Solve [4*(4/5-1+1/5)]-(5/3-2)div(-1/3)^2-2^-2

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

Evaluate

$$\frac{11}{4}=2.75$$

Solution Steps

Subtract 1 from \frac{4}{5} to get -\frac{1}{5}.

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

Add -\frac{1}{5} and \frac{1}{5} to get 0.

$$4\times 0-\frac{\frac{5}{3}-2}{\left(-\frac{1}{3}\right)^{2}}-2^{-2}$$

Multiply 4 and 0 to get 0.

$$0-\frac{\frac{5}{3}-2}{\left(-\frac{1}{3}\right)^{2}}-2^{-2}$$

Subtract 2 from \frac{5}{3} to get -\frac{1}{3}.

$$0-\frac{-\frac{1}{3}}{\left(-\frac{1}{3}\right)^{2}}-2^{-2}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$0-\frac{-\frac{1}{3}}{\frac{1}{9}}-2^{-2}$$

Divide -\frac{1}{3} by \frac{1}{9} by multiplying -\frac{1}{3} by the reciprocal of \frac{1}{9}.

$$0-\left(-\frac{1}{3}\times 9\right)-2^{-2}$$

Multiply -\frac{1}{3} and 9 to get -3.

$$0-\left(-3\right)-2^{-2}$$

The opposite of -3 is 3.

$$0+3-2^{-2}$$

Add 0 and 3 to get 3.

$$3-2^{-2}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$3-\frac{1}{4}$$

Subtract \frac{1}{4} from 3 to get \frac{11}{4}.

$$\frac{11}{4}$$

Factor

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2.75$$