Solve 100*10^3-0.5176*14.3*500*465/frac{100*10^3*285-0.43*14.3*500*465^2{(0.8-0.5176)*(465-35)}+14.3*500*465}

$$\frac { 100 \times 10 ^ { 3 } - 0.5176 \times 14.3 \times 500 \times 465 } { \frac { 100 \times 10 ^ { 3 } \times 285 - 0.43 \times 14.3 \times 500 \times 465 ^ { 2 } } { ( 0.8 - 0.5176 ) \times ( 465 - 35 ) } + 14.3 \times 500 \times 465 }$$

Evaluate

$$\frac{246034984174}{290690900625}\approx 0.846380068$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$\frac{100\times 1000-0.5176\times 14.3\times 500\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 100 and 1000 to get 100000.

$$\frac{100000-0.5176\times 14.3\times 500\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 0.5176 and 14.3 to get 7.40168.

$$\frac{100000-7.40168\times 500\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 7.40168 and 500 to get 3700.84.

$$\frac{100000-3700.84\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 3700.84 and 465 to get 1720890.6.

$$\frac{100000-1720890.6}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Subtract 1720890.6 from 100000 to get -1620890.6.

$$\frac{-1620890.6}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{-1620890.6}{\frac{100\times 1000\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 100 and 1000 to get 100000.

$$\frac{-1620890.6}{\frac{100000\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 100000 and 285 to get 28500000.

$$\frac{-1620890.6}{\frac{28500000-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 0.43 and 14.3 to get 6.149.

$$\frac{-1620890.6}{\frac{28500000-6.149\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 6.149 and 500 to get 3074.5.

$$\frac{-1620890.6}{\frac{28500000-3074.5\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Calculate 465 to the power of 2 and get 216225.

$$\frac{-1620890.6}{\frac{28500000-3074.5\times 216225}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiply 3074.5 and 216225 to get 664783762.5.

$$\frac{-1620890.6}{\frac{28500000-664783762.5}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Subtract 664783762.5 from 28500000 to get -636283762.5.

$$\frac{-1620890.6}{\frac{-636283762.5}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Subtract 0.5176 from 0.8 to get 0.2824.

$$\frac{-1620890.6}{\frac{-636283762.5}{0.2824\left(465-35\right)}+14.3\times 500\times 465}$$

Subtract 35 from 465 to get 430.

$$\frac{-1620890.6}{\frac{-636283762.5}{0.2824\times 430}+14.3\times 500\times 465}$$

Multiply 0.2824 and 430 to get 121.432.

$$\frac{-1620890.6}{\frac{-636283762.5}{121.432}+14.3\times 500\times 465}$$

Expand \frac{-636283762.5}{121.432} by multiplying both numerator and the denominator by 1000.

$$\frac{-1620890.6}{\frac{-636283762500}{121432}+14.3\times 500\times 465}$$

Reduce the fraction \frac{-636283762500}{121432} to lowest terms by extracting and canceling out 4.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+14.3\times 500\times 465}$$

Multiply 14.3 and 500 to get 7150.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+7150\times 465}$$

Multiply 7150 and 465 to get 3324750.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+3324750}$$

Convert 3324750 to fraction \frac{100932760500}{30358}.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+\frac{100932760500}{30358}}$$

Since -\frac{159070940625}{30358} and \frac{100932760500}{30358} have the same denominator, add them by adding their numerators.

$$\frac{-1620890.6}{\frac{-159070940625+100932760500}{30358}}$$

Add -159070940625 and 100932760500 to get -58138180125.

$$\frac{-1620890.6}{-\frac{58138180125}{30358}}$$

Divide -1620890.6 by -\frac{58138180125}{30358} by multiplying -1620890.6 by the reciprocal of -\frac{58138180125}{30358}.

$$-1620890.6\left(-\frac{30358}{58138180125}\right)$$

Convert decimal number -1620890.6 to fraction -\frac{16208906}{10}. Reduce the fraction -\frac{16208906}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{8104453}{5}\left(-\frac{30358}{58138180125}\right)$$

Multiply -\frac{8104453}{5} times -\frac{30358}{58138180125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8104453\left(-30358\right)}{5\times 58138180125}$$

Do the multiplications in the fraction \frac{-8104453\left(-30358\right)}{5\times 58138180125}.

$$\frac{246034984174}{290690900625}$$

Factor

$$\frac{2 \cdot 43 \cdot 353 \cdot 165397 \cdot 7 ^ {2}}{3 \cdot 155035147 \cdot 5 ^ {4}} = 0.8463800677799423$$