Solve 3.6:(51/5-7)+(1/2)^3*0.4^2=

$$3.6 : ( 5 \frac { 1 } { 5 } - 7 ) + ( \frac { 1 } { 2 } ) ^ { 3 } \cdot 0.4 ^ { 2 } =$$

Evaluate

$$-1.98$$

Solution Steps

Multiply 5 and 5 to get 25.

$$\frac{3.6}{\frac{25+1}{5}-7}+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Add 25 and 1 to get 26.

$$\frac{3.6}{\frac{26}{5}-7}+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Convert 7 to fraction \frac{35}{5}.

$$\frac{3.6}{\frac{26}{5}-\frac{35}{5}}+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Since \frac{26}{5} and \frac{35}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3.6}{\frac{26-35}{5}}+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Subtract 35 from 26 to get -9.

$$\frac{3.6}{-\frac{9}{5}}+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Divide 3.6 by -\frac{9}{5} by multiplying 3.6 by the reciprocal of -\frac{9}{5}.

$$3.6\left(-\frac{5}{9}\right)+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Convert decimal number 3.6 to fraction \frac{36}{10}. Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{18}{5}\left(-\frac{5}{9}\right)+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Multiply \frac{18}{5} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18\left(-5\right)}{5\times 9}+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Do the multiplications in the fraction \frac{18\left(-5\right)}{5\times 9}.

$$\frac{-90}{45}+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Divide -90 by 45 to get -2.

$$-2+\left(\frac{1}{2}\right)^{3}\times 0.4^{2}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$-2+\frac{1}{8}\times 0.4^{2}$$

Calculate 0.4 to the power of 2 and get 0.16.

$$-2+\frac{1}{8}\times 0.16$$

Convert decimal number 0.16 to fraction \frac{16}{100}. Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$-2+\frac{1}{8}\times \frac{4}{25}$$

Multiply \frac{1}{8} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$-2+\frac{1\times 4}{8\times 25}$$

Do the multiplications in the fraction \frac{1\times 4}{8\times 25}.

$$-2+\frac{4}{200}$$

Reduce the fraction \frac{4}{200} to lowest terms by extracting and canceling out 4.

$$-2+\frac{1}{50}$$

Convert -2 to fraction -\frac{100}{50}.

$$-\frac{100}{50}+\frac{1}{50}$$

Since -\frac{100}{50} and \frac{1}{50} have the same denominator, add them by adding their numerators.

$$\frac{-100+1}{50}$$

Add -100 and 1 to get -99.

$$-\frac{99}{50}$$

Factor

$$-1.98$$