Solve {31/13-8/3}*(-2/5*7/2)

$$\{ \frac { 31 } { 13 } - \frac { 8 } { 3 } \} \cdot ( - \frac { 2 } { 5 } \times \frac { 7 } { 2 } )$$

Evaluate

$$\frac{77}{195}\approx 0.394871795$$

Solution Steps

Least common multiple of 13 and 3 is 39. Convert \frac{31}{13} and \frac{8}{3} to fractions with denominator 39.

$$\left(\frac{93}{39}-\frac{104}{39}\right)\left(-\frac{2}{5}\right)\times \frac{7}{2}$$

Since \frac{93}{39} and \frac{104}{39} have the same denominator, subtract them by subtracting their numerators.

$$\frac{93-104}{39}\left(-\frac{2}{5}\right)\times \frac{7}{2}$$

Subtract 104 from 93 to get -11.

$$-\frac{11}{39}\left(-\frac{2}{5}\right)\times \frac{7}{2}$$

Multiply -\frac{11}{39} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\left(-2\right)}{39\times 5}\times \frac{7}{2}$$

Do the multiplications in the fraction \frac{-11\left(-2\right)}{39\times 5}.

$$\frac{22}{195}\times \frac{7}{2}$$

Multiply \frac{22}{195} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 7}{195\times 2}$$

Do the multiplications in the fraction \frac{22\times 7}{195\times 2}.

$$\frac{154}{390}$$

Reduce the fraction \frac{154}{390} to lowest terms by extracting and canceling out 2.

$$\frac{77}{195}$$

Factor

$$\frac{7 \cdot 11}{3 \cdot 5 \cdot 13} = 0.39487179487179486$$