Evaluate 5/9-(1/3)÷(6/7)

$\frac{5}{9} - \frac{1}{3} \div \frac{6}{7}$

Step 1

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{9} - (\frac{1}{3} \cdot \frac{7}{6})$

Multiply $\frac{1}{3} \cdot \frac{7}{6}$ .

Multiply $\frac{1}{3}$ by $\frac{7}{6}$ .

$\frac{5}{9} - \frac{7}{3 \cdot 6}$

Multiply $3$ by $6$ .

$\frac{5}{9} - \frac{7}{18}$

Step 2

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{9} \cdot \frac{2}{2} - \frac{7}{18}$

Step 3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{9}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{9 \cdot 2} - \frac{7}{18}$

Multiply $9$ by $2$ .

$\frac{5 \cdot 2}{18} - \frac{7}{18}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 - 7}{18}$

Step 5

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 - 7}{18}$

Subtract $7$ from $10$ .

$\frac{3}{18}$

Step 6

Cancel the common factor of $3$ and $18$ .

Factor $3$ out of $3$ .

$\frac{3 (1)}{18}$

Cancel the common factors.

Factor $3$ out of $18$ .

$\frac{3 \cdot 1}{3 \cdot 6}$

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 6}$

Rewrite the expression.

$\frac{1}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$