Solve 1-((95div100)*(94div99)*(93div98)*92div97)*(91div96))

$$1-((95 \div 100) \times (94 \div 99) \times (93 \div 98) \times 92 \div 97) \times (91 \div 96))$$

Evaluate

$$\frac{2478143}{10755360}\approx 0.230410047$$

Solution Steps

Reduce the fraction \frac{95}{100} to lowest terms by extracting and canceling out 5.

$$1-\frac{\frac{19}{20}\times \frac{94}{99}\times \frac{93}{98}\times 92}{97}\times \frac{91}{96}$$

Multiply \frac{19}{20} times \frac{94}{99} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{\frac{19\times 94}{20\times 99}\times \frac{93}{98}\times 92}{97}\times \frac{91}{96}$$

Do the multiplications in the fraction \frac{19\times 94}{20\times 99}.

$$1-\frac{\frac{1786}{1980}\times \frac{93}{98}\times 92}{97}\times \frac{91}{96}$$

Reduce the fraction \frac{1786}{1980} to lowest terms by extracting and canceling out 2.

$$1-\frac{\frac{893}{990}\times \frac{93}{98}\times 92}{97}\times \frac{91}{96}$$

Multiply \frac{893}{990} times \frac{93}{98} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{\frac{893\times 93}{990\times 98}\times 92}{97}\times \frac{91}{96}$$

Do the multiplications in the fraction \frac{893\times 93}{990\times 98}.

$$1-\frac{\frac{83049}{97020}\times 92}{97}\times \frac{91}{96}$$

Reduce the fraction \frac{83049}{97020} to lowest terms by extracting and canceling out 3.

$$1-\frac{\frac{27683}{32340}\times 92}{97}\times \frac{91}{96}$$

Express \frac{27683}{32340}\times 92 as a single fraction.

$$1-\frac{\frac{27683\times 92}{32340}}{97}\times \frac{91}{96}$$

Multiply 27683 and 92 to get 2546836.

$$1-\frac{\frac{2546836}{32340}}{97}\times \frac{91}{96}$$

Reduce the fraction \frac{2546836}{32340} to lowest terms by extracting and canceling out 4.

$$1-\frac{\frac{636709}{8085}}{97}\times \frac{91}{96}$$

Express \frac{\frac{636709}{8085}}{97} as a single fraction.

$$1-\frac{636709}{8085\times 97}\times \frac{91}{96}$$

Multiply 8085 and 97 to get 784245.

$$1-\frac{636709}{784245}\times \frac{91}{96}$$

Multiply \frac{636709}{784245} times \frac{91}{96} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{636709\times 91}{784245\times 96}$$

Do the multiplications in the fraction \frac{636709\times 91}{784245\times 96}.

$$1-\frac{57940519}{75287520}$$

Reduce the fraction \frac{57940519}{75287520} to lowest terms by extracting and canceling out 7.

$$1-\frac{8277217}{10755360}$$

Convert 1 to fraction \frac{10755360}{10755360}.

$$\frac{10755360}{10755360}-\frac{8277217}{10755360}$$

Since \frac{10755360}{10755360} and \frac{8277217}{10755360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10755360-8277217}{10755360}$$

Subtract 8277217 from 10755360 to get 2478143.

$$\frac{2478143}{10755360}$$

Factor

$$\frac{983 \cdot 2521}{2 ^ {5} \cdot 3 ^ {2} \cdot 5 \cdot 7 \cdot 11 \cdot 97} = 0.2304100467115931$$