Solve [(-32/3)div(-14/7)]-1/9

$$[ ( - 3 \frac { 2 } { 3 } ) \div ( - 1 \frac { 4 } { 7 } ) ] - \frac { 1 } { 9 }$$

Evaluate

$$\frac{20}{9}\approx 2.222222222$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\frac{-\frac{9+2}{3}}{-\frac{1\times 7+4}{7}}-\frac{1}{9}$$

Add 9 and 2 to get 11.

$$\frac{-\frac{11}{3}}{-\frac{1\times 7+4}{7}}-\frac{1}{9}$$

Multiply 1 and 7 to get 7.

$$\frac{-\frac{11}{3}}{-\frac{7+4}{7}}-\frac{1}{9}$$

Add 7 and 4 to get 11.

$$\frac{-\frac{11}{3}}{-\frac{11}{7}}-\frac{1}{9}$$

Divide -\frac{11}{3} by -\frac{11}{7} by multiplying -\frac{11}{3} by the reciprocal of -\frac{11}{7}.

$$-\frac{11}{3}\left(-\frac{7}{11}\right)-\frac{1}{9}$$

Multiply -\frac{11}{3} times -\frac{7}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\left(-7\right)}{3\times 11}-\frac{1}{9}$$

Do the multiplications in the fraction \frac{-11\left(-7\right)}{3\times 11}.

$$\frac{77}{33}-\frac{1}{9}$$

Reduce the fraction \frac{77}{33} to lowest terms by extracting and canceling out 11.

$$\frac{7}{3}-\frac{1}{9}$$

Least common multiple of 3 and 9 is 9. Convert \frac{7}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{21}{9}-\frac{1}{9}$$

Since \frac{21}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-1}{9}$$

Subtract 1 from 21 to get 20.

$$\frac{20}{9}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3 ^ {2}} = 2\frac{2}{9} = 2.2222222222222223$$