Solve -5/-16*(16/5+16/25-16)

$$- \frac { 5 } { - 16 } \times ( \frac { 16 } { 5 } + \frac { 16 } { 25 } - 16 )$$

Evaluate

$$-\frac{19}{5}=-3.8$$

Solution Steps

Fraction \frac{5}{-16} can be rewritten as -\frac{5}{16} by extracting the negative sign.

$$\left(-\left(-\frac{5}{16}\right)\right)\left(\frac{16}{5}+\frac{16}{25}-16\right)$$

The opposite of -\frac{5}{16} is \frac{5}{16}.

$$\frac{5}{16}\left(\frac{16}{5}+\frac{16}{25}-16\right)$$

Least common multiple of 5 and 25 is 25. Convert \frac{16}{5} and \frac{16}{25} to fractions with denominator 25.

$$\frac{5}{16}\left(\frac{80}{25}+\frac{16}{25}-16\right)$$

Since \frac{80}{25} and \frac{16}{25} have the same denominator, add them by adding their numerators.

$$\frac{5}{16}\left(\frac{80+16}{25}-16\right)$$

Add 80 and 16 to get 96.

$$\frac{5}{16}\left(\frac{96}{25}-16\right)$$

Convert 16 to fraction \frac{400}{25}.

$$\frac{5}{16}\left(\frac{96}{25}-\frac{400}{25}\right)$$

Since \frac{96}{25} and \frac{400}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{16}\times \frac{96-400}{25}$$

Subtract 400 from 96 to get -304.

$$\frac{5}{16}\left(-\frac{304}{25}\right)$$

Multiply \frac{5}{16} times -\frac{304}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-304\right)}{16\times 25}$$

Do the multiplications in the fraction \frac{5\left(-304\right)}{16\times 25}.

$$\frac{-1520}{400}$$

Reduce the fraction \frac{-1520}{400} to lowest terms by extracting and canceling out 80.

$$-\frac{19}{5}$$

Factor

$$-\frac{19}{5} = -3\frac{4}{5} = -3.8$$