Solve (-81/3)-(+12)-(-701/2)-(-81/3)

$$( - 8 \frac { 1 } { 3 } ) - ( + 12 ) - ( - 70 \frac { 1 } { 2 } ) - ( - 8 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{117}{2}=58.5$$

Solution Steps

Multiply 8 and 3 to get 24.

$$-\frac{24+1}{3}-12-\left(-\frac{70\times 2+1}{2}\right)-\left(-\frac{8\times 3+1}{3}\right)$$

Add 24 and 1 to get 25.

$$-\frac{25}{3}-12-\left(-\frac{70\times 2+1}{2}\right)-\left(-\frac{8\times 3+1}{3}\right)$$

Convert 12 to fraction \frac{36}{3}.

$$-\frac{25}{3}-\frac{36}{3}-\left(-\frac{70\times 2+1}{2}\right)-\left(-\frac{8\times 3+1}{3}\right)$$

Since -\frac{25}{3} and \frac{36}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-25-36}{3}-\left(-\frac{70\times 2+1}{2}\right)-\left(-\frac{8\times 3+1}{3}\right)$$

Subtract 36 from -25 to get -61.

$$-\frac{61}{3}-\left(-\frac{70\times 2+1}{2}\right)-\left(-\frac{8\times 3+1}{3}\right)$$

Multiply 70 and 2 to get 140.

$$-\frac{61}{3}-\left(-\frac{140+1}{2}\right)-\left(-\frac{8\times 3+1}{3}\right)$$

Add 140 and 1 to get 141.

$$-\frac{61}{3}-\left(-\frac{141}{2}\right)-\left(-\frac{8\times 3+1}{3}\right)$$

The opposite of -\frac{141}{2} is \frac{141}{2}.

$$-\frac{61}{3}+\frac{141}{2}-\left(-\frac{8\times 3+1}{3}\right)$$

Least common multiple of 3 and 2 is 6. Convert -\frac{61}{3} and \frac{141}{2} to fractions with denominator 6.

$$-\frac{122}{6}+\frac{423}{6}-\left(-\frac{8\times 3+1}{3}\right)$$

Since -\frac{122}{6} and \frac{423}{6} have the same denominator, add them by adding their numerators.

$$\frac{-122+423}{6}-\left(-\frac{8\times 3+1}{3}\right)$$

Add -122 and 423 to get 301.

$$\frac{301}{6}-\left(-\frac{8\times 3+1}{3}\right)$$

Multiply 8 and 3 to get 24.

$$\frac{301}{6}-\left(-\frac{24+1}{3}\right)$$

Add 24 and 1 to get 25.

$$\frac{301}{6}-\left(-\frac{25}{3}\right)$$

The opposite of -\frac{25}{3} is \frac{25}{3}.

$$\frac{301}{6}+\frac{25}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{301}{6} and \frac{25}{3} to fractions with denominator 6.

$$\frac{301}{6}+\frac{50}{6}$$

Since \frac{301}{6} and \frac{50}{6} have the same denominator, add them by adding their numerators.

$$\frac{301+50}{6}$$

Add 301 and 50 to get 351.

$$\frac{351}{6}$$

Reduce the fraction \frac{351}{6} to lowest terms by extracting and canceling out 3.

$$\frac{117}{2}$$

Factor

$$\frac{3 ^ {2} \cdot 13}{2} = 58\frac{1}{2} = 58.5$$