Solve 7[(1/2)^2+3/4(-2/5)]+[-1/3(+frac{6}{5})+(frac{1}{2})^2]

$$7 [ ( \frac { 1 } { 2 } ) ^ { 2 } + \frac { 3 } { 4 } ( - \frac { 2 } { 5 } ) ] + [ - \frac { 1 } { 3 } ( + \frac { 6 } { 5 } ) + ( \frac { 1 } { 2 } ) ^ { 2 } ]$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

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

$$7\left(\frac{1}{4}+\frac{3}{4}\left(-\frac{2}{5}\right)\right)-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Multiply \frac{3}{4} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$7\left(\frac{1}{4}+\frac{3\left(-2\right)}{4\times 5}\right)-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Do the multiplications in the fraction \frac{3\left(-2\right)}{4\times 5}.

$$7\left(\frac{1}{4}+\frac{-6}{20}\right)-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{-6}{20} to lowest terms by extracting and canceling out 2.

$$7\left(\frac{1}{4}-\frac{3}{10}\right)-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Least common multiple of 4 and 10 is 20. Convert \frac{1}{4} and \frac{3}{10} to fractions with denominator 20.

$$7\left(\frac{5}{20}-\frac{6}{20}\right)-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Since \frac{5}{20} and \frac{6}{20} have the same denominator, subtract them by subtracting their numerators.

$$7\times \frac{5-6}{20}-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Subtract 6 from 5 to get -1.

$$7\left(-\frac{1}{20}\right)-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Express 7\left(-\frac{1}{20}\right) as a single fraction.

$$\frac{7\left(-1\right)}{20}-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Multiply 7 and -1 to get -7.

$$\frac{-7}{20}-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Fraction \frac{-7}{20} can be rewritten as -\frac{7}{20} by extracting the negative sign.

$$-\frac{7}{20}-\frac{1}{3}\times \frac{6}{5}+\left(\frac{1}{2}\right)^{2}$$

Multiply -\frac{1}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{7}{20}+\frac{-6}{3\times 5}+\left(\frac{1}{2}\right)^{2}$$

Do the multiplications in the fraction \frac{-6}{3\times 5}.

$$-\frac{7}{20}+\frac{-6}{15}+\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{-6}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{7}{20}-\frac{2}{5}+\left(\frac{1}{2}\right)^{2}$$

Least common multiple of 20 and 5 is 20. Convert -\frac{7}{20} and \frac{2}{5} to fractions with denominator 20.

$$-\frac{7}{20}-\frac{8}{20}+\left(\frac{1}{2}\right)^{2}$$

Since -\frac{7}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-8}{20}+\left(\frac{1}{2}\right)^{2}$$

Subtract 8 from -7 to get -15.

$$\frac{-15}{20}+\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{-15}{20} to lowest terms by extracting and canceling out 5.

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

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

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

Since -\frac{3}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add -3 and 1 to get -2.

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

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{1}{2} = -0.5$$