Solve (-7.7)+[(-65/6)+(-3.3)]+11/6

$$( - 7.7 ) + [ ( - 6 \frac { 5 } { 6 } ) + ( - 3.3 ) ] + 1 \frac { 1 } { 6 }$$

Evaluate

$$-\frac{50}{3}\approx -16.666666667$$

Solution Steps

Multiply 6 and 6 to get 36.

$$-7.7-\frac{36+5}{6}-3.3+\frac{1\times 6+1}{6}$$

Add 36 and 5 to get 41.

$$-7.7-\frac{41}{6}-3.3+\frac{1\times 6+1}{6}$$

Convert decimal number -7.7 to fraction -\frac{77}{10}.

$$-\frac{77}{10}-\frac{41}{6}-3.3+\frac{1\times 6+1}{6}$$

Least common multiple of 10 and 6 is 30. Convert -\frac{77}{10} and \frac{41}{6} to fractions with denominator 30.

$$-\frac{231}{30}-\frac{205}{30}-3.3+\frac{1\times 6+1}{6}$$

Since -\frac{231}{30} and \frac{205}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-231-205}{30}-3.3+\frac{1\times 6+1}{6}$$

Subtract 205 from -231 to get -436.

$$\frac{-436}{30}-3.3+\frac{1\times 6+1}{6}$$

Reduce the fraction \frac{-436}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{218}{15}-3.3+\frac{1\times 6+1}{6}$$

Convert decimal number 3.3 to fraction \frac{33}{10}.

$$-\frac{218}{15}-\frac{33}{10}+\frac{1\times 6+1}{6}$$

Least common multiple of 15 and 10 is 30. Convert -\frac{218}{15} and \frac{33}{10} to fractions with denominator 30.

$$-\frac{436}{30}-\frac{99}{30}+\frac{1\times 6+1}{6}$$

Since -\frac{436}{30} and \frac{99}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-436-99}{30}+\frac{1\times 6+1}{6}$$

Subtract 99 from -436 to get -535.

$$\frac{-535}{30}+\frac{1\times 6+1}{6}$$

Reduce the fraction \frac{-535}{30} to lowest terms by extracting and canceling out 5.

$$-\frac{107}{6}+\frac{1\times 6+1}{6}$$

Multiply 1 and 6 to get 6.

$$-\frac{107}{6}+\frac{6+1}{6}$$

Add 6 and 1 to get 7.

$$-\frac{107}{6}+\frac{7}{6}$$

Since -\frac{107}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{-107+7}{6}$$

Add -107 and 7 to get -100.

$$\frac{-100}{6}$$

Reduce the fraction \frac{-100}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{50}{3}$$

Factor

$$-\frac{50}{3} = -16\frac{2}{3} = -16.666666666666668$$