Algebra Examples

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

Convert $1 \frac{2}{3}$ to an improper fraction.

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

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

Add $1$ and $\frac{2}{3}$ .

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Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $3$ and $2$ .

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

Convert $1 \frac{2}{9}$ to an improper fraction.

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

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

Add $1$ and $\frac{2}{9}$ .

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Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $9$ and $2$ .

$\frac{5}{3} \div \frac{11}{9}$

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{3} \cdot \frac{9}{11}$

Cancel the common factor of $3$ .

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Factor $3$ out of $9$ .

$\frac{5}{3} \cdot \frac{3 (3)}{11}$

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 \cdot 3}{11}$

Rewrite the expression.

$5 (\frac{3}{11})$

Combine $5$ and $\frac{3}{11}$ .

$\frac{5 \cdot 3}{11}$

Multiply $5$ by $3$ .

$\frac{15}{11}$