Solve 991/9100/9999/999999/100frac{101}{99}

$$99 \frac { 1 } { 9 } \frac { 100 } { 99 } \frac { 99 } { 99 } 99 \frac { 99 } { 100 } \frac { 101 } { 99 }$$

Evaluate

$$\frac{9099292}{891}\approx 10212.448933782$$

Solution Steps

Divide 99 by 99 to get 1.

$$\frac{99\times 9+1}{9}\times \frac{100}{99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Multiply 99 and 9 to get 891.

$$\frac{891+1}{9}\times \frac{100}{99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Add 891 and 1 to get 892.

$$\frac{892}{9}\times \frac{100}{99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Multiply \frac{892}{9} times \frac{100}{99} by multiplying numerator times numerator and denominator times denominator.

$$\frac{892\times 100}{9\times 99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Do the multiplications in the fraction \frac{892\times 100}{9\times 99}.

$$\frac{89200}{891}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Multiply \frac{89200}{891} and 1 to get \frac{89200}{891}.

$$\frac{89200}{891}\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Multiply 99 and 100 to get 9900.

$$\frac{89200}{891}\times \frac{9900+99}{100}\times \frac{101}{99}$$

Add 9900 and 99 to get 9999.

$$\frac{89200}{891}\times \frac{9999}{100}\times \frac{101}{99}$$

Multiply \frac{89200}{891} times \frac{9999}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{89200\times 9999}{891\times 100}\times \frac{101}{99}$$

Do the multiplications in the fraction \frac{89200\times 9999}{891\times 100}.

$$\frac{891910800}{89100}\times \frac{101}{99}$$

Reduce the fraction \frac{891910800}{89100} to lowest terms by extracting and canceling out 9900.

$$\frac{90092}{9}\times \frac{101}{99}$$

Multiply \frac{90092}{9} times \frac{101}{99} by multiplying numerator times numerator and denominator times denominator.

$$\frac{90092\times 101}{9\times 99}$$

Do the multiplications in the fraction \frac{90092\times 101}{9\times 99}.

$$\frac{9099292}{891}$$

Factor

$$\frac{2 ^ {2} \cdot 101 ^ {2} \cdot 223}{3 ^ {4} \cdot 11} = 10212\frac{400}{891} = 10212.448933782267$$