Solve -7*[51/2*(-15/6)]div23/4

$$- 7 \cdot [ 5 \frac { 1 } { 2 } \times ( - 1 \frac { 5 } { 6 } ) ] \div 2 \frac { 3 } { 4 }$$

Evaluate

$$\frac{77}{3}\approx 25.666666667$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\frac{-7\times \frac{10+1}{2}\left(-\frac{6+5}{6}\right)}{\frac{2\times 4+3}{4}}$$

Add 10 and 1 to get 11.

$$\frac{-7\times \frac{11}{2}\left(-\frac{6+5}{6}\right)}{\frac{2\times 4+3}{4}}$$

Express -7\times \frac{11}{2} as a single fraction.

$$\frac{\frac{-7\times 11}{2}\left(-\frac{1\times 6+5}{6}\right)}{\frac{2\times 4+3}{4}}$$

Multiply -7 and 11 to get -77.

$$\frac{\frac{-77}{2}\left(-\frac{1\times 6+5}{6}\right)}{\frac{2\times 4+3}{4}}$$

Fraction \frac{-77}{2} can be rewritten as -\frac{77}{2} by extracting the negative sign.

$$\frac{-\frac{77}{2}\left(-\frac{6+5}{6}\right)}{\frac{2\times 4+3}{4}}$$

Add 6 and 5 to get 11.

$$\frac{-\frac{77}{2}\left(-\frac{11}{6}\right)}{\frac{2\times 4+3}{4}}$$

Multiply -\frac{77}{2} times -\frac{11}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-77\left(-11\right)}{2\times 6}}{\frac{2\times 4+3}{4}}$$

Do the multiplications in the fraction \frac{-77\left(-11\right)}{2\times 6}.

$$\frac{\frac{847}{12}}{\frac{2\times 4+3}{4}}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{847}{12}}{\frac{8+3}{4}}$$

Add 8 and 3 to get 11.

$$\frac{\frac{847}{12}}{\frac{11}{4}}$$

Divide \frac{847}{12} by \frac{11}{4} by multiplying \frac{847}{12} by the reciprocal of \frac{11}{4}.

$$\frac{847}{12}\times \frac{4}{11}$$

Multiply \frac{847}{12} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{847\times 4}{12\times 11}$$

Do the multiplications in the fraction \frac{847\times 4}{12\times 11}.

$$\frac{3388}{132}$$

Reduce the fraction \frac{3388}{132} to lowest terms by extracting and canceling out 44.

$$\frac{77}{3}$$

Factor

$$\frac{7 \cdot 11}{3} = 25\frac{2}{3} = 25.666666666666668$$