Solve 19*left(1/9.5-1/2015.5right)

$$19 \times \left( \frac{ 1 }{ 9.5 } - \frac{ 1 }{ 2015.5 } \right)$$

Evaluate

$$\frac{8024}{4031}\approx 1.990573059$$

Solution Steps

Expand \frac{1}{9.5} by multiplying both numerator and the denominator by 10.

$$19\left(\frac{10}{95}-\frac{1}{2015.5}\right)$$

Reduce the fraction \frac{10}{95} to lowest terms by extracting and canceling out 5.

$$19\left(\frac{2}{19}-\frac{1}{2015.5}\right)$$

Expand \frac{1}{2015.5} by multiplying both numerator and the denominator by 10.

$$19\left(\frac{2}{19}-\frac{10}{20155}\right)$$

Reduce the fraction \frac{10}{20155} to lowest terms by extracting and canceling out 5.

$$19\left(\frac{2}{19}-\frac{2}{4031}\right)$$

Least common multiple of 19 and 4031 is 76589. Convert \frac{2}{19} and \frac{2}{4031} to fractions with denominator 76589.

$$19\left(\frac{8062}{76589}-\frac{38}{76589}\right)$$

Since \frac{8062}{76589} and \frac{38}{76589} have the same denominator, subtract them by subtracting their numerators.

$$19\times \frac{8062-38}{76589}$$

Subtract 38 from 8062 to get 8024.

$$19\times \frac{8024}{76589}$$

Express 19\times \frac{8024}{76589} as a single fraction.

$$\frac{19\times 8024}{76589}$$

Multiply 19 and 8024 to get 152456.

$$\frac{152456}{76589}$$

Reduce the fraction \frac{152456}{76589} to lowest terms by extracting and canceling out 19.

$$\frac{8024}{4031}$$

Factor

$$\frac{17 \cdot 59 \cdot 2 ^ {3}}{29 \cdot 139} = 1\frac{3993}{4031} = 1.9905730587943438$$