Solve E=-3/2div(8/12-5/4)

$$E = \frac { - 3 } { 2 } \div ( \frac { 8 } { 12 } - \frac { 5 } { 4 } )$$

Solve for E

$$E = \frac{18}{7} = 2\frac{4}{7} \approx 2.571428571$$

Steps for Solving Linear Equation

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

$$E=\frac{-\frac{3}{2}}{\frac{8}{12}-\frac{5}{4}}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$E=\frac{-\frac{3}{2}}{\frac{2}{3}-\frac{5}{4}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$E=\frac{-\frac{3}{2}}{\frac{8}{12}-\frac{15}{12}}$$

Since \frac{8}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$E=\frac{-\frac{3}{2}}{\frac{8-15}{12}}$$

Subtract 15 from 8 to get -7.

$$E=\frac{-\frac{3}{2}}{-\frac{7}{12}}$$

Divide -\frac{3}{2} by -\frac{7}{12} by multiplying -\frac{3}{2} by the reciprocal of -\frac{7}{12}.

$$E=-\frac{3}{2}\left(-\frac{12}{7}\right)$$

Multiply -\frac{3}{2} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$E=\frac{-3\left(-12\right)}{2\times 7}$$

Do the multiplications in the fraction \frac{-3\left(-12\right)}{2\times 7}.

$$E=\frac{36}{14}$$

Reduce the fraction \frac{36}{14} to lowest terms by extracting and canceling out 2.

$$E=\frac{18}{7}$$

Assign E

$$E≔\frac{18}{7}$$