Solve 21.22/21.22{frac{21.22/frac{21.64{}}}}

$$\frac{ 21.22 }{ \frac{ 21.22 }{ \frac{ 21.22 }{ \frac{ 21.64 }{ } } } }$$

Evaluate

$$\frac{1061}{1082}\approx 0.980591497$$

Solution Steps

Divide 21.22 by \frac{21.22}{\frac{21.22}{\frac{21.64}{1}}} by multiplying 21.22 by the reciprocal of \frac{21.22}{\frac{21.22}{\frac{21.64}{1}}}.

$$\frac{21.22\times \frac{21.22}{\frac{21.64}{1}}}{21.22}$$

Cancel out 21.22 and 21.22.

$$\frac{21.22}{\frac{21.64}{1}}$$

Anything divided by one gives itself.

$$\frac{21.22}{21.64}$$

Expand \frac{21.22}{21.64} by multiplying both numerator and the denominator by 100.

$$\frac{2122}{2164}$$

Reduce the fraction \frac{2122}{2164} to lowest terms by extracting and canceling out 2.

$$\frac{1061}{1082}$$

Factor

$$\frac{1061}{2 \cdot 541} = 0.9805914972273567$$