Evaluate 5/3*(7/15-2/10)

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{2}{10})$

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2$ .

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{2 (1)}{10})$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{2 \cdot 1}{2 \cdot 5})$

Cancel the common factor.

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{2 \cdot 1}{2 \cdot 5})$

Rewrite the expression.

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{1}{5})$

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{1}{5} \cdot \frac{3}{3})$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{3}{5 \cdot 3})$

Multiply $5$ by $3$ .

$\frac{5}{3} \cdot (\frac{7}{15} - \frac{3}{15})$

Simplify the expression.

Combine the numerators over the common denominator.

$\frac{5}{3} \cdot \frac{7 - 3}{15}$

Subtract $3$ from $7$ .

$\frac{5}{3} \cdot \frac{4}{15}$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$\frac{5}{3} \cdot \frac{4}{5 (3)}$

Cancel the common factor.

$\frac{5}{3} \cdot \frac{4}{5 \cdot 3}$

Rewrite the expression.

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

Multiply $\frac{1}{3}$ by $\frac{4}{3}$ .

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

Multiply $3$ by $3$ .

$\frac{4}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$