Solve 19*left(1/9-1/2014right)

$$19 \times \left( \frac{ 1 }{ 9 } - \frac{ 1 }{ 2014 } \right)$$

Evaluate

$$\frac{2005}{954}\approx 2.101677149$$

Solution Steps

Least common multiple of 9 and 2014 is 18126. Convert \frac{1}{9} and \frac{1}{2014} to fractions with denominator 18126.

$$19\left(\frac{2014}{18126}-\frac{9}{18126}\right)$$

Since \frac{2014}{18126} and \frac{9}{18126} have the same denominator, subtract them by subtracting their numerators.

$$19\times \frac{2014-9}{18126}$$

Subtract 9 from 2014 to get 2005.

$$19\times \frac{2005}{18126}$$

Express 19\times \frac{2005}{18126} as a single fraction.

$$\frac{19\times 2005}{18126}$$

Multiply 19 and 2005 to get 38095.

$$\frac{38095}{18126}$$

Reduce the fraction \frac{38095}{18126} to lowest terms by extracting and canceling out 19.

$$\frac{2005}{954}$$

Factor

$$\frac{5 \cdot 401}{2 \cdot 3 ^ {2} \cdot 53} = 2\frac{97}{954} = 2.10167714884696$$