Solve (5/8*-9/7)+(3/7*5/8)-(frac{5}{8}*frac{-2}{7})

$$( \frac { 5 } { 8 } \times \frac { - 9 } { 7 } ) + ( \frac { 3 } { 7 } \times \frac { 5 } { 8 } ) - ( \frac { 5 } { 8 } \times \frac { - 2 } { 7 } )$$

Evaluate

$$-\frac{5}{14}\approx -0.357142857$$

Solution Steps

Fraction \frac{-9}{7} can be rewritten as -\frac{9}{7} by extracting the negative sign.

$$\frac{5}{8}\left(-\frac{9}{7}\right)+\frac{3}{7}\times \frac{5}{8}-\frac{5}{8}\times \frac{-2}{7}$$

Multiply \frac{5}{8} times -\frac{9}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-9\right)}{8\times 7}+\frac{3}{7}\times \frac{5}{8}-\frac{5}{8}\times \frac{-2}{7}$$

Do the multiplications in the fraction \frac{5\left(-9\right)}{8\times 7}.

$$\frac{-45}{56}+\frac{3}{7}\times \frac{5}{8}-\frac{5}{8}\times \frac{-2}{7}$$

Fraction \frac{-45}{56} can be rewritten as -\frac{45}{56} by extracting the negative sign.

$$-\frac{45}{56}+\frac{3}{7}\times \frac{5}{8}-\frac{5}{8}\times \frac{-2}{7}$$

Multiply \frac{3}{7} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{45}{56}+\frac{3\times 5}{7\times 8}-\frac{5}{8}\times \frac{-2}{7}$$

Do the multiplications in the fraction \frac{3\times 5}{7\times 8}.

$$-\frac{45}{56}+\frac{15}{56}-\frac{5}{8}\times \frac{-2}{7}$$

Since -\frac{45}{56} and \frac{15}{56} have the same denominator, add them by adding their numerators.

$$\frac{-45+15}{56}-\frac{5}{8}\times \frac{-2}{7}$$

Add -45 and 15 to get -30.

$$\frac{-30}{56}-\frac{5}{8}\times \frac{-2}{7}$$

Reduce the fraction \frac{-30}{56} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{28}-\frac{5}{8}\times \frac{-2}{7}$$

Fraction \frac{-2}{7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

$$-\frac{15}{28}-\frac{5}{8}\left(-\frac{2}{7}\right)$$

Multiply \frac{5}{8} times -\frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{15}{28}-\frac{5\left(-2\right)}{8\times 7}$$

Do the multiplications in the fraction \frac{5\left(-2\right)}{8\times 7}.

$$-\frac{15}{28}-\frac{-10}{56}$$

Reduce the fraction \frac{-10}{56} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{28}-\left(-\frac{5}{28}\right)$$

The opposite of -\frac{5}{28} is \frac{5}{28}.

$$-\frac{15}{28}+\frac{5}{28}$$

Since -\frac{15}{28} and \frac{5}{28} have the same denominator, add them by adding their numerators.

$$\frac{-15+5}{28}$$

Add -15 and 5 to get -10.

$$\frac{-10}{28}$$

Reduce the fraction \frac{-10}{28} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{14}$$

Factor

$$-\frac{5}{14} = -0.35714285714285715$$