Solve 7/4+frac{4{5}}+6=

$$\frac{ 7 }{ 4+ \frac{ 4 }{ 5 } } +6=$$

Evaluate

$$\frac{179}{24}\approx 7.458333333$$

Solution Steps

Convert 4 to fraction \frac{20}{5}.

$$\frac{7}{\frac{20}{5}+\frac{4}{5}}+6$$

Since \frac{20}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{7}{\frac{20+4}{5}}+6$$

Add 20 and 4 to get 24.

$$\frac{7}{\frac{24}{5}}+6$$

Divide 7 by \frac{24}{5} by multiplying 7 by the reciprocal of \frac{24}{5}.

$$7\times \frac{5}{24}+6$$

Express 7\times \frac{5}{24} as a single fraction.

$$\frac{7\times 5}{24}+6$$

Multiply 7 and 5 to get 35.

$$\frac{35}{24}+6$$

Convert 6 to fraction \frac{144}{24}.

$$\frac{35}{24}+\frac{144}{24}$$

Since \frac{35}{24} and \frac{144}{24} have the same denominator, add them by adding their numerators.

$$\frac{35+144}{24}$$

Add 35 and 144 to get 179.

$$\frac{179}{24}$$

Factor

$$\frac{179}{2 ^ {3} \cdot 3} = 7\frac{11}{24} = 7.458333333333333$$