Solve 2/5-[5+-(3/10-2/15)]+1=

$$\frac { 2 } { 5 } - [ 5 + - ( \frac { 3 } { 10 } - \frac { 2 } { 15 } ) ] + 1 =$$

Evaluate

$$-\frac{103}{30}\approx -3.433333333$$

Solution Steps

Least common multiple of 10 and 15 is 30. Convert \frac{3}{10} and \frac{2}{15} to fractions with denominator 30.

$$\frac{2}{5}-\left(5-\left(\frac{9}{30}-\frac{4}{30}\right)\right)+1$$

Since \frac{9}{30} and \frac{4}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}-\left(5-\frac{9-4}{30}\right)+1$$

Subtract 4 from 9 to get 5.

$$\frac{2}{5}-\left(5-\frac{5}{30}\right)+1$$

Reduce the fraction \frac{5}{30} to lowest terms by extracting and canceling out 5.

$$\frac{2}{5}-\left(5-\frac{1}{6}\right)+1$$

Convert 5 to fraction \frac{30}{6}.

$$\frac{2}{5}-\left(\frac{30}{6}-\frac{1}{6}\right)+1$$

Since \frac{30}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}-\frac{30-1}{6}+1$$

Subtract 1 from 30 to get 29.

$$\frac{2}{5}-\frac{29}{6}+1$$

Least common multiple of 5 and 6 is 30. Convert \frac{2}{5} and \frac{29}{6} to fractions with denominator 30.

$$\frac{12}{30}-\frac{145}{30}+1$$

Since \frac{12}{30} and \frac{145}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-145}{30}+1$$

Subtract 145 from 12 to get -133.

$$-\frac{133}{30}+1$$

Convert 1 to fraction \frac{30}{30}.

$$-\frac{133}{30}+\frac{30}{30}$$

Since -\frac{133}{30} and \frac{30}{30} have the same denominator, add them by adding their numerators.

$$\frac{-133+30}{30}$$

Add -133 and 30 to get -103.

$$-\frac{103}{30}$$

Factor

$$-\frac{103}{30} = -3\frac{13}{30} = -3.433333333333333$$