Solve a+left(3-1/3right)a/2+2a/3

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

Evaluate

$$3a$$

Short Solution Steps

Convert 3 to fraction \frac{9}{3}.

$$a+\left(\frac{9}{3}-\frac{1}{3}\right)\times \frac{a}{2}+\frac{2a}{3}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$a+\frac{9-1}{3}\times \frac{a}{2}+\frac{2a}{3}$$

Subtract 1 from 9 to get 8.

$$a+\frac{8}{3}\times \frac{a}{2}+\frac{2a}{3}$$

Multiply \frac{8}{3} times \frac{a}{2} by multiplying numerator times numerator and denominator times denominator.

$$a+\frac{8a}{3\times 2}+\frac{2a}{3}$$

Cancel out 2 in both numerator and denominator.

$$a+\frac{4a}{3}+\frac{2a}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{3}{3}.

$$\frac{3a}{3}+\frac{4a}{3}+\frac{2a}{3}$$

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

$$\frac{3a+4a}{3}+\frac{2a}{3}$$

Combine like terms in 3a+4a.

$$\frac{7a}{3}+\frac{2a}{3}$$

Since \frac{7a}{3} and \frac{2a}{3} have the same denominator, add them by adding their numerators.

$$\frac{7a+2a}{3}$$

Combine like terms in 7a+2a.

$$\frac{9a}{3}$$

Divide 9a by 3 to get 3a.

$$3a$$

Expand

$$3a$$

Short Solution Steps

Convert 3 to fraction \frac{9}{3}.

$$a+\left(\frac{9}{3}-\frac{1}{3}\right)\times \frac{a}{2}+\frac{2a}{3}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$a+\frac{9-1}{3}\times \frac{a}{2}+\frac{2a}{3}$$

Subtract 1 from 9 to get 8.

$$a+\frac{8}{3}\times \frac{a}{2}+\frac{2a}{3}$$

Multiply \frac{8}{3} times \frac{a}{2} by multiplying numerator times numerator and denominator times denominator.

$$a+\frac{8a}{3\times 2}+\frac{2a}{3}$$

Cancel out 2 in both numerator and denominator.

$$a+\frac{4a}{3}+\frac{2a}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{3}{3}.

$$\frac{3a}{3}+\frac{4a}{3}+\frac{2a}{3}$$

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

$$\frac{3a+4a}{3}+\frac{2a}{3}$$

Combine like terms in 3a+4a.

$$\frac{7a}{3}+\frac{2a}{3}$$

Since \frac{7a}{3} and \frac{2a}{3} have the same denominator, add them by adding their numerators.

$$\frac{7a+2a}{3}$$

Combine like terms in 7a+2a.

$$\frac{9a}{3}$$

Divide 9a by 3 to get 3a.

$$3a$$