Solve B=2/3+4/8/frac{-5{4}div3/2}

$$B = \frac { \frac { 2 } { 3 } + \frac { 4 } { 8 } } { \frac { - 5 } { 4 } \div \frac { 3 } { 2 } }$$

Solve for B

$$B = -\frac{7}{5} = -1\frac{2}{5} = -1.4$$

Steps for Solving Linear Equation

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

$$B=\frac{\frac{2}{3}+\frac{1}{2}}{\frac{\frac{-5}{4}}{\frac{3}{2}}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$B=\frac{\frac{4}{6}+\frac{3}{6}}{\frac{\frac{-5}{4}}{\frac{3}{2}}}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$B=\frac{\frac{4+3}{6}}{\frac{\frac{-5}{4}}{\frac{3}{2}}}$$

Add 4 and 3 to get 7.

$$B=\frac{\frac{7}{6}}{\frac{\frac{-5}{4}}{\frac{3}{2}}}$$

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$B=\frac{\frac{7}{6}}{\frac{-\frac{5}{4}}{\frac{3}{2}}}$$

Divide -\frac{5}{4} by \frac{3}{2} by multiplying -\frac{5}{4} by the reciprocal of \frac{3}{2}.

$$B=\frac{\frac{7}{6}}{-\frac{5}{4}\times \frac{2}{3}}$$

Multiply -\frac{5}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$B=\frac{\frac{7}{6}}{\frac{-5\times 2}{4\times 3}}$$

Do the multiplications in the fraction \frac{-5\times 2}{4\times 3}.

$$B=\frac{\frac{7}{6}}{\frac{-10}{12}}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$B=\frac{\frac{7}{6}}{-\frac{5}{6}}$$

Divide \frac{7}{6} by -\frac{5}{6} by multiplying \frac{7}{6} by the reciprocal of -\frac{5}{6}.

$$B=\frac{7}{6}\left(-\frac{6}{5}\right)$$

Multiply \frac{7}{6} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$B=\frac{7\left(-6\right)}{6\times 5}$$

Do the multiplications in the fraction \frac{7\left(-6\right)}{6\times 5}.

$$B=\frac{-42}{30}$$

Reduce the fraction \frac{-42}{30} to lowest terms by extracting and canceling out 6.

$$B=-\frac{7}{5}$$

Assign B

$$B≔-\frac{7}{5}$$