Solve -4+7/2(7)/1+frac{7{2}}

$$\frac{ -4+ \frac{ 7 }{ 2 } (7) }{ 1+ \frac{ 7 }{ 2 } }$$

Evaluate

$$\frac{41}{9}\approx 4.555555556$$

Solution Steps

Express \frac{7}{2}\times 7 as a single fraction.

$$\frac{-4+\frac{7\times 7}{2}}{1+\frac{7}{2}}$$

Multiply 7 and 7 to get 49.

$$\frac{-4+\frac{49}{2}}{1+\frac{7}{2}}$$

Convert -4 to fraction -\frac{8}{2}.

$$\frac{-\frac{8}{2}+\frac{49}{2}}{1+\frac{7}{2}}$$

Since -\frac{8}{2} and \frac{49}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-8+49}{2}}{1+\frac{7}{2}}$$

Add -8 and 49 to get 41.

$$\frac{\frac{41}{2}}{1+\frac{7}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{41}{2}}{\frac{2}{2}+\frac{7}{2}}$$

Since \frac{2}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{41}{2}}{\frac{2+7}{2}}$$

Add 2 and 7 to get 9.

$$\frac{\frac{41}{2}}{\frac{9}{2}}$$

Divide \frac{41}{2} by \frac{9}{2} by multiplying \frac{41}{2} by the reciprocal of \frac{9}{2}.

$$\frac{41}{2}\times \frac{2}{9}$$

Multiply \frac{41}{2} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41\times 2}{2\times 9}$$

Cancel out 2 in both numerator and denominator.

$$\frac{41}{9}$$

Factor

$$\frac{41}{3 ^ {2}} = 4\frac{5}{9} = 4.555555555555555$$