Solve -3/4*221/25div33/5div(-11/2)*1frac{21}{50}*(-1.8)-(-2)^2*2.5*(-4frac{1}{20})

$$- \frac { 3 } { 4 } \times 2 \frac { 21 } { 25 } \div 3 \frac { 3 } { 5 } \div ( - 1 \frac { 1 } { 2 } ) \times 1 \frac { 21 } { 50 } \times ( - 1.8 ) - ( - 2 ) ^ { 2 } \times 2.5 \times ( - 4 \frac { 1 } { 20 } )$$

Evaluate

$$39.4918$$

Solution Steps

Multiply 2 and 25 to get 50.

$$\frac{\frac{-\frac{3}{4}\times \frac{50+21}{25}}{\frac{3\times 5+3}{5}}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Add 50 and 21 to get 71.

$$\frac{\frac{-\frac{3}{4}\times \frac{71}{25}}{\frac{3\times 5+3}{5}}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply -\frac{3}{4} times \frac{71}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{-3\times 71}{4\times 25}}{\frac{3\times 5+3}{5}}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Do the multiplications in the fraction \frac{-3\times 71}{4\times 25}.

$$\frac{\frac{\frac{-213}{100}}{\frac{3\times 5+3}{5}}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Fraction \frac{-213}{100} can be rewritten as -\frac{213}{100} by extracting the negative sign.

$$\frac{\frac{-\frac{213}{100}}{\frac{3\times 5+3}{5}}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{-\frac{213}{100}}{\frac{15+3}{5}}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Add 15 and 3 to get 18.

$$\frac{\frac{-\frac{213}{100}}{\frac{18}{5}}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Divide -\frac{213}{100} by \frac{18}{5} by multiplying -\frac{213}{100} by the reciprocal of \frac{18}{5}.

$$\frac{-\frac{213}{100}\times \frac{5}{18}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply -\frac{213}{100} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-213\times 5}{100\times 18}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Do the multiplications in the fraction \frac{-213\times 5}{100\times 18}.

$$\frac{\frac{-1065}{1800}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Reduce the fraction \frac{-1065}{1800} to lowest terms by extracting and canceling out 15.

$$\frac{-\frac{71}{120}}{-\frac{1\times 2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply 1 and 2 to get 2.

$$\frac{-\frac{71}{120}}{-\frac{2+1}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Add 2 and 1 to get 3.

$$\frac{-\frac{71}{120}}{-\frac{3}{2}}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Divide -\frac{71}{120} by -\frac{3}{2} by multiplying -\frac{71}{120} by the reciprocal of -\frac{3}{2}.

$$-\frac{71}{120}\left(-\frac{2}{3}\right)\times \frac{50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply -\frac{71}{120} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-71\left(-2\right)}{120\times 3}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Do the multiplications in the fraction \frac{-71\left(-2\right)}{120\times 3}.

$$\frac{142}{360}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Reduce the fraction \frac{142}{360} to lowest terms by extracting and canceling out 2.

$$\frac{71}{180}\times \frac{1\times 50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply 1 and 50 to get 50.

$$\frac{71}{180}\times \frac{50+21}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Add 50 and 21 to get 71.

$$\frac{71}{180}\times \frac{71}{50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply \frac{71}{180} times \frac{71}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{71\times 71}{180\times 50}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Do the multiplications in the fraction \frac{71\times 71}{180\times 50}.

$$\frac{5041}{9000}\left(-1.8\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Convert decimal number -1.8 to fraction -\frac{18}{10}. Reduce the fraction -\frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{5041}{9000}\left(-\frac{9}{5}\right)-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply \frac{5041}{9000} times -\frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5041\left(-9\right)}{9000\times 5}-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Do the multiplications in the fraction \frac{5041\left(-9\right)}{9000\times 5}.

$$\frac{-45369}{45000}-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Reduce the fraction \frac{-45369}{45000} to lowest terms by extracting and canceling out 9.

$$-\frac{5041}{5000}-\left(-2\right)^{2}\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Calculate -2 to the power of 2 and get 4.

$$-\frac{5041}{5000}-4\times 2.5\left(-\frac{4\times 20+1}{20}\right)$$

Multiply 4 and 2.5 to get 10.

$$-\frac{5041}{5000}-10\left(-\frac{4\times 20+1}{20}\right)$$

Multiply 4 and 20 to get 80.

$$-\frac{5041}{5000}-10\left(-\frac{80+1}{20}\right)$$

Add 80 and 1 to get 81.

$$-\frac{5041}{5000}-10\left(-\frac{81}{20}\right)$$

Express 10\left(-\frac{81}{20}\right) as a single fraction.

$$-\frac{5041}{5000}-\frac{10\left(-81\right)}{20}$$

Multiply 10 and -81 to get -810.

$$-\frac{5041}{5000}-\frac{-810}{20}$$

Reduce the fraction \frac{-810}{20} to lowest terms by extracting and canceling out 10.

$$-\frac{5041}{5000}-\left(-\frac{81}{2}\right)$$

The opposite of -\frac{81}{2} is \frac{81}{2}.

$$-\frac{5041}{5000}+\frac{81}{2}$$

Least common multiple of 5000 and 2 is 5000. Convert -\frac{5041}{5000} and \frac{81}{2} to fractions with denominator 5000.

$$-\frac{5041}{5000}+\frac{202500}{5000}$$

Since -\frac{5041}{5000} and \frac{202500}{5000} have the same denominator, add them by adding their numerators.

$$\frac{-5041+202500}{5000}$$

Add -5041 and 202500 to get 197459.

$$\frac{197459}{5000}$$

Factor

$$\frac{379 \cdot 521}{2 ^ {3} \cdot 5 ^ {4}} = 39\frac{2459}{5000} = 39.4918$$