Solve 5/4-5/2/frac{4{5}-3/2}

$$\frac { \frac { 5 } { 4 } - \frac { 5 } { 2 } } { \frac { 4 } { 5 } - \frac { 3 } { 2 } }$$

Evaluate

$$\frac{25}{14}\approx 1.785714286$$

Solution Steps

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

$$\frac{\frac{5}{4}-\frac{10}{4}}{\frac{4}{5}-\frac{3}{2}}$$

Since \frac{5}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-10}{4}}{\frac{4}{5}-\frac{3}{2}}$$

Subtract 10 from 5 to get -5.

$$\frac{-\frac{5}{4}}{\frac{4}{5}-\frac{3}{2}}$$

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

$$\frac{-\frac{5}{4}}{\frac{8}{10}-\frac{15}{10}}$$

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

$$\frac{-\frac{5}{4}}{\frac{8-15}{10}}$$

Subtract 15 from 8 to get -7.

$$\frac{-\frac{5}{4}}{-\frac{7}{10}}$$

Divide -\frac{5}{4} by -\frac{7}{10} by multiplying -\frac{5}{4} by the reciprocal of -\frac{7}{10}.

$$-\frac{5}{4}\left(-\frac{10}{7}\right)$$

Multiply -\frac{5}{4} times -\frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-10\right)}{4\times 7}$$

Do the multiplications in the fraction \frac{-5\left(-10\right)}{4\times 7}.

$$\frac{50}{28}$$

Reduce the fraction \frac{50}{28} to lowest terms by extracting and canceling out 2.

$$\frac{25}{14}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 7} = 1\frac{11}{14} = 1.7857142857142858$$