Solve (2)(-7.7)+[(-65/6)+(-3.3)]+11/6

$$( 2 ) ( - 7.7 ) + [ ( - 6 \frac { 5 } { 6 } ) + ( - 3.3 ) ] + 1 \frac { 1 } { 6 }$$

Evaluate

$$-\frac{731}{30}\approx -24.366666667$$

Solution Steps

Multiply 2 and -7.7 to get -15.4.

$$-15.4-\frac{6\times 6+5}{6}-3.3+\frac{1\times 6+1}{6}$$

Multiply 6 and 6 to get 36.

$$-15.4-\frac{36+5}{6}-3.3+\frac{1\times 6+1}{6}$$

Add 36 and 5 to get 41.

$$-15.4-\frac{41}{6}-3.3+\frac{1\times 6+1}{6}$$

Convert decimal number -15.4 to fraction -\frac{154}{10}. Reduce the fraction -\frac{154}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{77}{5}-\frac{41}{6}-3.3+\frac{1\times 6+1}{6}$$

Least common multiple of 5 and 6 is 30. Convert -\frac{77}{5} and \frac{41}{6} to fractions with denominator 30.

$$-\frac{462}{30}-\frac{205}{30}-3.3+\frac{1\times 6+1}{6}$$

Since -\frac{462}{30} and \frac{205}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-462-205}{30}-3.3+\frac{1\times 6+1}{6}$$

Subtract 205 from -462 to get -667.

$$-\frac{667}{30}-3.3+\frac{1\times 6+1}{6}$$

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

$$-\frac{667}{30}-\frac{33}{10}+\frac{1\times 6+1}{6}$$

Least common multiple of 30 and 10 is 30. Convert -\frac{667}{30} and \frac{33}{10} to fractions with denominator 30.

$$-\frac{667}{30}-\frac{99}{30}+\frac{1\times 6+1}{6}$$

Since -\frac{667}{30} and \frac{99}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-667-99}{30}+\frac{1\times 6+1}{6}$$

Subtract 99 from -667 to get -766.

$$\frac{-766}{30}+\frac{1\times 6+1}{6}$$

Reduce the fraction \frac{-766}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{383}{15}+\frac{1\times 6+1}{6}$$

Multiply 1 and 6 to get 6.

$$-\frac{383}{15}+\frac{6+1}{6}$$

Add 6 and 1 to get 7.

$$-\frac{383}{15}+\frac{7}{6}$$

Least common multiple of 15 and 6 is 30. Convert -\frac{383}{15} and \frac{7}{6} to fractions with denominator 30.

$$-\frac{766}{30}+\frac{35}{30}$$

Since -\frac{766}{30} and \frac{35}{30} have the same denominator, add them by adding their numerators.

$$\frac{-766+35}{30}$$

Add -766 and 35 to get -731.

$$-\frac{731}{30}$$

Factor

$$-\frac{731}{30} = -24\frac{11}{30} = -24.366666666666667$$