Solve (3(1)^2/2-(7)^3/3-(1)^2/2-(1)^2)

$$( \frac { 3 ( 1 ) ^ { 2 } } { 2 } - \frac { ( 7 ) ^ { 3 } } { 3 } - \frac { ( 1 ) ^ { 2 } } { 2 } - ( 1 ) ^ { 2 } )$$

Evaluate

$$-\frac{343}{3}\approx -114.333333333$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\frac{3\times 1}{2}-\frac{7^{3}}{3}-\frac{1^{2}}{2}-1^{2}$$

Multiply 3 and 1 to get 3.

$$\frac{3}{2}-\frac{7^{3}}{3}-\frac{1^{2}}{2}-1^{2}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{3}{2}-\frac{343}{3}-\frac{1^{2}}{2}-1^{2}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{343}{3} to fractions with denominator 6.

$$\frac{9}{6}-\frac{686}{6}-\frac{1^{2}}{2}-1^{2}$$

Since \frac{9}{6} and \frac{686}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-686}{6}-\frac{1^{2}}{2}-1^{2}$$

Subtract 686 from 9 to get -677.

$$-\frac{677}{6}-\frac{1^{2}}{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$-\frac{677}{6}-\frac{1}{2}-1^{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{677}{6} and \frac{1}{2} to fractions with denominator 6.

$$-\frac{677}{6}-\frac{3}{6}-1^{2}$$

Since -\frac{677}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-677-3}{6}-1^{2}$$

Subtract 3 from -677 to get -680.

$$\frac{-680}{6}-1^{2}$$

Reduce the fraction \frac{-680}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{340}{3}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$-\frac{340}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$-\frac{340}{3}-\frac{3}{3}$$

Since -\frac{340}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-340-3}{3}$$

Subtract 3 from -340 to get -343.

$$-\frac{343}{3}$$

Factor

$$-\frac{343}{3} = -114\frac{1}{3} = -114.33333333333333$$