Solve (-21/8)*(-129/51)+(-123/42)*31/13-(-4frac{2}{9})*6

$$( - 2 \frac { 1 } { 8 } ) \cdot ( - 1 \frac { 29 } { 51 } ) + ( - 1 \frac { 23 } { 42 } ) \cdot 3 \frac { 1 } { 13 } - ( - 4 \frac { 2 } { 9 } ) \cdot 6$$

Evaluate

$$\frac{502}{21}\approx 23.904761905$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\left(-\frac{16+1}{8}\right)\left(-\frac{1\times 51+29}{51}\right)+\left(-\frac{1\times 42+23}{42}\right)\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Add 16 and 1 to get 17.

$$-\frac{17}{8}\left(-\frac{51+29}{51}\right)+\left(-\frac{1\times 42+23}{42}\right)\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Add 51 and 29 to get 80.

$$-\frac{17}{8}\left(-\frac{80}{51}\right)+\left(-\frac{1\times 42+23}{42}\right)\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Multiply -\frac{17}{8} times -\frac{80}{51} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-17\left(-80\right)}{8\times 51}+\left(-\frac{1\times 42+23}{42}\right)\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Do the multiplications in the fraction \frac{-17\left(-80\right)}{8\times 51}.

$$\frac{1360}{408}+\left(-\frac{1\times 42+23}{42}\right)\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Reduce the fraction \frac{1360}{408} to lowest terms by extracting and canceling out 136.

$$\frac{10}{3}+\left(-\frac{1\times 42+23}{42}\right)\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Multiply 1 and 42 to get 42.

$$\frac{10}{3}+\left(-\frac{42+23}{42}\right)\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Add 42 and 23 to get 65.

$$\frac{10}{3}-\frac{65}{42}\times \frac{3\times 13+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Multiply 3 and 13 to get 39.

$$\frac{10}{3}-\frac{65}{42}\times \frac{39+1}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Add 39 and 1 to get 40.

$$\frac{10}{3}-\frac{65}{42}\times \frac{40}{13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Multiply -\frac{65}{42} times \frac{40}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{3}+\frac{-65\times 40}{42\times 13}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Do the multiplications in the fraction \frac{-65\times 40}{42\times 13}.

$$\frac{10}{3}+\frac{-2600}{546}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Reduce the fraction \frac{-2600}{546} to lowest terms by extracting and canceling out 26.

$$\frac{10}{3}-\frac{100}{21}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Least common multiple of 3 and 21 is 21. Convert \frac{10}{3} and \frac{100}{21} to fractions with denominator 21.

$$\frac{70}{21}-\frac{100}{21}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Since \frac{70}{21} and \frac{100}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{70-100}{21}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Subtract 100 from 70 to get -30.

$$\frac{-30}{21}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Reduce the fraction \frac{-30}{21} to lowest terms by extracting and canceling out 3.

$$-\frac{10}{7}-\left(-\frac{4\times 9+2}{9}\right)\times 6$$

Multiply 4 and 9 to get 36.

$$-\frac{10}{7}-\left(-\frac{36+2}{9}\right)\times 6$$

Add 36 and 2 to get 38.

$$-\frac{10}{7}-\left(-\frac{38}{9}\times 6\right)$$

Express -\frac{38}{9}\times 6 as a single fraction.

$$-\frac{10}{7}-\frac{-38\times 6}{9}$$

Multiply -38 and 6 to get -228.

$$-\frac{10}{7}-\frac{-228}{9}$$

Reduce the fraction \frac{-228}{9} to lowest terms by extracting and canceling out 3.

$$-\frac{10}{7}-\left(-\frac{76}{3}\right)$$

The opposite of -\frac{76}{3} is \frac{76}{3}.

$$-\frac{10}{7}+\frac{76}{3}$$

Least common multiple of 7 and 3 is 21. Convert -\frac{10}{7} and \frac{76}{3} to fractions with denominator 21.

$$-\frac{30}{21}+\frac{532}{21}$$

Since -\frac{30}{21} and \frac{532}{21} have the same denominator, add them by adding their numerators.

$$\frac{-30+532}{21}$$

Add -30 and 532 to get 502.

$$\frac{502}{21}$$

Factor

$$\frac{2 \cdot 251}{3 \cdot 7} = 23\frac{19}{21} = 23.904761904761905$$