Solve (-5v/6)+(-92/3)+(-31/2)=

$$( - 5 \frac { v } { 6 } ) + ( - 9 \frac { 2 } { 3 } ) + ( - 3 \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{-5v-79}{6}$$

Short Solution Steps

Express -5\times \frac{v}{6} as a single fraction.

$$\frac{-5v}{6}-\frac{9\times 3+2}{3}-\frac{3\times 2+1}{2}$$

Multiply 9 and 3 to get 27.

$$\frac{-5v}{6}-\frac{27+2}{3}-\frac{3\times 2+1}{2}$$

Add 27 and 2 to get 29.

$$\frac{-5v}{6}-\frac{29}{3}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{-5v}{6}-\frac{29}{3}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{-5v}{6}-\frac{29}{3}-\frac{7}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{29}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{-5v}{6}-\frac{58}{6}-\frac{21}{6}$$

Since -\frac{58}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5v}{6}+\frac{-58-21}{6}$$

Subtract 21 from -58 to get -79.

$$\frac{-5v}{6}-\frac{79}{6}$$

Since \frac{-5v}{6} and \frac{79}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5v-79}{6}$$

Expand

$$\frac{-5v-79}{6}$$

Short Solution Steps

Express -5\times \frac{v}{6} as a single fraction.

$$\frac{-5v}{6}-\frac{9\times 3+2}{3}-\frac{3\times 2+1}{2}$$

Multiply 9 and 3 to get 27.

$$\frac{-5v}{6}-\frac{27+2}{3}-\frac{3\times 2+1}{2}$$

Add 27 and 2 to get 29.

$$\frac{-5v}{6}-\frac{29}{3}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{-5v}{6}-\frac{29}{3}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{-5v}{6}-\frac{29}{3}-\frac{7}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{29}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{-5v}{6}-\frac{58}{6}-\frac{21}{6}$$

Since -\frac{58}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5v}{6}+\frac{-58-21}{6}$$

Subtract 21 from -58 to get -79.

$$\frac{-5v}{6}-\frac{79}{6}$$

Since \frac{-5v}{6} and \frac{79}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5v-79}{6}$$