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

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

Evaluate

$$\frac{15}{64}=0.234375$$

Solution Steps

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

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

Since \frac{2}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 2 to get -1.

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

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

$$\frac{-\frac{1}{4}}{\frac{9}{15}-\frac{25}{15}}$$

Since \frac{9}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{4}}{\frac{9-25}{15}}$$

Subtract 25 from 9 to get -16.

$$\frac{-\frac{1}{4}}{-\frac{16}{15}}$$

Divide -\frac{1}{4} by -\frac{16}{15} by multiplying -\frac{1}{4} by the reciprocal of -\frac{16}{15}.

$$-\frac{1}{4}\left(-\frac{15}{16}\right)$$

Multiply -\frac{1}{4} times -\frac{15}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-15\right)}{4\times 16}$$

Do the multiplications in the fraction \frac{-\left(-15\right)}{4\times 16}.

$$\frac{15}{64}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {6}} = 0.234375$$