Solve (2+1/2)(1-1/5)(2/3-1)

$$( 2 + \frac { 1 } { 2 } ) ( 1 - \frac { 1 } { 5 } ) ( \frac { 2 } { 3 } - 1 )$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

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

Convert 1 to fraction \frac{5}{5}.

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

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 5 to get 4.

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

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

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

Cancel out 5 in both numerator and denominator.

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

Divide 4 by 2 to get 2.

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

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{2}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{2-3}{3}$$

Subtract 3 from 2 to get -1.

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

Express 2\left(-\frac{1}{3}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

$$\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{2}{3}$$

Factor

$$-\frac{2}{3} = -0.6666666666666666$$