Simplify 9 1/7÷(16/14)

$9 \frac{1}{7} \div \frac{16}{14}$

Step 1

Convert $9 \frac{1}{7}$ to an improper fraction.

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

$(9 + \frac{1}{7}) \div \frac{16}{14}$

Add $9$ and $\frac{1}{7}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(9 \cdot \frac{7}{7} + \frac{1}{7}) \div \frac{16}{14}$

Combine $9$ and $\frac{7}{7}$ .

$(\frac{9 \cdot 7}{7} + \frac{1}{7}) \div \frac{16}{14}$

Combine the numerators over the common denominator.

$\frac{9 \cdot 7 + 1}{7} \div \frac{16}{14}$

Simplify the numerator.

Multiply $9$ by $7$ .

$\frac{63 + 1}{7} \div \frac{16}{14}$

Add $63$ and $1$ .

$\frac{64}{7} \div \frac{16}{14}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{64}{7} \cdot \frac{14}{16}$

Step 3

Cancel the common factor of $16$ .

Factor $16$ out of $64$ .

$\frac{16 (4)}{7} \cdot \frac{14}{16}$

Cancel the common factor.

$\frac{16 \cdot 4}{7} \cdot \frac{14}{16}$

Rewrite the expression.

$\frac{4}{7} \cdot 14$

Step 4

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$\frac{4}{7} \cdot (7 (2))$

Cancel the common factor.

$\frac{4}{7} \cdot (7 \cdot 2)$

Rewrite the expression.

$4 \cdot 2$

Step 5

Multiply $4$ by $2$ .

$8$