Solve 2/frac{2{9}-3/7}

$$\frac { 2 } { \frac { 2 } { 9 } - \frac { 3 } { 7 } }$$

Evaluate

$$-\frac{126}{13}\approx -9.692307692$$

Solution Steps

Least common multiple of 9 and 7 is 63. Convert \frac{2}{9} and \frac{3}{7} to fractions with denominator 63.

$$\frac{2}{\frac{14}{63}-\frac{27}{63}}$$

Since \frac{14}{63} and \frac{27}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{\frac{14-27}{63}}$$

Subtract 27 from 14 to get -13.

$$\frac{2}{-\frac{13}{63}}$$

Divide 2 by -\frac{13}{63} by multiplying 2 by the reciprocal of -\frac{13}{63}.

$$2\left(-\frac{63}{13}\right)$$

Express 2\left(-\frac{63}{13}\right) as a single fraction.

$$\frac{2\left(-63\right)}{13}$$

Multiply 2 and -63 to get -126.

$$\frac{-126}{13}$$

Fraction \frac{-126}{13} can be rewritten as -\frac{126}{13} by extracting the negative sign.

$$-\frac{126}{13}$$

Factor

$$-\frac{126}{13} = -9\frac{9}{13} = -9.692307692307692$$