Solve 166.5+(33/4-5/17)

$$166.5+( \frac{ \frac{ 33 }{ 4 } -5 }{ 17 } )$$

Evaluate

$$\frac{11335}{68}\approx 166.691176471$$

Solution Steps

Convert 5 to fraction \frac{20}{4}.

$$166.5+\frac{\frac{33}{4}-\frac{20}{4}}{17}$$

Since \frac{33}{4} and \frac{20}{4} have the same denominator, subtract them by subtracting their numerators.

$$166.5+\frac{\frac{33-20}{4}}{17}$$

Subtract 20 from 33 to get 13.

$$166.5+\frac{\frac{13}{4}}{17}$$

Express \frac{\frac{13}{4}}{17} as a single fraction.

$$166.5+\frac{13}{4\times 17}$$

Multiply 4 and 17 to get 68.

$$166.5+\frac{13}{68}$$

Convert decimal number 166.5 to fraction \frac{1665}{10}. Reduce the fraction \frac{1665}{10} to lowest terms by extracting and canceling out 5.

$$\frac{333}{2}+\frac{13}{68}$$

Least common multiple of 2 and 68 is 68. Convert \frac{333}{2} and \frac{13}{68} to fractions with denominator 68.

$$\frac{11322}{68}+\frac{13}{68}$$

Since \frac{11322}{68} and \frac{13}{68} have the same denominator, add them by adding their numerators.

$$\frac{11322+13}{68}$$

Add 11322 and 13 to get 11335.

$$\frac{11335}{68}$$

Factor

$$\frac{5 \cdot 2267}{17 \cdot 2 ^ {2}} = 166\frac{47}{68} = 166.69117647058823$$