Solve {[(-3/20-1/4+6/5)+(-5/4)^2(-frac{4}{25})]:(-1+frac{1}{3})}:(-frac{1}{3})^2-frac{3}{10}

$$\{ [ ( - \frac { 3 } { 20 } - \frac { 1 } { 4 } + \frac { 6 } { 5 } ) + ( - \frac { 5 } { 4 } ) ^ { 2 } ( - \frac { 4 } { 25 } ) ] : ( - 1 + \frac { 1 } { 3 } ) \} : ( - \frac { 1 } { 3 } ) ^ { 2 } - \frac { 3 } { 10 }$$

Evaluate

$$-\frac{309}{40}=-7.725$$

Solution Steps

Least common multiple of 20 and 4 is 20. Convert -\frac{3}{20} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{-\frac{3}{20}-\frac{5}{20}+\frac{6}{5}+\left(-\frac{5}{4}\right)^{2}\left(-\frac{4}{25}\right)}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Since -\frac{3}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{-3-5}{20}+\frac{6}{5}+\left(-\frac{5}{4}\right)^{2}\left(-\frac{4}{25}\right)}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Subtract 5 from -3 to get -8.

$$\frac{\frac{\frac{-8}{20}+\frac{6}{5}+\left(-\frac{5}{4}\right)^{2}\left(-\frac{4}{25}\right)}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Reduce the fraction \frac{-8}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{-\frac{2}{5}+\frac{6}{5}+\left(-\frac{5}{4}\right)^{2}\left(-\frac{4}{25}\right)}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Since -\frac{2}{5} and \frac{6}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{-2+6}{5}+\left(-\frac{5}{4}\right)^{2}\left(-\frac{4}{25}\right)}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Add -2 and 6 to get 4.

$$\frac{\frac{\frac{4}{5}+\left(-\frac{5}{4}\right)^{2}\left(-\frac{4}{25}\right)}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Calculate -\frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{\frac{\frac{4}{5}+\frac{25}{16}\left(-\frac{4}{25}\right)}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Multiply \frac{25}{16} times -\frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{4}{5}+\frac{25\left(-4\right)}{16\times 25}}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Cancel out 25 in both numerator and denominator.

$$\frac{\frac{\frac{4}{5}+\frac{-4}{16}}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Reduce the fraction \frac{-4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{\frac{4}{5}-\frac{1}{4}}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Least common multiple of 5 and 4 is 20. Convert \frac{4}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{\frac{16}{20}-\frac{5}{20}}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Since \frac{16}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{16-5}{20}}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Subtract 5 from 16 to get 11.

$$\frac{\frac{\frac{11}{20}}{-1+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Convert -1 to fraction -\frac{3}{3}.

$$\frac{\frac{\frac{11}{20}}{-\frac{3}{3}+\frac{1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Since -\frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{11}{20}}{\frac{-3+1}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Add -3 and 1 to get -2.

$$\frac{\frac{\frac{11}{20}}{-\frac{2}{3}}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Divide \frac{11}{20} by -\frac{2}{3} by multiplying \frac{11}{20} by the reciprocal of -\frac{2}{3}.

$$\frac{\frac{11}{20}\left(-\frac{3}{2}\right)}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Multiply \frac{11}{20} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11\left(-3\right)}{20\times 2}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Do the multiplications in the fraction \frac{11\left(-3\right)}{20\times 2}.

$$\frac{\frac{-33}{40}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Fraction \frac{-33}{40} can be rewritten as -\frac{33}{40} by extracting the negative sign.

$$\frac{-\frac{33}{40}}{\left(-\frac{1}{3}\right)^{2}}-\frac{3}{10}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{-\frac{33}{40}}{\frac{1}{9}}-\frac{3}{10}$$

Divide -\frac{33}{40} by \frac{1}{9} by multiplying -\frac{33}{40} by the reciprocal of \frac{1}{9}.

$$-\frac{33}{40}\times 9-\frac{3}{10}$$

Express -\frac{33}{40}\times 9 as a single fraction.

$$\frac{-33\times 9}{40}-\frac{3}{10}$$

Multiply -33 and 9 to get -297.

$$\frac{-297}{40}-\frac{3}{10}$$

Fraction \frac{-297}{40} can be rewritten as -\frac{297}{40} by extracting the negative sign.

$$-\frac{297}{40}-\frac{3}{10}$$

Least common multiple of 40 and 10 is 40. Convert -\frac{297}{40} and \frac{3}{10} to fractions with denominator 40.

$$-\frac{297}{40}-\frac{12}{40}$$

Since -\frac{297}{40} and \frac{12}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-297-12}{40}$$

Subtract 12 from -297 to get -309.

$$-\frac{309}{40}$$

Factor

$$-\frac{309}{40} = -7\frac{29}{40} = -7.725$$