Divide (-5/6)÷(3/10)

$- \frac{5}{6} \div \frac{3}{10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- \frac{5}{6} \cdot \frac{10}{3}$

Step 2

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{- 5}{6} \cdot \frac{10}{3}$

Factor $2$ out of $6$ .

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

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Multiply $- 5$ by $5$ .

$\frac{- 25}{3 \cdot 3}$

Step 5

Multiply $3$ by $3$ .

$\frac{- 25}{9}$

Step 6

Move the negative in front of the fraction.

$- \frac{25}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{9}$

Decimal Form:

$- 2.\overline{7}$

Mixed Number Form:

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