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

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

Evaluate

$$\frac{65}{9}\approx 7.222222222$$

Solution Steps

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

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

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

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

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

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

Add 2 and 3 to get 5.

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

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

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

Multiply 2 and -1 to get -2.

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

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

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

Convert 5 to fraction \frac{15}{3}.

$$\frac{5}{3}\left(-\frac{2}{3}+\frac{15}{3}\right)$$

Since -\frac{2}{3} and \frac{15}{3} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}\times \frac{-2+15}{3}$$

Add -2 and 15 to get 13.

$$\frac{5}{3}\times \frac{13}{3}$$

Multiply \frac{5}{3} times \frac{13}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 13}{3\times 3}$$

Do the multiplications in the fraction \frac{5\times 13}{3\times 3}.

$$\frac{65}{9}$$

Factor

$$\frac{5 \cdot 13}{3 ^ {2}} = 7\frac{2}{9} = 7.222222222222222$$