Solve left|-19/15+43/18right|-19/15=

$$\left| - \frac{ 19 }{ 15 } + \frac{ 43 }{ 18 } \right| - \frac{ 19 }{ 15 } =$$

Evaluate

$$-\frac{13}{90}\approx -0.144444444$$

Solution Steps

Least common multiple of 15 and 18 is 90. Convert -\frac{19}{15} and \frac{43}{18} to fractions with denominator 90.

$$|-\frac{114}{90}+\frac{215}{90}|-\frac{19}{15}$$

Since -\frac{114}{90} and \frac{215}{90} have the same denominator, add them by adding their numerators.

$$|\frac{-114+215}{90}|-\frac{19}{15}$$

Add -114 and 215 to get 101.

$$|\frac{101}{90}|-\frac{19}{15}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{101}{90} is \frac{101}{90}.

$$\frac{101}{90}-\frac{19}{15}$$

Least common multiple of 90 and 15 is 90. Convert \frac{101}{90} and \frac{19}{15} to fractions with denominator 90.

$$\frac{101}{90}-\frac{114}{90}$$

Since \frac{101}{90} and \frac{114}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{101-114}{90}$$

Subtract 114 from 101 to get -13.

$$-\frac{13}{90}$$

Factor

$$-\frac{13}{90} = -0.14444444444444443$$