \frac{-7}{8} can be rewritten as -\frac{7}{8} by extracting the negative sign.

$$\left(-\frac{7}{8}-\frac{\frac{5}{14}}{\frac{3}{2}+1}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Convert 1 to fraction \frac{2}{2}.

$$\left(-\frac{7}{8}-\frac{\frac{5}{14}}{\frac{3}{2}+\frac{2}{2}}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\left(-\frac{7}{8}-\frac{\frac{5}{14}}{\frac{3+2}{2}}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Add 3 and 2 to get 5.

$$\left(-\frac{7}{8}-\frac{\frac{5}{14}}{\frac{5}{2}}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Divide \frac{5}{14} by \frac{5}{2} by multiplying \frac{5}{14} by the reciprocal of \frac{5}{2}.

$$\left(-\frac{7}{8}-\frac{5}{14}\times \frac{2}{5}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Multiply \frac{5}{14} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\left(-\frac{7}{8}-\frac{5\times 2}{14\times 5}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Cancel out 5 in both numerator and denominator.

$$\left(-\frac{7}{8}-\frac{2}{14}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{7}{8}-\frac{1}{7}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Least common multiple of 8 and 7 is 56. Convert -\frac{7}{8} and \frac{1}{7} to fractions with denominator 56.

$$\left(-\frac{49}{56}-\frac{8}{56}\right)\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Since -\frac{49}{56} and \frac{8}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-49-8}{56}\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Subtract 8 from -49 to get -57.

$$-\frac{57}{56}\times \frac{2}{5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Multiply -\frac{57}{56} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-57\times 2}{56\times 5}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Do the multiplications in the fraction \frac{-57\times 2}{56\times 5}.

$$\frac{-114}{280}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Reduce the fraction \frac{-114}{280} to lowest terms by extracting and canceling out 2.

$$-\frac{57}{140}\left(\frac{1}{3}-\frac{1}{5}\right)\left(-5\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$-\frac{57}{140}\left(\frac{5}{15}-\frac{3}{15}\right)\left(-5\right)$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{57}{140}\times \frac{5-3}{15}\left(-5\right)$$

Subtract 3 from 5 to get 2.

$$-\frac{57}{140}\times \frac{2}{15}\left(-5\right)$$

Multiply -\frac{57}{140} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-57\times 2}{140\times 15}\left(-5\right)$$

Do the multiplications in the fraction \frac{-57\times 2}{140\times 15}.

$$\frac{-114}{2100}\left(-5\right)$$

Reduce the fraction \frac{-114}{2100} to lowest terms by extracting and canceling out 6.

$$-\frac{19}{350}\left(-5\right)$$

Express -\frac{19}{350}\left(-5\right) as a single fraction.

$$\frac{-19\left(-5\right)}{350}$$

Multiply -19 and -5 to get 95.

$$\frac{95}{350}$$

Reduce the fraction \frac{95}{350} to lowest terms by extracting and canceling out 5.

$$\frac{19}{70}$$

Factor

$$\frac{19}{2 \cdot 5 \cdot 7} = 0.2714285714285714$$