Solve [2/5(1/2-1)+(6/5)^2]:1/2+2(-frac{1}{10})^2=

$$[ \frac { 2 } { 5 } ( \frac { 1 } { 2 } - 1 ) + ( \frac { 6 } { 5 } ) ^ { 2 } ] : \frac { 1 } { 2 } + 2 ( - \frac { 1 } { 10 } ) ^ { 2 } =$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{2}{5}\left(\frac{1}{2}-\frac{2}{2}\right)+\left(\frac{6}{5}\right)^{2}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{5}\times \frac{1-2}{2}+\left(\frac{6}{5}\right)^{2}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Subtract 2 from 1 to get -1.

$$\frac{\frac{2}{5}\left(-\frac{1}{2}\right)+\left(\frac{6}{5}\right)^{2}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Multiply \frac{2}{5} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\left(-1\right)}{5\times 2}+\left(\frac{6}{5}\right)^{2}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{-1}{5}+\left(\frac{6}{5}\right)^{2}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$\frac{-\frac{1}{5}+\left(\frac{6}{5}\right)^{2}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$\frac{-\frac{1}{5}+\frac{36}{25}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Least common multiple of 5 and 25 is 25. Convert -\frac{1}{5} and \frac{36}{25} to fractions with denominator 25.

$$\frac{-\frac{5}{25}+\frac{36}{25}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Since -\frac{5}{25} and \frac{36}{25} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5+36}{25}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Add -5 and 36 to get 31.

$$\frac{\frac{31}{25}}{\frac{1}{2}}+2\left(-\frac{1}{10}\right)^{2}$$

Divide \frac{31}{25} by \frac{1}{2} by multiplying \frac{31}{25} by the reciprocal of \frac{1}{2}.

$$\frac{31}{25}\times 2+2\left(-\frac{1}{10}\right)^{2}$$

Express \frac{31}{25}\times 2 as a single fraction.

$$\frac{31\times 2}{25}+2\left(-\frac{1}{10}\right)^{2}$$

Multiply 31 and 2 to get 62.

$$\frac{62}{25}+2\left(-\frac{1}{10}\right)^{2}$$

Calculate -\frac{1}{10} to the power of 2 and get \frac{1}{100}.

$$\frac{62}{25}+2\times \frac{1}{100}$$

Multiply 2 and \frac{1}{100} to get \frac{2}{100}.

$$\frac{62}{25}+\frac{2}{100}$$

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{62}{25}+\frac{1}{50}$$

Least common multiple of 25 and 50 is 50. Convert \frac{62}{25} and \frac{1}{50} to fractions with denominator 50.

$$\frac{124}{50}+\frac{1}{50}$$

Since \frac{124}{50} and \frac{1}{50} have the same denominator, add them by adding their numerators.

$$\frac{124+1}{50}$$

Add 124 and 1 to get 125.

$$\frac{125}{50}$$

Reduce the fraction \frac{125}{50} to lowest terms by extracting and canceling out 25.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$