Evaluate 7/3*(2/3-2/9)

$\frac{7}{3} \cdot (\frac{2}{3} - \frac{2}{9})$

Step 1

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

$\frac{7}{3} \cdot (\frac{2}{3} \cdot \frac{3}{3} - \frac{2}{9})$

Step 2

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{7}{3} \cdot (\frac{2 \cdot 3}{3 \cdot 3} - \frac{2}{9})$

Multiply $3$ by $3$ .

$\frac{7}{3} \cdot (\frac{2 \cdot 3}{9} - \frac{2}{9})$

Step 3

Combine the numerators over the common denominator.

$\frac{7}{3} \cdot \frac{2 \cdot 3 - 2}{9}$

Step 4

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{7}{3} \cdot \frac{6 - 2}{9}$

Subtract $2$ from $6$ .

$\frac{7}{3} \cdot \frac{4}{9}$

Step 5

Multiply $\frac{7}{3} \cdot \frac{4}{9}$ .

Multiply $\frac{7}{3}$ by $\frac{4}{9}$ .

$\frac{7 \cdot 4}{3 \cdot 9}$

Multiply $7$ by $4$ .

$\frac{28}{3 \cdot 9}$

Multiply $3$ by $9$ .

$\frac{28}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{28}{27}$

Decimal Form:

$1.\overline{037}$

Mixed Number Form:

$1 \frac{1}{27}$