Solve 1/8+3^2/11+{left(2/3right)}^2

$$\frac{ 1 }{ 8 } + \frac{ { 3 }^{ 2 } }{ 11 } + { \left( \frac{ 2 }{ 3 } \right) }^{ 2 }$$

Evaluate

$$\frac{1099}{792}\approx 1.387626263$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{8}+\frac{9}{11}+\left(\frac{2}{3}\right)^{2}$$

Least common multiple of 8 and 11 is 88. Convert \frac{1}{8} and \frac{9}{11} to fractions with denominator 88.

$$\frac{11}{88}+\frac{72}{88}+\left(\frac{2}{3}\right)^{2}$$

Since \frac{11}{88} and \frac{72}{88} have the same denominator, add them by adding their numerators.

$$\frac{11+72}{88}+\left(\frac{2}{3}\right)^{2}$$

Add 11 and 72 to get 83.

$$\frac{83}{88}+\left(\frac{2}{3}\right)^{2}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{83}{88}+\frac{4}{9}$$

Least common multiple of 88 and 9 is 792. Convert \frac{83}{88} and \frac{4}{9} to fractions with denominator 792.

$$\frac{747}{792}+\frac{352}{792}$$

Since \frac{747}{792} and \frac{352}{792} have the same denominator, add them by adding their numerators.

$$\frac{747+352}{792}$$

Add 747 and 352 to get 1099.

$$\frac{1099}{792}$$

Factor

$$\frac{7 \cdot 157}{2 ^ {3} \cdot 3 ^ {2} \cdot 11} = 1\frac{307}{792} = 1.3876262626262625$$