Solve left|-1-4/15+2+7/18right|-1-4/15=

$$\left| -1- \frac{ 4 }{ 15 } +2+ \frac{ 7 }{ 18 } \right| -1- \frac{ 4 }{ 15 } =$$

Evaluate

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

Solution Steps

Convert -1 to fraction -\frac{15}{15}.

$$|-\frac{15}{15}-\frac{4}{15}+2+\frac{7}{18}|-1-\frac{4}{15}$$

Since -\frac{15}{15} and \frac{4}{15} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{-15-4}{15}+2+\frac{7}{18}|-1-\frac{4}{15}$$

Subtract 4 from -15 to get -19.

$$|-\frac{19}{15}+2+\frac{7}{18}|-1-\frac{4}{15}$$

Convert 2 to fraction \frac{30}{15}.

$$|-\frac{19}{15}+\frac{30}{15}+\frac{7}{18}|-1-\frac{4}{15}$$

Since -\frac{19}{15} and \frac{30}{15} have the same denominator, add them by adding their numerators.

$$|\frac{-19+30}{15}+\frac{7}{18}|-1-\frac{4}{15}$$

Add -19 and 30 to get 11.

$$|\frac{11}{15}+\frac{7}{18}|-1-\frac{4}{15}$$

Least common multiple of 15 and 18 is 90. Convert \frac{11}{15} and \frac{7}{18} to fractions with denominator 90.

$$|\frac{66}{90}+\frac{35}{90}|-1-\frac{4}{15}$$

Since \frac{66}{90} and \frac{35}{90} have the same denominator, add them by adding their numerators.

$$|\frac{66+35}{90}|-1-\frac{4}{15}$$

Add 66 and 35 to get 101.

$$|\frac{101}{90}|-1-\frac{4}{15}$$

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}.

$$\frac{101}{90}-1-\frac{4}{15}$$

Convert 1 to fraction \frac{90}{90}.

$$\frac{101}{90}-\frac{90}{90}-\frac{4}{15}$$

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

$$\frac{101-90}{90}-\frac{4}{15}$$

Subtract 90 from 101 to get 11.

$$\frac{11}{90}-\frac{4}{15}$$

Least common multiple of 90 and 15 is 90. Convert \frac{11}{90} and \frac{4}{15} to fractions with denominator 90.

$$\frac{11}{90}-\frac{24}{90}$$

Since \frac{11}{90} and \frac{24}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-24}{90}$$

Subtract 24 from 11 to get -13.

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

Factor

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