Solve -5/4+5/2*[(-3/5)^2-(1/2)^4*(-3.2)]div(-2frac{4}{5})

$$- \frac { 5 } { 4 } + \frac { 5 } { 2 } \times [ ( - \frac { 3 } { 5 } ) ^ { 2 } - ( \frac { 1 } { 2 } ) ^ { 4 } \times ( - 3.2 ) ] \div ( - 2 \frac { 4 } { 5 } )$$

Evaluate

$$-1.75$$

Solution Steps

Calculate -\frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\left(\frac{1}{2}\right)^{4}\left(-3.2\right)\right)}{-\frac{2\times 5+4}{5}}$$

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{1}{16}\left(-3.2\right)\right)}{-\frac{2\times 5+4}{5}}$$

Convert decimal number -3.2 to fraction -\frac{32}{10}. Reduce the fraction -\frac{32}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{1}{16}\left(-\frac{16}{5}\right)\right)}{-\frac{2\times 5+4}{5}}$$

Multiply \frac{1}{16} times -\frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{1\left(-16\right)}{16\times 5}\right)}{-\frac{2\times 5+4}{5}}$$

Do the multiplications in the fraction \frac{1\left(-16\right)}{16\times 5}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{-16}{80}\right)}{-\frac{2\times 5+4}{5}}$$

Reduce the fraction \frac{-16}{80} to lowest terms by extracting and canceling out 16.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\left(-\frac{1}{5}\right)\right)}{-\frac{2\times 5+4}{5}}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}+\frac{1}{5}\right)}{-\frac{2\times 5+4}{5}}$$

Least common multiple of 25 and 5 is 25. Convert \frac{9}{25} and \frac{1}{5} to fractions with denominator 25.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}+\frac{5}{25}\right)}{-\frac{2\times 5+4}{5}}$$

Since \frac{9}{25} and \frac{5}{25} have the same denominator, add them by adding their numerators.

$$-\frac{5}{4}+\frac{\frac{5}{2}\times \frac{9+5}{25}}{-\frac{2\times 5+4}{5}}$$

Add 9 and 5 to get 14.

$$-\frac{5}{4}+\frac{\frac{5}{2}\times \frac{14}{25}}{-\frac{2\times 5+4}{5}}$$

Multiply \frac{5}{2} times \frac{14}{25} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{4}+\frac{\frac{5\times 14}{2\times 25}}{-\frac{2\times 5+4}{5}}$$

Do the multiplications in the fraction \frac{5\times 14}{2\times 25}.

$$-\frac{5}{4}+\frac{\frac{70}{50}}{-\frac{2\times 5+4}{5}}$$

Reduce the fraction \frac{70}{50} to lowest terms by extracting and canceling out 10.

$$-\frac{5}{4}+\frac{\frac{7}{5}}{-\frac{2\times 5+4}{5}}$$

Multiply 2 and 5 to get 10.

$$-\frac{5}{4}+\frac{\frac{7}{5}}{-\frac{10+4}{5}}$$

Add 10 and 4 to get 14.

$$-\frac{5}{4}+\frac{\frac{7}{5}}{-\frac{14}{5}}$$

Divide \frac{7}{5} by -\frac{14}{5} by multiplying \frac{7}{5} by the reciprocal of -\frac{14}{5}.

$$-\frac{5}{4}+\frac{7}{5}\left(-\frac{5}{14}\right)$$

Multiply \frac{7}{5} times -\frac{5}{14} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{4}+\frac{7\left(-5\right)}{5\times 14}$$

Do the multiplications in the fraction \frac{7\left(-5\right)}{5\times 14}.

$$-\frac{5}{4}+\frac{-35}{70}$$

Reduce the fraction \frac{-35}{70} to lowest terms by extracting and canceling out 35.

$$-\frac{5}{4}-\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

$$-\frac{5}{4}-\frac{2}{4}$$

Since -\frac{5}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-2}{4}$$

Subtract 2 from -5 to get -7.

$$-\frac{7}{4}$$

Factor

$$-1.75$$