Solve 2/3/7-2/frac{3{7}}=?

$$\frac { \frac { 2 } { 3 } } { 7 } - \frac { 2 } { \frac { 3 } { 7 } } = ?$$

Evaluate

$$-\frac{32}{7}\approx -4.571428571$$

Solution Steps

Express \frac{\frac{2}{3}}{7} as a single fraction.

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

Multiply 3 and 7 to get 21.

$$\frac{2}{21}-\frac{2}{\frac{3}{7}}$$

Divide 2 by \frac{3}{7} by multiplying 2 by the reciprocal of \frac{3}{7}.

$$\frac{2}{21}-2\times \frac{7}{3}$$

Express 2\times \frac{7}{3} as a single fraction.

$$\frac{2}{21}-\frac{2\times 7}{3}$$

Multiply 2 and 7 to get 14.

$$\frac{2}{21}-\frac{14}{3}$$

Least common multiple of 21 and 3 is 21. Convert \frac{2}{21} and \frac{14}{3} to fractions with denominator 21.

$$\frac{2}{21}-\frac{98}{21}$$

Since \frac{2}{21} and \frac{98}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-98}{21}$$

Subtract 98 from 2 to get -96.

$$\frac{-96}{21}$$

Reduce the fraction \frac{-96}{21} to lowest terms by extracting and canceling out 3.

$$-\frac{32}{7}$$

Factor

$$-\frac{32}{7} = -4\frac{4}{7} = -4.571428571428571$$