Solve 1/4left(-3/4-1/2right)+1/5left(-frac{3}{5}+frac{1}{2}right)

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

Evaluate

$$-\frac{133}{400}=-0.3325$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since -\frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from -3 to get -5.

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

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

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

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

$$\frac{-5}{16}+\frac{1}{5}\left(-\frac{3}{5}+\frac{1}{2}\right)$$

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

$$-\frac{5}{16}+\frac{1}{5}\left(-\frac{3}{5}+\frac{1}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert -\frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$-\frac{5}{16}+\frac{1}{5}\left(-\frac{6}{10}+\frac{5}{10}\right)$$

Since -\frac{6}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$-\frac{5}{16}+\frac{1}{5}\times \frac{-6+5}{10}$$

Add -6 and 5 to get -1.

$$-\frac{5}{16}+\frac{1}{5}\left(-\frac{1}{10}\right)$$

Multiply \frac{1}{5} times -\frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{16}+\frac{1\left(-1\right)}{5\times 10}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{5\times 10}.

$$-\frac{5}{16}+\frac{-1}{50}$$

Fraction \frac{-1}{50} can be rewritten as -\frac{1}{50} by extracting the negative sign.

$$-\frac{5}{16}-\frac{1}{50}$$

Least common multiple of 16 and 50 is 400. Convert -\frac{5}{16} and \frac{1}{50} to fractions with denominator 400.

$$-\frac{125}{400}-\frac{8}{400}$$

Since -\frac{125}{400} and \frac{8}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-125-8}{400}$$

Subtract 8 from -125 to get -133.

$$-\frac{133}{400}$$

Factor

$$-\frac{133}{400} = -0.3325$$