Solve 2+3*4^-1-2*5^-1/3^2*2^-2-5

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

Evaluate

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

Solution Steps

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

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

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

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

Add 2 and \frac{3}{4} to get \frac{11}{4}.

$$\frac{\frac{11}{4}-2\times 5^{-1}}{3^{2}\times 2^{-2}-5}$$

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{\frac{11}{4}-2\times \frac{1}{5}}{3^{2}\times 2^{-2}-5}$$

Multiply 2 and \frac{1}{5} to get \frac{2}{5}.

$$\frac{\frac{11}{4}-\frac{2}{5}}{3^{2}\times 2^{-2}-5}$$

Subtract \frac{2}{5} from \frac{11}{4} to get \frac{47}{20}.

$$\frac{\frac{47}{20}}{3^{2}\times 2^{-2}-5}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{47}{20}}{9\times 2^{-2}-5}$$

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

$$\frac{\frac{47}{20}}{9\times \frac{1}{4}-5}$$

Multiply 9 and \frac{1}{4} to get \frac{9}{4}.

$$\frac{\frac{47}{20}}{\frac{9}{4}-5}$$

Subtract 5 from \frac{9}{4} to get -\frac{11}{4}.

$$\frac{\frac{47}{20}}{-\frac{11}{4}}$$

Divide \frac{47}{20} by -\frac{11}{4} by multiplying \frac{47}{20} by the reciprocal of -\frac{11}{4}.

$$\frac{47}{20}\left(-\frac{4}{11}\right)$$

Multiply \frac{47}{20} and -\frac{4}{11} to get -\frac{47}{55}.

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

Factor

$$-\frac{47}{55} = -0.8545454545454545$$