Write the Fraction in Simplest Form 5 5/9÷2 2/3

$5 \frac{5}{9} \div 2 \frac{2}{3}$

Step 1

Convert $5 \frac{5}{9}$ to an improper fraction.

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

$(5 + \frac{5}{9}) \div 2 \frac{2}{3}$

Add $5$ and $\frac{5}{9}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

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

Combine $5$ and $\frac{9}{9}$ .

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

Combine the numerators over the common denominator.

$\frac{5 \cdot 9 + 5}{9} \div 2 \frac{2}{3}$

Simplify the numerator.

Multiply $5$ by $9$ .

$\frac{45 + 5}{9} \div 2 \frac{2}{3}$

Add $45$ and $5$ .

$\frac{50}{9} \div 2 \frac{2}{3}$

Step 2

Convert $2 \frac{2}{3}$ to an improper fraction.

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

$\frac{50}{9} \div (2 + \frac{2}{3})$

Add $2$ and $\frac{2}{3}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{50}{9} \div (2 \cdot \frac{3}{3} + \frac{2}{3})$

Combine $2$ and $\frac{3}{3}$ .

$\frac{50}{9} \div (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{50}{9} \div \frac{2 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{50}{9} \div \frac{6 + 2}{3}$

Add $6$ and $2$ .

$\frac{50}{9} \div \frac{8}{3}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{50}{9} \cdot \frac{3}{8}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $50$ .

$\frac{2 (25)}{9} \cdot \frac{3}{8}$

Factor $2$ out of $8$ .

$\frac{2 \cdot 25}{9} \cdot \frac{3}{2 \cdot 4}$

Cancel the common factor.

$\frac{2 \cdot 25}{9} \cdot \frac{3}{2 \cdot 4}$

Rewrite the expression.

$\frac{25}{9} \cdot \frac{3}{4}$

Step 5

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{25}{3 (3)} \cdot \frac{3}{4}$

Cancel the common factor.

$\frac{25}{3 \cdot 3} \cdot \frac{3}{4}$

Rewrite the expression.

$\frac{25}{3} \cdot \frac{1}{4}$

Step 6

Multiply $\frac{25}{3}$ by $\frac{1}{4}$ .

$\frac{25}{3 \cdot 4}$

Step 7

Multiply $3$ by $4$ .

$\frac{25}{12}$

Write the Fraction in Simplest Form 5 5/9÷2 2/3

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