Solve -7/3div(-12/10)-5/10*(-7/3+(-frac{12}{10}))

$$- \frac{ 7 }{ 3 } \div (- \frac{ 12 }{ 10 } )- \frac{ 5 }{ 10 } \times (- \frac{ 7 }{ 3 } +(- \frac{ 12 }{ 10 } ))$$

Evaluate

$$\frac{167}{45}\approx 3.711111111$$

Solution Steps

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{7}{3}}{-\frac{6}{5}}-\frac{5}{10}\left(-\frac{7}{3}-\frac{12}{10}\right)$$

Divide -\frac{7}{3} by -\frac{6}{5} by multiplying -\frac{7}{3} by the reciprocal of -\frac{6}{5}.

$$-\frac{7}{3}\left(-\frac{5}{6}\right)-\frac{5}{10}\left(-\frac{7}{3}-\frac{12}{10}\right)$$

Multiply -\frac{7}{3} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7\left(-5\right)}{3\times 6}-\frac{5}{10}\left(-\frac{7}{3}-\frac{12}{10}\right)$$

Do the multiplications in the fraction \frac{-7\left(-5\right)}{3\times 6}.

$$\frac{35}{18}-\frac{5}{10}\left(-\frac{7}{3}-\frac{12}{10}\right)$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{35}{18}-\frac{1}{2}\left(-\frac{7}{3}-\frac{12}{10}\right)$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{35}{18}-\frac{1}{2}\left(-\frac{7}{3}-\frac{6}{5}\right)$$

Least common multiple of 3 and 5 is 15. Convert -\frac{7}{3} and \frac{6}{5} to fractions with denominator 15.

$$\frac{35}{18}-\frac{1}{2}\left(-\frac{35}{15}-\frac{18}{15}\right)$$

Since -\frac{35}{15} and \frac{18}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35}{18}-\frac{1}{2}\times \frac{-35-18}{15}$$

Subtract 18 from -35 to get -53.

$$\frac{35}{18}-\frac{1}{2}\left(-\frac{53}{15}\right)$$

Multiply \frac{1}{2} times -\frac{53}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{18}-\frac{1\left(-53\right)}{2\times 15}$$

Do the multiplications in the fraction \frac{1\left(-53\right)}{2\times 15}.

$$\frac{35}{18}-\frac{-53}{30}$$

Fraction \frac{-53}{30} can be rewritten as -\frac{53}{30} by extracting the negative sign.

$$\frac{35}{18}-\left(-\frac{53}{30}\right)$$

The opposite of -\frac{53}{30} is \frac{53}{30}.

$$\frac{35}{18}+\frac{53}{30}$$

Least common multiple of 18 and 30 is 90. Convert \frac{35}{18} and \frac{53}{30} to fractions with denominator 90.

$$\frac{175}{90}+\frac{159}{90}$$

Since \frac{175}{90} and \frac{159}{90} have the same denominator, add them by adding their numerators.

$$\frac{175+159}{90}$$

Add 175 and 159 to get 334.

$$\frac{334}{90}$$

Reduce the fraction \frac{334}{90} to lowest terms by extracting and canceling out 2.

$$\frac{167}{45}$$

Factor

$$\frac{167}{3 ^ {2} \cdot 5} = 3\frac{32}{45} = 3.7111111111111112$$