Solve 2/30-(23/120-(-5/36))

$$\frac{ 2 }{ 30 } -( \frac{ 23 }{ 120 } -(- \frac{ 5 }{ 36 } ))$$

Evaluate

$$-\frac{19}{72}\approx -0.263888889$$

Solution Steps

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{1}{15}-\left(\frac{23}{120}-\left(-\frac{5}{36}\right)\right)$$

The opposite of -\frac{5}{36} is \frac{5}{36}.

$$\frac{1}{15}-\left(\frac{23}{120}+\frac{5}{36}\right)$$

Least common multiple of 120 and 36 is 360. Convert \frac{23}{120} and \frac{5}{36} to fractions with denominator 360.

$$\frac{1}{15}-\left(\frac{69}{360}+\frac{50}{360}\right)$$

Since \frac{69}{360} and \frac{50}{360} have the same denominator, add them by adding their numerators.

$$\frac{1}{15}-\frac{69+50}{360}$$

Add 69 and 50 to get 119.

$$\frac{1}{15}-\frac{119}{360}$$

Least common multiple of 15 and 360 is 360. Convert \frac{1}{15} and \frac{119}{360} to fractions with denominator 360.

$$\frac{24}{360}-\frac{119}{360}$$

Since \frac{24}{360} and \frac{119}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-119}{360}$$

Subtract 119 from 24 to get -95.

$$\frac{-95}{360}$$

Reduce the fraction \frac{-95}{360} to lowest terms by extracting and canceling out 5.

$$-\frac{19}{72}$$

Factor

$$-\frac{19}{72} = -0.2638888888888889$$