Solve 1/frac{1{42}-1/9}

$$\frac { 1 } { \frac { 1 } { 42 } - \frac { 1 } { 9 } }$$

Evaluate

$$-\frac{126}{11}\approx -11.454545455$$

Solution Steps

Least common multiple of 42 and 9 is 126. Convert \frac{1}{42} and \frac{1}{9} to fractions with denominator 126.

$$\frac{1}{\frac{3}{126}-\frac{14}{126}}$$

Since \frac{3}{126} and \frac{14}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{3-14}{126}}$$

Subtract 14 from 3 to get -11.

$$\frac{1}{-\frac{11}{126}}$$

Divide 1 by -\frac{11}{126} by multiplying 1 by the reciprocal of -\frac{11}{126}.

$$1\left(-\frac{126}{11}\right)$$

Multiply 1 and -\frac{126}{11} to get -\frac{126}{11}.

$$-\frac{126}{11}$$

Factor

$$-\frac{126}{11} = -11\frac{5}{11} = -11.454545454545455$$