Solve 21/4*(-31/3)div13/7

$$2 \frac { 1 } { 4 } \times ( - 3 \frac { 1 } { 3 } ) \div 1 \frac { 3 } { 7 }$$

Evaluate

$$-\frac{21}{4}=-5.25$$

Solution Steps

Multiply 2 and 4 to get 8.

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

Add 8 and 1 to get 9.

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

Multiply 3 and 3 to get 9.

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

Add 9 and 1 to get 10.

$$\frac{\frac{9}{4}\left(-\frac{10}{3}\right)}{\frac{1\times 7+3}{7}}$$

Multiply \frac{9}{4} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\left(-10\right)}{4\times 3}}{\frac{1\times 7+3}{7}}$$

Do the multiplications in the fraction \frac{9\left(-10\right)}{4\times 3}.

$$\frac{\frac{-90}{12}}{\frac{1\times 7+3}{7}}$$

Reduce the fraction \frac{-90}{12} to lowest terms by extracting and canceling out 6.

$$\frac{-\frac{15}{2}}{\frac{1\times 7+3}{7}}$$

Multiply 1 and 7 to get 7.

$$\frac{-\frac{15}{2}}{\frac{7+3}{7}}$$

Add 7 and 3 to get 10.

$$\frac{-\frac{15}{2}}{\frac{10}{7}}$$

Divide -\frac{15}{2} by \frac{10}{7} by multiplying -\frac{15}{2} by the reciprocal of \frac{10}{7}.

$$-\frac{15}{2}\times \frac{7}{10}$$

Multiply -\frac{15}{2} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-15\times 7}{2\times 10}$$

Do the multiplications in the fraction \frac{-15\times 7}{2\times 10}.

$$\frac{-105}{20}$$

Reduce the fraction \frac{-105}{20} to lowest terms by extracting and canceling out 5.

$$-\frac{21}{4}$$

Factor

$$-\frac{21}{4} = -5\frac{1}{4} = -5.25$$