Solve frac{1/frac{1{1}}+7/5}{1/6+4/9}

$$\frac { \frac { 1 } { \frac { 1 } { 1 } } + \frac { 7 } { 5 } } { \frac { 1 } { 6 } + \frac { 4 } { 9 } }$$

Evaluate

$$\frac{216}{55}\approx 3.927272727$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{1}{1}+\frac{7}{5}}{\frac{1}{6}+\frac{4}{9}}$$

Divide 1 by 1 to get 1.

$$\frac{1+\frac{7}{5}}{\frac{1}{6}+\frac{4}{9}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{5}{5}+\frac{7}{5}}{\frac{1}{6}+\frac{4}{9}}$$

Since \frac{5}{5} and \frac{7}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+7}{5}}{\frac{1}{6}+\frac{4}{9}}$$

Add 5 and 7 to get 12.

$$\frac{\frac{12}{5}}{\frac{1}{6}+\frac{4}{9}}$$

Least common multiple of 6 and 9 is 18. Convert \frac{1}{6} and \frac{4}{9} to fractions with denominator 18.

$$\frac{\frac{12}{5}}{\frac{3}{18}+\frac{8}{18}}$$

Since \frac{3}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12}{5}}{\frac{3+8}{18}}$$

Add 3 and 8 to get 11.

$$\frac{\frac{12}{5}}{\frac{11}{18}}$$

Divide \frac{12}{5} by \frac{11}{18} by multiplying \frac{12}{5} by the reciprocal of \frac{11}{18}.

$$\frac{12}{5}\times \frac{18}{11}$$

Multiply \frac{12}{5} times \frac{18}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 18}{5\times 11}$$

Do the multiplications in the fraction \frac{12\times 18}{5\times 11}.

$$\frac{216}{55}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {3}}{5 \cdot 11} = 3\frac{51}{55} = 3.9272727272727272$$