Solve 5.5(1-1/1.33)

$$5.5 ( 1 - \frac { 1 } { 1.33 } )$$

Evaluate

$$\frac{363}{266}\approx 1.364661654$$

Solution Steps

Expand \frac{1}{1.33} by multiplying both numerator and the denominator by 100.

$$5.5\left(1-\frac{100}{133}\right)$$

Convert 1 to fraction \frac{133}{133}.

$$5.5\left(\frac{133}{133}-\frac{100}{133}\right)$$

Since \frac{133}{133} and \frac{100}{133} have the same denominator, subtract them by subtracting their numerators.

$$5.5\times \frac{133-100}{133}$$

Subtract 100 from 133 to get 33.

$$5.5\times \frac{33}{133}$$

Convert decimal number 5.5 to fraction \frac{55}{10}. Reduce the fraction \frac{55}{10} to lowest terms by extracting and canceling out 5.

$$\frac{11}{2}\times \frac{33}{133}$$

Multiply \frac{11}{2} times \frac{33}{133} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 33}{2\times 133}$$

Do the multiplications in the fraction \frac{11\times 33}{2\times 133}.

$$\frac{363}{266}$$

Factor

$$\frac{3 \cdot 11 ^ {2}}{2 \cdot 7 \cdot 19} = 1\frac{97}{266} = 1.3646616541353382$$