Solve (8+21/7*(-31/9))*(-7/4)

$$( 8 + 2 \frac { 1 } { 7 } \cdot ( - 3 \frac { 1 } { 9 } ) ) \cdot ( - \frac { 7 } { 4 } )$$

Evaluate

$$-\frac{7}{3}\approx -2.333333333$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\left(8+\frac{14+1}{7}\left(-\frac{3\times 9+1}{9}\right)\right)\left(-\frac{7}{4}\right)$$

Add 14 and 1 to get 15.

$$\left(8+\frac{15}{7}\left(-\frac{3\times 9+1}{9}\right)\right)\left(-\frac{7}{4}\right)$$

Multiply 3 and 9 to get 27.

$$\left(8+\frac{15}{7}\left(-\frac{27+1}{9}\right)\right)\left(-\frac{7}{4}\right)$$

Add 27 and 1 to get 28.

$$\left(8+\frac{15}{7}\left(-\frac{28}{9}\right)\right)\left(-\frac{7}{4}\right)$$

Multiply \frac{15}{7} times -\frac{28}{9} by multiplying numerator times numerator and denominator times denominator.

$$\left(8+\frac{15\left(-28\right)}{7\times 9}\right)\left(-\frac{7}{4}\right)$$

Do the multiplications in the fraction \frac{15\left(-28\right)}{7\times 9}.

$$\left(8+\frac{-420}{63}\right)\left(-\frac{7}{4}\right)$$

Reduce the fraction \frac{-420}{63} to lowest terms by extracting and canceling out 21.

$$\left(8-\frac{20}{3}\right)\left(-\frac{7}{4}\right)$$

Convert 8 to fraction \frac{24}{3}.

$$\left(\frac{24}{3}-\frac{20}{3}\right)\left(-\frac{7}{4}\right)$$

Since \frac{24}{3} and \frac{20}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-20}{3}\left(-\frac{7}{4}\right)$$

Subtract 20 from 24 to get 4.

$$\frac{4}{3}\left(-\frac{7}{4}\right)$$

Multiply \frac{4}{3} times -\frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-7\right)}{3\times 4}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-7}{3}$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$-\frac{7}{3}$$

Factor

$$-\frac{7}{3} = -2\frac{1}{3} = -2.3333333333333335$$