Solve 7/4-2/2/frac{4{5}-3/2}

$$\frac { \frac { 7 } { 4 } - \frac { 2 } { 2 } } { \frac { 4 } { 5 } - \frac { 3 } { 2 } }$$

Evaluate

$$-\frac{15}{14}\approx -1.071428571$$

Solution Steps

Divide 2 by 2 to get 1.

$$\frac{\frac{7}{4}-1}{\frac{4}{5}-\frac{3}{2}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{7}{4}-\frac{4}{4}}{\frac{4}{5}-\frac{3}{2}}$$

Since \frac{7}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-4}{4}}{\frac{4}{5}-\frac{3}{2}}$$

Subtract 4 from 7 to get 3.

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

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

$$\frac{\frac{3}{4}}{\frac{8}{10}-\frac{15}{10}}$$

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

$$\frac{\frac{3}{4}}{\frac{8-15}{10}}$$

Subtract 15 from 8 to get -7.

$$\frac{\frac{3}{4}}{-\frac{7}{10}}$$

Divide \frac{3}{4} by -\frac{7}{10} by multiplying \frac{3}{4} by the reciprocal of -\frac{7}{10}.

$$\frac{3}{4}\left(-\frac{10}{7}\right)$$

Multiply \frac{3}{4} times -\frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-10\right)}{4\times 7}$$

Do the multiplications in the fraction \frac{3\left(-10\right)}{4\times 7}.

$$\frac{-30}{28}$$

Reduce the fraction \frac{-30}{28} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{14}$$

Factor

$$-\frac{15}{14} = -1\frac{1}{14} = -1.0714285714285714$$