Write the Fraction in Simplest Form 3 1/3÷2 5/6

$3 \frac{1}{3} \div 2 \frac{5}{6}$

Step 1

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

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

$(3 + \frac{1}{3}) \div 2 \frac{5}{6}$

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

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(3 \cdot \frac{3}{3} + \frac{1}{3}) \div 2 \frac{5}{6}$

Combine $3$ and $\frac{3}{3}$ .

$(\frac{3 \cdot 3}{3} + \frac{1}{3}) \div 2 \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 1}{3} \div 2 \frac{5}{6}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 + 1}{3} \div 2 \frac{5}{6}$

Add $9$ and $1$ .

$\frac{10}{3} \div 2 \frac{5}{6}$

Step 2

Convert $2 \frac{5}{6}$ to an improper fraction.

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

$\frac{10}{3} \div (2 + \frac{5}{6})$

Add $2$ and $\frac{5}{6}$ .

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

$\frac{10}{3} \div (2 \cdot \frac{6}{6} + \frac{5}{6})$

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

$\frac{10}{3} \div (\frac{2 \cdot 6}{6} + \frac{5}{6})$

Combine the numerators over the common denominator.

$\frac{10}{3} \div \frac{2 \cdot 6 + 5}{6}$

Simplify the numerator.

Multiply $2$ by $6$ .

$\frac{10}{3} \div \frac{12 + 5}{6}$

Add $12$ and $5$ .

$\frac{10}{3} \div \frac{17}{6}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{10}{3} \cdot \frac{6}{17}$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{10}{3} \cdot \frac{3 (2)}{17}$

Cancel the common factor.

$\frac{10}{3} \cdot \frac{3 \cdot 2}{17}$

Rewrite the expression.

$10 (\frac{2}{17})$

Step 5

Combine $10$ and $\frac{2}{17}$ .

$\frac{10 \cdot 2}{17}$

Step 6

Multiply $10$ by $2$ .

$\frac{20}{17}$

Write the Fraction in Simplest Form 3 1/3÷2 5/6

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