Solve 1/2+3/2left(-0.125+0.25/-frac{1{5}-0.2}right)

$$\frac{ 1 }{ 2 } + \frac{ 3 }{ 2 } \left( -0.125+ \frac{ 0.25 }{ - \frac{ 1 }{ 5 } -0.2 } \right)$$

Evaluate

$$-0.625$$

Solution Steps

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125+\frac{0.25}{-\frac{1}{5}-\frac{1}{5}}\right)$$

Since -\frac{1}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125+\frac{0.25}{\frac{-1-1}{5}}\right)$$

Subtract 1 from -1 to get -2.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125+\frac{0.25}{-\frac{2}{5}}\right)$$

Divide 0.25 by -\frac{2}{5} by multiplying 0.25 by the reciprocal of -\frac{2}{5}.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125+0.25\left(-\frac{5}{2}\right)\right)$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125+\frac{1}{4}\left(-\frac{5}{2}\right)\right)$$

Multiply \frac{1}{4} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125+\frac{1\left(-5\right)}{4\times 2}\right)$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{4\times 2}.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125+\frac{-5}{8}\right)$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$\frac{1}{2}+\frac{3}{2}\left(-0.125-\frac{5}{8}\right)$$

Convert decimal number -0.125 to fraction -\frac{125}{1000}. Reduce the fraction -\frac{125}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{1}{2}+\frac{3}{2}\left(-\frac{1}{8}-\frac{5}{8}\right)$$

Since -\frac{1}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}+\frac{3}{2}\times \frac{-1-5}{8}$$

Subtract 5 from -1 to get -6.

$$\frac{1}{2}+\frac{3}{2}\times \frac{-6}{8}$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{3}{2} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\left(-3\right)}{2\times 4}.

$$\frac{1}{2}+\frac{-9}{8}$$

Fraction \frac{-9}{8} can be rewritten as -\frac{9}{8} by extracting the negative sign.

$$\frac{1}{2}-\frac{9}{8}$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{9}{8} to fractions with denominator 8.

$$\frac{4}{8}-\frac{9}{8}$$

Since \frac{4}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-9}{8}$$

Subtract 9 from 4 to get -5.

$$-\frac{5}{8}$$

Factor

$$-0.625$$