Solve 7/2-5/frac{7{2}-6}

$$\frac { \frac { 7 } { 2 } - 5 } { \frac { 7 } { 2 } - 6 }$$

Evaluate

$$\frac{3}{5}=0.6$$

Solution Steps

Convert 5 to fraction \frac{10}{2}.

$$\frac{\frac{7}{2}-\frac{10}{2}}{\frac{7}{2}-6}$$

Since \frac{7}{2} and \frac{10}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-10}{2}}{\frac{7}{2}-6}$$

Subtract 10 from 7 to get -3.

$$\frac{-\frac{3}{2}}{\frac{7}{2}-6}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{-\frac{3}{2}}{\frac{7}{2}-\frac{12}{2}}$$

Since \frac{7}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{3}{2}}{\frac{7-12}{2}}$$

Subtract 12 from 7 to get -5.

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

Divide -\frac{3}{2} by -\frac{5}{2} by multiplying -\frac{3}{2} by the reciprocal of -\frac{5}{2}.

$$-\frac{3}{2}\left(-\frac{2}{5}\right)$$

Multiply -\frac{3}{2} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-2\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{-3\left(-2\right)}{2\times 5}.

$$\frac{6}{10}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$