Evaluate 5 1/3÷2 2/9

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

Step 1

Convert $5 \frac{1}{3}$ to an improper fraction.

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

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

Add $5$ and $\frac{1}{3}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(5 \cdot \frac{3}{3} + \frac{1}{3}) \div 2 \frac{2}{9}$

Combine $5$ and $\frac{3}{3}$ .

$(\frac{5 \cdot 3}{3} + \frac{1}{3}) \div 2 \frac{2}{9}$

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 + 1}{3} \div 2 \frac{2}{9}$

Add $15$ and $1$ .

$\frac{16}{3} \div 2 \frac{2}{9}$

Step 2

Convert $2 \frac{2}{9}$ to an improper fraction.

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

$\frac{16}{3} \div (2 + \frac{2}{9})$

Add $2$ and $\frac{2}{9}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{16}{3} \div (2 \cdot \frac{9}{9} + \frac{2}{9})$

Combine $2$ and $\frac{9}{9}$ .

$\frac{16}{3} \div (\frac{2 \cdot 9}{9} + \frac{2}{9})$

Combine the numerators over the common denominator.

$\frac{16}{3} \div \frac{2 \cdot 9 + 2}{9}$

Simplify the numerator.

Multiply $2$ by $9$ .

$\frac{16}{3} \div \frac{18 + 2}{9}$

Add $18$ and $2$ .

$\frac{16}{3} \div \frac{20}{9}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{16}{3} \cdot \frac{9}{20}$

Step 4

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$\frac{4 (4)}{3} \cdot \frac{9}{20}$

Factor $4$ out of $20$ .

$\frac{4 \cdot 4}{3} \cdot \frac{9}{4 \cdot 5}$

Cancel the common factor.

$\frac{4 \cdot 4}{3} \cdot \frac{9}{4 \cdot 5}$

Rewrite the expression.

$\frac{4}{3} \cdot \frac{9}{5}$

Step 5

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{4}{3} \cdot \frac{3 (3)}{5}$

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 \cdot 3}{5}$

Rewrite the expression.

$4 (\frac{3}{5})$

Step 6

Combine $4$ and $\frac{3}{5}$ .

$\frac{4 \cdot 3}{5}$

Step 7

Multiply $4$ by $3$ .

$\frac{12}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{5}$

Decimal Form:

$2.4$

Mixed Number Form:

$2 \frac{2}{5}$

Evaluate 5 1/3÷2 2/9

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