Solve 4/3*(1/6-9/4)

$$\frac { 4 } { 3 } \cdot ( \frac { 1 } { 6 } - \frac { 9 } { 4 } )$$

Evaluate

$$-\frac{25}{9}\approx -2.777777778$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{9}{4} to fractions with denominator 12.

$$\frac{4}{3}\left(\frac{2}{12}-\frac{27}{12}\right)$$

Since \frac{2}{12} and \frac{27}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}\times \frac{2-27}{12}$$

Subtract 27 from 2 to get -25.

$$\frac{4}{3}\left(-\frac{25}{12}\right)$$

Multiply \frac{4}{3} times -\frac{25}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-25\right)}{3\times 12}$$

Do the multiplications in the fraction \frac{4\left(-25\right)}{3\times 12}.

$$\frac{-100}{36}$$

Reduce the fraction \frac{-100}{36} to lowest terms by extracting and canceling out 4.

$$-\frac{25}{9}$$

Factor

$$-\frac{25}{9} = -2\frac{7}{9} = -2.7777777777777777$$