Solve (-1)^3*12/7*5/7div(-3/4)*(-2.5)*2/5div(-0.45)*2frac{1}{3}div(-frac{5}{7})

$$( - 1 ) ^ { 3 } \times 1 \frac { 2 } { 7 } \times \frac { 5 } { 7 } \div ( - \frac { 3 } { 4 } ) \times ( - 2.5 ) \times \frac { 2 } { 5 } \div ( - 0.45 ) \times 2 \frac { 1 } { 3 } \div ( - \frac { 5 } { 7 } )$$

Evaluate

$$-\frac{80}{9}\approx -8.888888889$$

Solution Steps

Calculate -1 to the power of 3 and get -1.

$$\frac{\frac{\frac{-\frac{7+2}{7}\times \frac{5}{7}}{-\frac{3}{4}}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Add 7 and 2 to get 9.

$$\frac{\frac{\frac{-\frac{9}{7}\times \frac{5}{7}}{-\frac{3}{4}}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Multiply -\frac{9}{7} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{\frac{-9\times 5}{7\times 7}}{-\frac{3}{4}}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Do the multiplications in the fraction \frac{-9\times 5}{7\times 7}.

$$\frac{\frac{\frac{\frac{-45}{49}}{-\frac{3}{4}}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Fraction \frac{-45}{49} can be rewritten as -\frac{45}{49} by extracting the negative sign.

$$\frac{\frac{\frac{-\frac{45}{49}}{-\frac{3}{4}}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Divide -\frac{45}{49} by -\frac{3}{4} by multiplying -\frac{45}{49} by the reciprocal of -\frac{3}{4}.

$$\frac{\frac{-\frac{45}{49}\left(-\frac{4}{3}\right)\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Multiply -\frac{45}{49} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{-45\left(-4\right)}{49\times 3}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Do the multiplications in the fraction \frac{-45\left(-4\right)}{49\times 3}.

$$\frac{\frac{\frac{180}{147}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Reduce the fraction \frac{180}{147} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{\frac{60}{49}\left(-2.5\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Convert decimal number -2.5 to fraction -\frac{25}{10}. Reduce the fraction -\frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{\frac{60}{49}\left(-\frac{5}{2}\right)\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Multiply \frac{60}{49} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{60\left(-5\right)}{49\times 2}\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Do the multiplications in the fraction \frac{60\left(-5\right)}{49\times 2}.

$$\frac{\frac{\frac{-300}{98}\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Reduce the fraction \frac{-300}{98} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{-\frac{150}{49}\times \frac{2}{5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Multiply -\frac{150}{49} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{-150\times 2}{49\times 5}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Do the multiplications in the fraction \frac{-150\times 2}{49\times 5}.

$$\frac{\frac{\frac{-300}{245}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Reduce the fraction \frac{-300}{245} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{-\frac{60}{49}}{-0.45}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Express \frac{-\frac{60}{49}}{-0.45} as a single fraction.

$$\frac{\frac{-60}{49\left(-0.45\right)}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Multiply 49 and -0.45 to get -22.05.

$$\frac{\frac{-60}{-22.05}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Expand \frac{-60}{-22.05} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{-6000}{-2205}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Reduce the fraction \frac{-6000}{-2205} to lowest terms by extracting and canceling out -15.

$$\frac{\frac{400}{147}\times \frac{2\times 3+1}{3}}{-\frac{5}{7}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{400}{147}\times \frac{6+1}{3}}{-\frac{5}{7}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{400}{147}\times \frac{7}{3}}{-\frac{5}{7}}$$

Multiply \frac{400}{147} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{400\times 7}{147\times 3}}{-\frac{5}{7}}$$

Do the multiplications in the fraction \frac{400\times 7}{147\times 3}.

$$\frac{\frac{2800}{441}}{-\frac{5}{7}}$$

Reduce the fraction \frac{2800}{441} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{400}{63}}{-\frac{5}{7}}$$

Divide \frac{400}{63} by -\frac{5}{7} by multiplying \frac{400}{63} by the reciprocal of -\frac{5}{7}.

$$\frac{400}{63}\left(-\frac{7}{5}\right)$$

Multiply \frac{400}{63} times -\frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{400\left(-7\right)}{63\times 5}$$

Do the multiplications in the fraction \frac{400\left(-7\right)}{63\times 5}.

$$\frac{-2800}{315}$$

Reduce the fraction \frac{-2800}{315} to lowest terms by extracting and canceling out 35.

$$-\frac{80}{9}$$

Factor

$$-\frac{80}{9} = -8\frac{8}{9} = -8.88888888888889$$