Write the Fraction in Simplest Form 5 1/6÷(5/9)

$5 \frac{1}{6} \div \frac{5}{9}$

Convert $5 \frac{1}{6}$ to an improper fraction.

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

$(5 + \frac{1}{6}) \div \frac{5}{9}$

Add $5$ and $\frac{1}{6}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(5 \cdot \frac{6}{6} + \frac{1}{6}) \div \frac{5}{9}$

Combine $5$ and $\frac{6}{6}$ .

$(\frac{5 \cdot 6}{6} + \frac{1}{6}) \div \frac{5}{9}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 6 + 1}{6} \div \frac{5}{9}$

Simplify the numerator.

Multiply $5$ by $6$ .

$\frac{30 + 1}{6} \div \frac{5}{9}$

Add $30$ and $1$ .

$\frac{31}{6} \div \frac{5}{9}$

To divide by a fraction, multiply by its reciprocal.

$\frac{31}{6} \cdot \frac{9}{5}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{31}{3 (2)} \cdot \frac{9}{5}$

Factor $3$ out of $9$ .

$\frac{31}{3 \cdot 2} \cdot \frac{3 \cdot 3}{5}$

Cancel the common factor.

$\frac{31}{3 \cdot 2} \cdot \frac{3 \cdot 3}{5}$

Rewrite the expression.

$\frac{31}{2} \cdot \frac{3}{5}$

Multiply $\frac{31}{2}$ by $\frac{3}{5}$ .

$\frac{31 \cdot 3}{2 \cdot 5}$

Multiply $31$ by $3$ .

$\frac{93}{2 \cdot 5}$

Multiply $2$ by $5$ .

$\frac{93}{10}$