Write the Fraction in Simplest Form 2 1/6÷(7/8)

$2 \frac{1}{6} \div \frac{7}{8}$

Step 1

Convert $2 \frac{1}{6}$ to an improper fraction.

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

$(2 + \frac{1}{6}) \div \frac{7}{8}$

Add $2$ and $\frac{1}{6}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(2 \cdot \frac{6}{6} + \frac{1}{6}) \div \frac{7}{8}$

Combine $2$ and $\frac{6}{6}$ .

$(\frac{2 \cdot 6}{6} + \frac{1}{6}) \div \frac{7}{8}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 6 + 1}{6} \div \frac{7}{8}$

Simplify the numerator.

Multiply $2$ by $6$ .

$\frac{12 + 1}{6} \div \frac{7}{8}$

Add $12$ and $1$ .

$\frac{13}{6} \div \frac{7}{8}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{13}{6} \cdot \frac{8}{7}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{13}{2 (3)} \cdot \frac{8}{7}$

Factor $2$ out of $8$ .

$\frac{13}{2 \cdot 3} \cdot \frac{2 \cdot 4}{7}$

Cancel the common factor.

$\frac{13}{2 \cdot 3} \cdot \frac{2 \cdot 4}{7}$

Rewrite the expression.

$\frac{13}{3} \cdot \frac{4}{7}$

Step 4

Multiply $\frac{13}{3}$ by $\frac{4}{7}$ .

$\frac{13 \cdot 4}{3 \cdot 7}$

Step 5

Multiply $13$ by $4$ .

$\frac{52}{3 \cdot 7}$

Step 6

Multiply $3$ by $7$ .

$\frac{52}{21}$