Solve 1/5+999*499/495*99/4

$$\frac { \frac { 1 } { 5 } + 999 \cdot \frac { 499 } { 495 } \cdot 99 } { 4 }$$

Evaluate

$$\frac{249251}{10}=24925.1$$

Solution Steps

Express 999\times \frac{499}{495} as a single fraction.

$$\frac{\frac{1}{5}+\frac{999\times 499}{495}\times 99}{4}$$

Multiply 999 and 499 to get 498501.

$$\frac{\frac{1}{5}+\frac{498501}{495}\times 99}{4}$$

Reduce the fraction \frac{498501}{495} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{1}{5}+\frac{55389}{55}\times 99}{4}$$

Express \frac{55389}{55}\times 99 as a single fraction.

$$\frac{\frac{1}{5}+\frac{55389\times 99}{55}}{4}$$

Multiply 55389 and 99 to get 5483511.

$$\frac{\frac{1}{5}+\frac{5483511}{55}}{4}$$

Reduce the fraction \frac{5483511}{55} to lowest terms by extracting and canceling out 11.

$$\frac{\frac{1}{5}+\frac{498501}{5}}{4}$$

Since \frac{1}{5} and \frac{498501}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+498501}{5}}{4}$$

Add 1 and 498501 to get 498502.

$$\frac{\frac{498502}{5}}{4}$$

Express \frac{\frac{498502}{5}}{4} as a single fraction.

$$\frac{498502}{5\times 4}$$

Multiply 5 and 4 to get 20.

$$\frac{498502}{20}$$

Reduce the fraction \frac{498502}{20} to lowest terms by extracting and canceling out 2.

$$\frac{249251}{10}$$

Factor

$$\frac{23 \cdot 10837}{2 \cdot 5} = 24925\frac{1}{10} = 24925.1$$