Solve 5/6:(3/2-4/5)=

$$\frac { 5 } { 6 } : ( \frac { 3 } { 2 } - \frac { 4 } { 5 } ) =$$

Evaluate

$$\frac{25}{21}\approx 1.19047619$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{4}{5} to fractions with denominator 10.

$$\frac{\frac{5}{6}}{\frac{15}{10}-\frac{8}{10}}$$

Since \frac{15}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{6}}{\frac{15-8}{10}}$$

Subtract 8 from 15 to get 7.

$$\frac{\frac{5}{6}}{\frac{7}{10}}$$

Divide \frac{5}{6} by \frac{7}{10} by multiplying \frac{5}{6} by the reciprocal of \frac{7}{10}.

$$\frac{5}{6}\times \frac{10}{7}$$

Multiply \frac{5}{6} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 10}{6\times 7}$$

Do the multiplications in the fraction \frac{5\times 10}{6\times 7}.

$$\frac{50}{42}$$

Reduce the fraction \frac{50}{42} to lowest terms by extracting and canceling out 2.

$$\frac{25}{21}$$

Factor

$$\frac{5 ^ {2}}{3 \cdot 7} = 1\frac{4}{21} = 1.1904761904761905$$