Solve B3/6(-3/4)+5/6-(-3/2)

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

Evaluate

$$-\frac{3B}{8}+\frac{7}{3}$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Multiply \frac{1}{2} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 4}.

$$B\times \frac{-3}{8}+\frac{5}{6}-\left(-\frac{3}{2}\right)$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$B\left(-\frac{3}{8}\right)+\frac{5}{6}-\left(-\frac{3}{2}\right)$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$B\left(-\frac{3}{8}\right)+\frac{5}{6}+\frac{3}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{3}{2} to fractions with denominator 6.

$$B\left(-\frac{3}{8}\right)+\frac{5}{6}+\frac{9}{6}$$

Since \frac{5}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$B\left(-\frac{3}{8}\right)+\frac{5+9}{6}$$

Add 5 and 9 to get 14.

$$B\left(-\frac{3}{8}\right)+\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$B\left(-\frac{3}{8}\right)+\frac{7}{3}$$

Factor

$$\frac{56-9B}{24}$$

Solution Steps

Factor out \frac{1}{24}.

$$\frac{-9B+56}{24}$$

Consider -9B+20+36. Multiply and combine like terms.

$$-9B+56$$

Rewrite the complete factored expression.

$$\frac{-9B+56}{24}$$