Solve 2/11+3/4*4/11+sqrt{4/25}=

$$\frac { 2 } { 11 } + \frac { 3 } { 4 } \cdot \frac { 4 } { 11 } + \sqrt { \frac { 4 } { 25 } } =$$

Evaluate

$$\frac{47}{55}\approx 0.854545455$$

Solution Steps

Multiply \frac{3}{4} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{11}+\frac{3\times 4}{4\times 11}+\sqrt{\frac{4}{25}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2}{11}+\frac{3}{11}+\sqrt{\frac{4}{25}}$$

Since \frac{2}{11} and \frac{3}{11} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{11}+\sqrt{\frac{4}{25}}$$

Add 2 and 3 to get 5.

$$\frac{5}{11}+\sqrt{\frac{4}{25}}$$

Rewrite the square root of the division \frac{4}{25} as the division of square roots \frac{\sqrt{4}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{5}{11}+\frac{2}{5}$$

Least common multiple of 11 and 5 is 55. Convert \frac{5}{11} and \frac{2}{5} to fractions with denominator 55.

$$\frac{25}{55}+\frac{22}{55}$$

Since \frac{25}{55} and \frac{22}{55} have the same denominator, add them by adding their numerators.

$$\frac{25+22}{55}$$

Add 25 and 22 to get 47.

$$\frac{47}{55}$$

Factor

$$\frac{47}{5 \cdot 11} = 0.8545454545454545$$