Evaluate 2 1/2*3 2/3

$2 \frac{1}{2} \cdot 3 \frac{2}{3}$

Convert $2 \frac{1}{2}$ to an improper fraction.

Expand detailed answer...

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{1}{2}) \cdot 3 \frac{2}{3}$

Add $2$ and $\frac{1}{2}$ .

Expand detailed answer...

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 3 \frac{2}{3}$

Combine $2$ and $\frac{2}{2}$ .

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \cdot 3 \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} \cdot 3 \frac{2}{3}$

Simplify the numerator.

Expand detailed answer...

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} \cdot 3 \frac{2}{3}$

Add $4$ and $1$ .

$\frac{5}{2} \cdot 3 \frac{2}{3}$

Convert $3 \frac{2}{3}$ to an improper fraction.

Expand detailed answer...

A mixed number is an addition of its whole and fractional parts.

$\frac{5}{2} \cdot (3 + \frac{2}{3})$

Add $3$ and $\frac{2}{3}$ .

Expand detailed answer...

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{2} \cdot (3 \cdot \frac{3}{3} + \frac{2}{3})$

Combine $3$ and $\frac{3}{3}$ .

$\frac{5}{2} \cdot (\frac{3 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{5}{2} \cdot \frac{3 \cdot 3 + 2}{3}$

Simplify the numerator.

Expand detailed answer...

Multiply $3$ by $3$ .

$\frac{5}{2} \cdot \frac{9 + 2}{3}$

Add $9$ and $2$ .

$\frac{5}{2} \cdot \frac{11}{3}$

Multiply $\frac{5}{2} \cdot \frac{11}{3}$ .

Expand detailed answer...

Multiply $\frac{5}{2}$ and $\frac{11}{3}$ .

$\frac{5 \cdot 11}{2 \cdot 3}$

Multiply $5$ by $11$ .

$\frac{55}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{55}{6}$

The result can be shown in multiple forms.

Exact Form:

$\frac{55}{6}$

Decimal Form:

$9.1\overline{6}$

Mixed Number Form:

$9 \frac{1}{6}$