Solve 313.64-231.8^2/200/199

$$\frac { 313.64 - \frac { 231.8 ^ { 2 } } { 200 } } { 199 }$$

Evaluate

$$\frac{224919}{995000}\approx 0.226049246$$

Solution Steps

Calculate 231.8 to the power of 2 and get 53731.24.

$$\frac{313.64-\frac{53731.24}{200}}{199}$$

Expand \frac{53731.24}{200} by multiplying both numerator and the denominator by 100.

$$\frac{313.64-\frac{5373124}{20000}}{199}$$

Reduce the fraction \frac{5373124}{20000} to lowest terms by extracting and canceling out 4.

$$\frac{313.64-\frac{1343281}{5000}}{199}$$

Convert decimal number 313.64 to fraction \frac{31364}{100}. Reduce the fraction \frac{31364}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7841}{25}-\frac{1343281}{5000}}{199}$$

Least common multiple of 25 and 5000 is 5000. Convert \frac{7841}{25} and \frac{1343281}{5000} to fractions with denominator 5000.

$$\frac{\frac{1568200}{5000}-\frac{1343281}{5000}}{199}$$

Since \frac{1568200}{5000} and \frac{1343281}{5000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1568200-1343281}{5000}}{199}$$

Subtract 1343281 from 1568200 to get 224919.

$$\frac{\frac{224919}{5000}}{199}$$

Express \frac{\frac{224919}{5000}}{199} as a single fraction.

$$\frac{224919}{5000\times 199}$$

Multiply 5000 and 199 to get 995000.

$$\frac{224919}{995000}$$

Factor

$$\frac{67 \cdot 373 \cdot 3 ^ {2}}{199 \cdot 2 ^ {3} \cdot 5 ^ {4}} = 0.22604924623115577$$