Solve 202/4-50/2sqrt{101/2frac{sqrt{101}}{2}}

$$\frac{ \frac{ 202 }{ 4 } -50 }{ 2 \frac{ \sqrt{ 101 } }{ 2 } \frac{ \sqrt{ 101 } }{ 2 } }$$

Evaluate

$$\frac{1}{101}\approx 0.00990099$$

Solution Steps

Multiply \frac{\sqrt{101}}{2} and \frac{\sqrt{101}}{2} to get \left(\frac{\sqrt{101}}{2}\right)^{2}.

$$\frac{\frac{202}{4}-50}{2\times \left(\frac{\sqrt{101}}{2}\right)^{2}}$$

Reduce the fraction \frac{202}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{101}{2}-50}{2\times \left(\frac{\sqrt{101}}{2}\right)^{2}}$$

Convert 50 to fraction \frac{100}{2}.

$$\frac{\frac{101}{2}-\frac{100}{2}}{2\times \left(\frac{\sqrt{101}}{2}\right)^{2}}$$

Since \frac{101}{2} and \frac{100}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{101-100}{2}}{2\times \left(\frac{\sqrt{101}}{2}\right)^{2}}$$

Subtract 100 from 101 to get 1.

$$\frac{\frac{1}{2}}{2\times \left(\frac{\sqrt{101}}{2}\right)^{2}}$$

To raise \frac{\sqrt{101}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{1}{2}}{2\times \frac{\left(\sqrt{101}\right)^{2}}{2^{2}}}$$

Express 2\times \frac{\left(\sqrt{101}\right)^{2}}{2^{2}} as a single fraction.

$$\frac{\frac{1}{2}}{\frac{2\left(\sqrt{101}\right)^{2}}{2^{2}}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{1}{2}}{\frac{\left(\sqrt{101}\right)^{2}}{2}}$$

Divide \frac{1}{2} by \frac{\left(\sqrt{101}\right)^{2}}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{\left(\sqrt{101}\right)^{2}}{2}.

$$\frac{2}{2\left(\sqrt{101}\right)^{2}}$$

The square of \sqrt{101} is 101.

$$\frac{2}{2\times 101}$$

Multiply 2 and 101 to get 202.

$$\frac{2}{202}$$

Reduce the fraction \frac{2}{202} to lowest terms by extracting and canceling out 2.

$$\frac{1}{101}$$

Factor

$$\frac{1}{101} = 0.009900990099009901$$