Solve 2,5-[(6-3/2)+(-5/3+1,2)]-3/6

$$2,5 - [ ( 6 - \frac { 3 } { 2 } ) + ( - \frac { 5 } { 3 } + 1,2 ) ] - \frac { 3 } { 6 }$$

Evaluate

$$-\frac{61}{30}\approx -2,033333333$$

Solution Steps

Convert 6 to fraction \frac{12}{2}.

$$2,5-\left(\frac{12}{2}-\frac{3}{2}-\frac{5}{3}+1,2\right)-\frac{3}{6}$$

Since \frac{12}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$2,5-\left(\frac{12-3}{2}-\frac{5}{3}+1,2\right)-\frac{3}{6}$$

Subtract 3 from 12 to get 9.

$$2,5-\left(\frac{9}{2}-\frac{5}{3}+1,2\right)-\frac{3}{6}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{5}{3} to fractions with denominator 6.

$$2,5-\left(\frac{27}{6}-\frac{10}{6}+1,2\right)-\frac{3}{6}$$

Since \frac{27}{6} and \frac{10}{6} have the same denominator, subtract them by subtracting their numerators.

$$2,5-\left(\frac{27-10}{6}+1,2\right)-\frac{3}{6}$$

Subtract 10 from 27 to get 17.

$$2,5-\left(\frac{17}{6}+1,2\right)-\frac{3}{6}$$

Convert decimal number 1,2 to fraction \frac{12}{10}. Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$2,5-\left(\frac{17}{6}+\frac{6}{5}\right)-\frac{3}{6}$$

Least common multiple of 6 and 5 is 30. Convert \frac{17}{6} and \frac{6}{5} to fractions with denominator 30.

$$2,5-\left(\frac{85}{30}+\frac{36}{30}\right)-\frac{3}{6}$$

Since \frac{85}{30} and \frac{36}{30} have the same denominator, add them by adding their numerators.

$$2,5-\frac{85+36}{30}-\frac{3}{6}$$

Add 85 and 36 to get 121.

$$2,5-\frac{121}{30}-\frac{3}{6}$$

Convert decimal number 2,5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{5}{2}-\frac{121}{30}-\frac{3}{6}$$

Least common multiple of 2 and 30 is 30. Convert \frac{5}{2} and \frac{121}{30} to fractions with denominator 30.

$$\frac{75}{30}-\frac{121}{30}-\frac{3}{6}$$

Since \frac{75}{30} and \frac{121}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-121}{30}-\frac{3}{6}$$

Subtract 121 from 75 to get -46.

$$\frac{-46}{30}-\frac{3}{6}$$

Reduce the fraction \frac{-46}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{23}{15}-\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{23}{15}-\frac{1}{2}$$

Least common multiple of 15 and 2 is 30. Convert -\frac{23}{15} and \frac{1}{2} to fractions with denominator 30.

$$-\frac{46}{30}-\frac{15}{30}$$

Since -\frac{46}{30} and \frac{15}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-46-15}{30}$$

Subtract 15 from -46 to get -61.

$$-\frac{61}{30}$$

Factor

$$-\frac{61}{30} = -2\frac{1}{30} = -2.033333333333333$$