Solve (40:(-22/15)-255/7:(-11/35)):(-217/9:4frac{2}{3}+1)*(-3frac{2}{3})

$$( 40 : ( - 2 \frac { 2 } { 15 } ) - 25 \frac { 5 } { 7 } : ( - 1 \frac { 1 } { 35 } ) ) : ( - 21 \frac { 7 } { 9 } : 4 \frac { 2 } { 3 } + 1 ) \cdot ( - 3 \frac { 2 } { 3 } )$$

Evaluate

$$\frac{25}{4}=6.25$$

Solution Steps

Multiply 2 and 15 to get 30.

$$\frac{\frac{40}{-\frac{30+2}{15}}-\frac{\frac{25\times 7+5}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Add 30 and 2 to get 32.

$$\frac{\frac{40}{-\frac{32}{15}}-\frac{\frac{25\times 7+5}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Divide 40 by -\frac{32}{15} by multiplying 40 by the reciprocal of -\frac{32}{15}.

$$\frac{40\left(-\frac{15}{32}\right)-\frac{\frac{25\times 7+5}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Express 40\left(-\frac{15}{32}\right) as a single fraction.

$$\frac{\frac{40\left(-15\right)}{32}-\frac{\frac{25\times 7+5}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply 40 and -15 to get -600.

$$\frac{\frac{-600}{32}-\frac{\frac{25\times 7+5}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Reduce the fraction \frac{-600}{32} to lowest terms by extracting and canceling out 8.

$$\frac{-\frac{75}{4}-\frac{\frac{25\times 7+5}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply 25 and 7 to get 175.

$$\frac{-\frac{75}{4}-\frac{\frac{175+5}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Add 175 and 5 to get 180.

$$\frac{-\frac{75}{4}-\frac{\frac{180}{7}}{-\frac{1\times 35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply 1 and 35 to get 35.

$$\frac{-\frac{75}{4}-\frac{\frac{180}{7}}{-\frac{35+1}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Add 35 and 1 to get 36.

$$\frac{-\frac{75}{4}-\frac{\frac{180}{7}}{-\frac{36}{35}}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Divide \frac{180}{7} by -\frac{36}{35} by multiplying \frac{180}{7} by the reciprocal of -\frac{36}{35}.

$$\frac{-\frac{75}{4}-\frac{180}{7}\left(-\frac{35}{36}\right)}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply \frac{180}{7} times -\frac{35}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{75}{4}-\frac{180\left(-35\right)}{7\times 36}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Do the multiplications in the fraction \frac{180\left(-35\right)}{7\times 36}.

$$\frac{-\frac{75}{4}-\frac{-6300}{252}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Divide -6300 by 252 to get -25.

$$\frac{-\frac{75}{4}-\left(-25\right)}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

The opposite of -25 is 25.

$$\frac{-\frac{75}{4}+25}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Convert 25 to fraction \frac{100}{4}.

$$\frac{-\frac{75}{4}+\frac{100}{4}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Since -\frac{75}{4} and \frac{100}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-75+100}{4}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Add -75 and 100 to get 25.

$$\frac{\frac{25}{4}}{\frac{-\frac{21\times 9+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply 21 and 9 to get 189.

$$\frac{\frac{25}{4}}{\frac{-\frac{189+7}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Add 189 and 7 to get 196.

$$\frac{\frac{25}{4}}{\frac{-\frac{196}{9}}{\frac{4\times 3+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{25}{4}}{\frac{-\frac{196}{9}}{\frac{12+2}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Add 12 and 2 to get 14.

$$\frac{\frac{25}{4}}{\frac{-\frac{196}{9}}{\frac{14}{3}}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Divide -\frac{196}{9} by \frac{14}{3} by multiplying -\frac{196}{9} by the reciprocal of \frac{14}{3}.

$$\frac{\frac{25}{4}}{-\frac{196}{9}\times \frac{3}{14}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply -\frac{196}{9} times \frac{3}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25}{4}}{\frac{-196\times 3}{9\times 14}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Do the multiplications in the fraction \frac{-196\times 3}{9\times 14}.

$$\frac{\frac{25}{4}}{\frac{-588}{126}+1}\left(-\frac{3\times 3+2}{3}\right)$$

Reduce the fraction \frac{-588}{126} to lowest terms by extracting and canceling out 42.

$$\frac{\frac{25}{4}}{-\frac{14}{3}+1}\left(-\frac{3\times 3+2}{3}\right)$$

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

$$\frac{\frac{25}{4}}{-\frac{14}{3}+\frac{3}{3}}\left(-\frac{3\times 3+2}{3}\right)$$

Since -\frac{14}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25}{4}}{\frac{-14+3}{3}}\left(-\frac{3\times 3+2}{3}\right)$$

Add -14 and 3 to get -11.

$$\frac{\frac{25}{4}}{-\frac{11}{3}}\left(-\frac{3\times 3+2}{3}\right)$$

Divide \frac{25}{4} by -\frac{11}{3} by multiplying \frac{25}{4} by the reciprocal of -\frac{11}{3}.

$$\frac{25}{4}\left(-\frac{3}{11}\right)\left(-\frac{3\times 3+2}{3}\right)$$

Multiply \frac{25}{4} times -\frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\left(-3\right)}{4\times 11}\left(-\frac{3\times 3+2}{3}\right)$$

Do the multiplications in the fraction \frac{25\left(-3\right)}{4\times 11}.

$$\frac{-75}{44}\left(-\frac{3\times 3+2}{3}\right)$$

Fraction \frac{-75}{44} can be rewritten as -\frac{75}{44} by extracting the negative sign.

$$-\frac{75}{44}\left(-\frac{3\times 3+2}{3}\right)$$

Multiply 3 and 3 to get 9.

$$-\frac{75}{44}\left(-\frac{9+2}{3}\right)$$

Add 9 and 2 to get 11.

$$-\frac{75}{44}\left(-\frac{11}{3}\right)$$

Multiply -\frac{75}{44} times -\frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-75\left(-11\right)}{44\times 3}$$

Do the multiplications in the fraction \frac{-75\left(-11\right)}{44\times 3}.

$$\frac{825}{132}$$

Reduce the fraction \frac{825}{132} to lowest terms by extracting and canceling out 33.

$$\frac{25}{4}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2}} = 6\frac{1}{4} = 6.25$$