Divide (1/9)÷(-1 1/3)

$\frac{1}{9} \div (- 1 \frac{1}{3})$

Step 1

Convert $1 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{1}{9} \div (- (1 + \frac{1}{3}))$

Add $1$ and $\frac{1}{3}$ .

Write $1$ as a fraction with a common denominator.

$\frac{1}{9} \div (- (\frac{3}{3} + \frac{1}{3}))$

Combine the numerators over the common denominator.

$\frac{1}{9} \div (- \frac{3 + 1}{3})$

Add $3$ and $1$ .

$\frac{1}{9} \div (- \frac{4}{3})$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{9} (- \frac{3}{4})$

Step 3

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{1}{9} \cdot \frac{- 3}{4}$

Factor $3$ out of $9$ .

$\frac{1}{3 (3)} \cdot \frac{- 3}{4}$

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

Step 5

Multiply $3$ by $4$ .

$\frac{- 1}{12}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{12}$

Decimal Form:

$- 0.08\overline{3}$