Solve -21/4*2/3+31/2div(-21/3)

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

Evaluate

$$-3$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\left(-\frac{8+1}{4}\right)\times \frac{2}{3}+\frac{\frac{3\times 2+1}{2}}{-\frac{2\times 3+1}{3}}$$

Add 8 and 1 to get 9.

$$-\frac{9}{4}\times \frac{2}{3}+\frac{\frac{3\times 2+1}{2}}{-\frac{2\times 3+1}{3}}$$

Multiply -\frac{9}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\times 2}{4\times 3}+\frac{\frac{3\times 2+1}{2}}{-\frac{2\times 3+1}{3}}$$

Do the multiplications in the fraction \frac{-9\times 2}{4\times 3}.

$$\frac{-18}{12}+\frac{\frac{3\times 2+1}{2}}{-\frac{2\times 3+1}{3}}$$

Reduce the fraction \frac{-18}{12} to lowest terms by extracting and canceling out 6.

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

Multiply 3 and 2 to get 6.

$$-\frac{3}{2}+\frac{\frac{6+1}{2}}{-\frac{2\times 3+1}{3}}$$

Add 6 and 1 to get 7.

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

Multiply 2 and 3 to get 6.

$$-\frac{3}{2}+\frac{\frac{7}{2}}{-\frac{6+1}{3}}$$

Add 6 and 1 to get 7.

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

Divide \frac{7}{2} by -\frac{7}{3} by multiplying \frac{7}{2} by the reciprocal of -\frac{7}{3}.

$$-\frac{3}{2}+\frac{7}{2}\left(-\frac{3}{7}\right)$$

Multiply \frac{7}{2} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 7 in both numerator and denominator.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-\frac{3}{2}-\frac{3}{2}$$

Since -\frac{3}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-3}{2}$$

Subtract 3 from -3 to get -6.

$$\frac{-6}{2}$$

Divide -6 by 2 to get -3.

$$-3$$

Factor

$$-3$$