Write the Fraction in Simplest Form 4 3/4÷(5/6)

$4 \frac{3}{4} \div \frac{5}{6}$

Step 1

Convert $4 \frac{3}{4}$ to an improper fraction.

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

$(4 + \frac{3}{4}) \div \frac{5}{6}$

Add $4$ and $\frac{3}{4}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(4 \cdot \frac{4}{4} + \frac{3}{4}) \div \frac{5}{6}$

Combine $4$ and $\frac{4}{4}$ .

$(\frac{4 \cdot 4}{4} + \frac{3}{4}) \div \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 + 3}{4} \div \frac{5}{6}$

Simplify the numerator.

Multiply $4$ by $4$ .

$\frac{16 + 3}{4} \div \frac{5}{6}$

Add $16$ and $3$ .

$\frac{19}{4} \div \frac{5}{6}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{19}{4} \cdot \frac{6}{5}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{19}{2 (2)} \cdot \frac{6}{5}$

Factor $2$ out of $6$ .

$\frac{19}{2 \cdot 2} \cdot \frac{2 \cdot 3}{5}$

Cancel the common factor.

$\frac{19}{2 \cdot 2} \cdot \frac{2 \cdot 3}{5}$

Rewrite the expression.

$\frac{19}{2} \cdot \frac{3}{5}$

Step 4

Multiply $\frac{19}{2}$ by $\frac{3}{5}$ .

$\frac{19 \cdot 3}{2 \cdot 5}$

Step 5

Multiply $19$ by $3$ .

$\frac{57}{2 \cdot 5}$

Step 6

Multiply $2$ by $5$ .

$\frac{57}{10}$