Solve -1/3+7*1/2-10+-3^3/3-73^2/2-30

$$\frac{ -1 }{ 3 } + \frac{ 7 \cdot 1 }{ 2 } -10+ \frac{ { -3 }^{ 3 } }{ 3 } - \frac{ 7 { 3 }^{ 2 } }{ 2 } -30$$

Evaluate

$$-\frac{232}{3}\approx -77.333333333$$

Solution Steps

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$-\frac{1}{3}+\frac{7\times 1}{2}-10+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Multiply 7 and 1 to get 7.

$$-\frac{1}{3}+\frac{7}{2}-10+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Least common multiple of 3 and 2 is 6. Convert -\frac{1}{3} and \frac{7}{2} to fractions with denominator 6.

$$-\frac{2}{6}+\frac{21}{6}-10+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Since -\frac{2}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{-2+21}{6}-10+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Add -2 and 21 to get 19.

$$\frac{19}{6}-10+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Convert 10 to fraction \frac{60}{6}.

$$\frac{19}{6}-\frac{60}{6}+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Since \frac{19}{6} and \frac{60}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-60}{6}+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Subtract 60 from 19 to get -41.

$$-\frac{41}{6}+\frac{\left(-3\right)^{3}}{3}-\frac{7\times 3^{2}}{2}-30$$

Calculate -3 to the power of 3 and get -27.

$$-\frac{41}{6}+\frac{-27}{3}-\frac{7\times 3^{2}}{2}-30$$

Divide -27 by 3 to get -9.

$$-\frac{41}{6}-9-\frac{7\times 3^{2}}{2}-30$$

Convert 9 to fraction \frac{54}{6}.

$$-\frac{41}{6}-\frac{54}{6}-\frac{7\times 3^{2}}{2}-30$$

Since -\frac{41}{6} and \frac{54}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-41-54}{6}-\frac{7\times 3^{2}}{2}-30$$

Subtract 54 from -41 to get -95.

$$-\frac{95}{6}-\frac{7\times 3^{2}}{2}-30$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{95}{6}-\frac{7\times 9}{2}-30$$

Multiply 7 and 9 to get 63.

$$-\frac{95}{6}-\frac{63}{2}-30$$

Least common multiple of 6 and 2 is 6. Convert -\frac{95}{6} and \frac{63}{2} to fractions with denominator 6.

$$-\frac{95}{6}-\frac{189}{6}-30$$

Since -\frac{95}{6} and \frac{189}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-95-189}{6}-30$$

Subtract 189 from -95 to get -284.

$$\frac{-284}{6}-30$$

Reduce the fraction \frac{-284}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{142}{3}-30$$

Convert 30 to fraction \frac{90}{3}.

$$-\frac{142}{3}-\frac{90}{3}$$

Since -\frac{142}{3} and \frac{90}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-142-90}{3}$$

Subtract 90 from -142 to get -232.

$$-\frac{232}{3}$$

Factor

$$-\frac{232}{3} = -77\frac{1}{3} = -77.33333333333333$$