Find the Exact Value 9/5(8/3-1/6)

$\frac{9}{5} (\frac{8}{3} - \frac{1}{6})$

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{5} \cdot (\frac{8}{3} \cdot \frac{2}{2} - \frac{1}{6})$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{3}$ by $\frac{2}{2}$ .

$\frac{9}{5} \cdot (\frac{8 \cdot 2}{3 \cdot 2} - \frac{1}{6})$

Multiply $3$ by $2$ .

$\frac{9}{5} \cdot (\frac{8 \cdot 2}{6} - \frac{1}{6})$

Combine the numerators over the common denominator.

$\frac{9}{5} \cdot \frac{8 \cdot 2 - 1}{6}$

Simplify the numerator.

Multiply $8$ by $2$ .

$\frac{9}{5} \cdot \frac{16 - 1}{6}$

Subtract $1$ from $16$ .

$\frac{9}{5} \cdot \frac{15}{6}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{3 (3)}{5} \cdot \frac{15}{6}$

Factor $3$ out of $6$ .

$\frac{3 \cdot 3}{5} \cdot \frac{15}{3 \cdot 2}$

Cancel the common factor.

$\frac{3 \cdot 3}{5} \cdot \frac{15}{3 \cdot 2}$

Rewrite the expression.

$\frac{3}{5} \cdot \frac{15}{2}$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $3$ by $3$ .

$\frac{9}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{2}$

Decimal Form:

$4.5$

Mixed Number Form:

$4 \frac{1}{2}$