Solve 6/5-5/3/frac{1{4}-3/2}

$$\frac { \frac { 6 } { 5 } - \frac { 5 } { 3 } } { \frac { 1 } { 4 } - \frac { 3 } { 2 } }$$

Evaluate

$$\frac{28}{75}\approx 0.373333333$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{6}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{\frac{18}{15}-\frac{25}{15}}{\frac{1}{4}-\frac{3}{2}}$$

Since \frac{18}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{18-25}{15}}{\frac{1}{4}-\frac{3}{2}}$$

Subtract 25 from 18 to get -7.

$$\frac{-\frac{7}{15}}{\frac{1}{4}-\frac{3}{2}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{-\frac{7}{15}}{\frac{1}{4}-\frac{6}{4}}$$

Since \frac{1}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{7}{15}}{\frac{1-6}{4}}$$

Subtract 6 from 1 to get -5.

$$\frac{-\frac{7}{15}}{-\frac{5}{4}}$$

Divide -\frac{7}{15} by -\frac{5}{4} by multiplying -\frac{7}{15} by the reciprocal of -\frac{5}{4}.

$$-\frac{7}{15}\left(-\frac{4}{5}\right)$$

Multiply -\frac{7}{15} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7\left(-4\right)}{15\times 5}$$

Do the multiplications in the fraction \frac{-7\left(-4\right)}{15\times 5}.

$$\frac{28}{75}$$

Factor

$$\frac{2 ^ {2} \cdot 7}{3 \cdot 5 ^ {2}} = 0.37333333333333335$$