Solve {l}{-1/4+(-4/5)}{*21/6-5/16}

$$\left. \begin{array} { l } { - \frac { 1 } { 4 } + ( - \frac { 4 } { 5 } ) } \\ { \times 2 \frac { 1 } { 6 } - \frac { 5 } { 16 } } \end{array} \right.$$

Evaluate

$$-\frac{551}{240}\approx -2.295833333$$

Solution Steps

Multiply 2 and 6 to get 12.

$$-\frac{1}{4}-\frac{4}{5}\times \frac{12+1}{6}-\frac{5}{16}$$

Add 12 and 1 to get 13.

$$-\frac{1}{4}-\frac{4}{5}\times \frac{13}{6}-\frac{5}{16}$$

Multiply -\frac{4}{5} times \frac{13}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{4}+\frac{-4\times 13}{5\times 6}-\frac{5}{16}$$

Do the multiplications in the fraction \frac{-4\times 13}{5\times 6}.

$$-\frac{1}{4}+\frac{-52}{30}-\frac{5}{16}$$

Reduce the fraction \frac{-52}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{4}-\frac{26}{15}-\frac{5}{16}$$

Least common multiple of 4 and 15 is 60. Convert -\frac{1}{4} and \frac{26}{15} to fractions with denominator 60.

$$-\frac{15}{60}-\frac{104}{60}-\frac{5}{16}$$

Since -\frac{15}{60} and \frac{104}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-104}{60}-\frac{5}{16}$$

Subtract 104 from -15 to get -119.

$$-\frac{119}{60}-\frac{5}{16}$$

Least common multiple of 60 and 16 is 240. Convert -\frac{119}{60} and \frac{5}{16} to fractions with denominator 240.

$$-\frac{476}{240}-\frac{75}{240}$$

Since -\frac{476}{240} and \frac{75}{240} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-476-75}{240}$$

Subtract 75 from -476 to get -551.

$$-\frac{551}{240}$$

Factor

$$-\frac{551}{240} = -2\frac{71}{240} = -2.2958333333333334$$