Solve 11/2div(-11/3)-31/4

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

Evaluate

$$-\frac{35}{8}=-4.375$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

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

Divide \frac{3}{2} by -\frac{4}{3} by multiplying \frac{3}{2} by the reciprocal of -\frac{4}{3}.

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

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

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

Do the multiplications in the fraction \frac{3\left(-3\right)}{2\times 4}.

$$\frac{-9}{8}-\frac{3\times 4+1}{4}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$-\frac{9}{8}-\frac{3\times 4+1}{4}$$

Multiply 3 and 4 to get 12.

$$-\frac{9}{8}-\frac{12+1}{4}$$

Add 12 and 1 to get 13.

$$-\frac{9}{8}-\frac{13}{4}$$

Least common multiple of 8 and 4 is 8. Convert -\frac{9}{8} and \frac{13}{4} to fractions with denominator 8.

$$-\frac{9}{8}-\frac{26}{8}$$

Since -\frac{9}{8} and \frac{26}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-26}{8}$$

Subtract 26 from -9 to get -35.

$$-\frac{35}{8}$$

Factor

$$-\frac{35}{8} = -4\frac{3}{8} = -4.375$$