Evaluate 6/7-(1/5)÷(1/3)*1/2

$\frac{6}{7} - \frac{1}{5} \div \frac{1}{3} \cdot \frac{1}{2}$

Step 1

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{6}{7} - (\frac{1}{5} \cdot 3) \cdot \frac{1}{2}$

Combine $\frac{1}{5}$ and $3$ .

$\frac{6}{7} - \frac{3}{5} \cdot \frac{1}{2}$

Multiply $- \frac{3}{5} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{3}{5}$ .

$\frac{6}{7} - \frac{3}{2 \cdot 5}$

Multiply $2$ by $5$ .

$\frac{6}{7} - \frac{3}{10}$

Step 2

To write $\frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{6}{7} \cdot \frac{10}{10} - \frac{3}{10}$

Step 3

To write $- \frac{3}{10}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{6}{7} \cdot \frac{10}{10} - \frac{3}{10} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $70$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6}{7}$ by $\frac{10}{10}$ .

$\frac{6 \cdot 10}{7 \cdot 10} - \frac{3}{10} \cdot \frac{7}{7}$

Multiply $7$ by $10$ .

$\frac{6 \cdot 10}{70} - \frac{3}{10} \cdot \frac{7}{7}$

Multiply $\frac{3}{10}$ by $\frac{7}{7}$ .

$\frac{6 \cdot 10}{70} - \frac{3 \cdot 7}{10 \cdot 7}$

Multiply $10$ by $7$ .

$\frac{6 \cdot 10}{70} - \frac{3 \cdot 7}{70}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 \cdot 10 - 3 \cdot 7}{70}$

Step 6

Simplify the numerator.

Multiply $6$ by $10$ .

$\frac{60 - 3 \cdot 7}{70}$

Multiply $- 3$ by $7$ .

$\frac{60 - 21}{70}$

Subtract $21$ from $60$ .

$\frac{39}{70}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{39}{70}$

Decimal Form:

$0.5\overline{571428}$