Solve 7/-frac{1{4}+38/28}=

$$\frac { 7 } { - \frac { 1 } { 4 } + \frac { 38 } { 28 } } =$$

Evaluate

$$\frac{196}{31}\approx 6.322580645$$

Solution Steps

Reduce the fraction \frac{38}{28} to lowest terms by extracting and canceling out 2.

$$\frac{7}{-\frac{1}{4}+\frac{19}{14}}$$

Least common multiple of 4 and 14 is 28. Convert -\frac{1}{4} and \frac{19}{14} to fractions with denominator 28.

$$\frac{7}{-\frac{7}{28}+\frac{38}{28}}$$

Since -\frac{7}{28} and \frac{38}{28} have the same denominator, add them by adding their numerators.

$$\frac{7}{\frac{-7+38}{28}}$$

Add -7 and 38 to get 31.

$$\frac{7}{\frac{31}{28}}$$

Divide 7 by \frac{31}{28} by multiplying 7 by the reciprocal of \frac{31}{28}.

$$7\times \frac{28}{31}$$

Express 7\times \frac{28}{31} as a single fraction.

$$\frac{7\times 28}{31}$$

Multiply 7 and 28 to get 196.

$$\frac{196}{31}$$

Factor

$$\frac{2 ^ {2} \cdot 7 ^ {2}}{31} = 6\frac{10}{31} = 6.32258064516129$$