Solve 1/5+(999+494/495)*99/4=?

$$\frac { \frac { 1 } { 5 } + ( 999 + \frac { 494 } { 495 } ) \times 99 } { 4 } = ?$$

Evaluate

$$24750$$

Solution Steps

Convert 999 to fraction \frac{494505}{495}.

$$\frac{\frac{1}{5}+\left(\frac{494505}{495}+\frac{494}{495}\right)\times 99}{4}$$

Since \frac{494505}{495} and \frac{494}{495} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{5}+\frac{494505+494}{495}\times 99}{4}$$

Add 494505 and 494 to get 494999.

$$\frac{\frac{1}{5}+\frac{494999}{495}\times 99}{4}$$

Express \frac{494999}{495}\times 99 as a single fraction.

$$\frac{\frac{1}{5}+\frac{494999\times 99}{495}}{4}$$

Multiply 494999 and 99 to get 49004901.

$$\frac{\frac{1}{5}+\frac{49004901}{495}}{4}$$

Reduce the fraction \frac{49004901}{495} to lowest terms by extracting and canceling out 99.

$$\frac{\frac{1}{5}+\frac{494999}{5}}{4}$$

Since \frac{1}{5} and \frac{494999}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+494999}{5}}{4}$$

Add 1 and 494999 to get 495000.

$$\frac{\frac{495000}{5}}{4}$$

Divide 495000 by 5 to get 99000.

$$\frac{99000}{4}$$

Divide 99000 by 4 to get 24750.

$$24750$$

Factor

$$2\times 3^{2}\times 5^{3}\times 11$$