Solve (3/7-2/5):(3/5-2/7)

$$( \frac { 3 } { 7 } - \frac { 2 } { 5 } ) : ( \frac { 3 } { 5 } - \frac { 2 } { 7 } )$$

Evaluate

$$\frac{1}{11}\approx 0.090909091$$

Solution Steps

Least common multiple of 7 and 5 is 35. Convert \frac{3}{7} and \frac{2}{5} to fractions with denominator 35.

$$\frac{\frac{15}{35}-\frac{14}{35}}{\frac{3}{5}-\frac{2}{7}}$$

Since \frac{15}{35} and \frac{14}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-14}{35}}{\frac{3}{5}-\frac{2}{7}}$$

Subtract 14 from 15 to get 1.

$$\frac{\frac{1}{35}}{\frac{3}{5}-\frac{2}{7}}$$

Least common multiple of 5 and 7 is 35. Convert \frac{3}{5} and \frac{2}{7} to fractions with denominator 35.

$$\frac{\frac{1}{35}}{\frac{21}{35}-\frac{10}{35}}$$

Since \frac{21}{35} and \frac{10}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{35}}{\frac{21-10}{35}}$$

Subtract 10 from 21 to get 11.

$$\frac{\frac{1}{35}}{\frac{11}{35}}$$

Divide \frac{1}{35} by \frac{11}{35} by multiplying \frac{1}{35} by the reciprocal of \frac{11}{35}.

$$\frac{1}{35}\times \frac{35}{11}$$

Multiply \frac{1}{35} times \frac{35}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 35}{35\times 11}$$

Cancel out 35 in both numerator and denominator.

$$\frac{1}{11}$$

Factor

$$\frac{1}{11} = 0.09090909090909091$$