Solve 102/9-(-41/9)-37-(-52/3)

$$10 \frac { 2 } { 9 } - ( - 4 \frac { 1 } { 9 } ) - 37 - ( - 5 \frac { 2 } { 3 } )$$

Evaluate

$$-17$$

Solution Steps

Multiply 10 and 9 to get 90.

$$\frac{90+2}{9}-\left(-\frac{4\times 9+1}{9}\right)-37-\left(-\frac{5\times 3+2}{3}\right)$$

Add 90 and 2 to get 92.

$$\frac{92}{9}-\left(-\frac{4\times 9+1}{9}\right)-37-\left(-\frac{5\times 3+2}{3}\right)$$

Multiply 4 and 9 to get 36.

$$\frac{92}{9}-\left(-\frac{36+1}{9}\right)-37-\left(-\frac{5\times 3+2}{3}\right)$$

Add 36 and 1 to get 37.

$$\frac{92}{9}-\left(-\frac{37}{9}\right)-37-\left(-\frac{5\times 3+2}{3}\right)$$

The opposite of -\frac{37}{9} is \frac{37}{9}.

$$\frac{92}{9}+\frac{37}{9}-37-\left(-\frac{5\times 3+2}{3}\right)$$

Since \frac{92}{9} and \frac{37}{9} have the same denominator, add them by adding their numerators.

$$\frac{92+37}{9}-37-\left(-\frac{5\times 3+2}{3}\right)$$

Add 92 and 37 to get 129.

$$\frac{129}{9}-37-\left(-\frac{5\times 3+2}{3}\right)$$

Reduce the fraction \frac{129}{9} to lowest terms by extracting and canceling out 3.

$$\frac{43}{3}-37-\left(-\frac{5\times 3+2}{3}\right)$$

Convert 37 to fraction \frac{111}{3}.

$$\frac{43}{3}-\frac{111}{3}-\left(-\frac{5\times 3+2}{3}\right)$$

Since \frac{43}{3} and \frac{111}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43-111}{3}-\left(-\frac{5\times 3+2}{3}\right)$$

Subtract 111 from 43 to get -68.

$$-\frac{68}{3}-\left(-\frac{5\times 3+2}{3}\right)$$

Multiply 5 and 3 to get 15.

$$-\frac{68}{3}-\left(-\frac{15+2}{3}\right)$$

Add 15 and 2 to get 17.

$$-\frac{68}{3}-\left(-\frac{17}{3}\right)$$

The opposite of -\frac{17}{3} is \frac{17}{3}.

$$-\frac{68}{3}+\frac{17}{3}$$

Since -\frac{68}{3} and \frac{17}{3} have the same denominator, add them by adding their numerators.

$$\frac{-68+17}{3}$$

Add -68 and 17 to get -51.

$$\frac{-51}{3}$$

Divide -51 by 3 to get -17.

$$-17$$

Factor

$$-17$$