Solve 3/5*(-1/4-1/6)*(-21/3)

$$\frac { 3 } { 5 } \times ( - \frac { 1 } { 4 } - \frac { 1 } { 6 } ) \cdot ( - 2 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

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

$$\frac{3}{5}\left(-\frac{3}{12}-\frac{2}{12}\right)\left(-\frac{2\times 3+1}{3}\right)$$

Since -\frac{3}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}\times \frac{-3-2}{12}\left(-\frac{2\times 3+1}{3}\right)$$

Subtract 2 from -3 to get -5.

$$\frac{3}{5}\left(-\frac{5}{12}\right)\left(-\frac{2\times 3+1}{3}\right)$$

Multiply \frac{3}{5} times -\frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-5\right)}{5\times 12}\left(-\frac{2\times 3+1}{3}\right)$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{5\times 12}.

$$\frac{-15}{60}\left(-\frac{2\times 3+1}{3}\right)$$

Reduce the fraction \frac{-15}{60} to lowest terms by extracting and canceling out 15.

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

Multiply 2 and 3 to get 6.

$$-\frac{1}{4}\left(-\frac{6+1}{3}\right)$$

Add 6 and 1 to get 7.

$$-\frac{1}{4}\left(-\frac{7}{3}\right)$$

Multiply -\frac{1}{4} times -\frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-7\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{-\left(-7\right)}{4\times 3}.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$