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

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

Evaluate

$$-\frac{2}{9}\approx -0.222222222$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$\left(-\frac{5}{15}-\frac{3}{15}\right)\left(\frac{1}{4}+\frac{1}{6}\right)$$

Since -\frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-3}{15}\left(\frac{1}{4}+\frac{1}{6}\right)$$

Subtract 3 from -5 to get -8.

$$-\frac{8}{15}\left(\frac{1}{4}+\frac{1}{6}\right)$$

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

$$-\frac{8}{15}\left(\frac{3}{12}+\frac{2}{12}\right)$$

Since \frac{3}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$-\frac{8}{15}\times \frac{3+2}{12}$$

Add 3 and 2 to get 5.

$$-\frac{8}{15}\times \frac{5}{12}$$

Multiply -\frac{8}{15} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8\times 5}{15\times 12}$$

Do the multiplications in the fraction \frac{-8\times 5}{15\times 12}.

$$\frac{-40}{180}$$

Reduce the fraction \frac{-40}{180} to lowest terms by extracting and canceling out 20.

$$-\frac{2}{9}$$

Factor

$$-\frac{2}{9} = -0.2222222222222222$$