Solve 11/3+14/5*(-2/3)^2

$$1 \frac { 1 } { 3 } + 1 \frac { 4 } { 5 } \times ( - \frac { 2 } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{32}{15}\approx 2.133333333$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{3+1}{3}+\frac{1\times 5+4}{5}\left(-\frac{2}{3}\right)^{2}$$

Add 3 and 1 to get 4.

$$\frac{4}{3}+\frac{1\times 5+4}{5}\left(-\frac{2}{3}\right)^{2}$$

Multiply 1 and 5 to get 5.

$$\frac{4}{3}+\frac{5+4}{5}\left(-\frac{2}{3}\right)^{2}$$

Add 5 and 4 to get 9.

$$\frac{4}{3}+\frac{9}{5}\left(-\frac{2}{3}\right)^{2}$$

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

$$\frac{4}{3}+\frac{9}{5}\times \frac{4}{9}$$

Multiply \frac{9}{5} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}+\frac{9\times 4}{5\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{4}{3}+\frac{4}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{20}{15}+\frac{12}{15}$$

Since \frac{20}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{20+12}{15}$$

Add 20 and 12 to get 32.

$$\frac{32}{15}$$

Factor

$$\frac{2 ^ {5}}{3 \cdot 5} = 2\frac{2}{15} = 2.1333333333333333$$