Solve 47.6/2*(47.6/2-8.4)*(47.6/2-18.7)*(47.6/2-20.5)

$$\frac{ 47.6 }{ 2 } \times ( \frac{ 47.6 }{ 2 } -8.4) \times ( \frac{ 47.6 }{ 2 } -18.7) \times ( \frac{ 47.6 }{ 2 } -20.5)$$

Evaluate

$$6168.5316$$

Solution Steps

Expand \frac{47.6}{2} by multiplying both numerator and the denominator by 10.

$$\frac{476}{20}\left(\frac{47.6}{2}-8.4\right)\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Reduce the fraction \frac{476}{20} to lowest terms by extracting and canceling out 4.

$$\frac{119}{5}\left(\frac{47.6}{2}-8.4\right)\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Expand \frac{47.6}{2} by multiplying both numerator and the denominator by 10.

$$\frac{119}{5}\left(\frac{476}{20}-8.4\right)\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Reduce the fraction \frac{476}{20} to lowest terms by extracting and canceling out 4.

$$\frac{119}{5}\left(\frac{119}{5}-8.4\right)\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Convert decimal number 8.4 to fraction \frac{84}{10}. Reduce the fraction \frac{84}{10} to lowest terms by extracting and canceling out 2.

$$\frac{119}{5}\left(\frac{119}{5}-\frac{42}{5}\right)\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Since \frac{119}{5} and \frac{42}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{119}{5}\times \frac{119-42}{5}\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Subtract 42 from 119 to get 77.

$$\frac{119}{5}\times \frac{77}{5}\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Multiply \frac{119}{5} times \frac{77}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{119\times 77}{5\times 5}\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Do the multiplications in the fraction \frac{119\times 77}{5\times 5}.

$$\frac{9163}{25}\left(\frac{47.6}{2}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Expand \frac{47.6}{2} by multiplying both numerator and the denominator by 10.

$$\frac{9163}{25}\left(\frac{476}{20}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Reduce the fraction \frac{476}{20} to lowest terms by extracting and canceling out 4.

$$\frac{9163}{25}\left(\frac{119}{5}-18.7\right)\left(\frac{47.6}{2}-20.5\right)$$

Convert decimal number 18.7 to fraction \frac{187}{10}.

$$\frac{9163}{25}\left(\frac{119}{5}-\frac{187}{10}\right)\left(\frac{47.6}{2}-20.5\right)$$

Least common multiple of 5 and 10 is 10. Convert \frac{119}{5} and \frac{187}{10} to fractions with denominator 10.

$$\frac{9163}{25}\left(\frac{238}{10}-\frac{187}{10}\right)\left(\frac{47.6}{2}-20.5\right)$$

Since \frac{238}{10} and \frac{187}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9163}{25}\times \frac{238-187}{10}\left(\frac{47.6}{2}-20.5\right)$$

Subtract 187 from 238 to get 51.

$$\frac{9163}{25}\times \frac{51}{10}\left(\frac{47.6}{2}-20.5\right)$$

Multiply \frac{9163}{25} times \frac{51}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9163\times 51}{25\times 10}\left(\frac{47.6}{2}-20.5\right)$$

Do the multiplications in the fraction \frac{9163\times 51}{25\times 10}.

$$\frac{467313}{250}\left(\frac{47.6}{2}-20.5\right)$$

Expand \frac{47.6}{2} by multiplying both numerator and the denominator by 10.

$$\frac{467313}{250}\left(\frac{476}{20}-20.5\right)$$

Reduce the fraction \frac{476}{20} to lowest terms by extracting and canceling out 4.

$$\frac{467313}{250}\left(\frac{119}{5}-20.5\right)$$

Convert decimal number 20.5 to fraction \frac{205}{10}. Reduce the fraction \frac{205}{10} to lowest terms by extracting and canceling out 5.

$$\frac{467313}{250}\left(\frac{119}{5}-\frac{41}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{119}{5} and \frac{41}{2} to fractions with denominator 10.

$$\frac{467313}{250}\left(\frac{238}{10}-\frac{205}{10}\right)$$

Since \frac{238}{10} and \frac{205}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{467313}{250}\times \frac{238-205}{10}$$

Subtract 205 from 238 to get 33.

$$\frac{467313}{250}\times \frac{33}{10}$$

Multiply \frac{467313}{250} times \frac{33}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{467313\times 33}{250\times 10}$$

Do the multiplications in the fraction \frac{467313\times 33}{250\times 10}.

$$\frac{15421329}{2500}$$

Factor

$$\frac{3 ^ {2} \cdot 7 ^ {2} \cdot 11 ^ {2} \cdot 17 ^ {2}}{2 ^ {2} \cdot 5 ^ {4}} = 6168\frac{1329}{2500} = 6168.5316$$