Algebra Examples

$\frac{2 \frac{2}{5}}{2 \frac{1}{10}}$

Step 1

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

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Step 1.1

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

$\frac{2 + \frac{2}{5}}{2 \frac{1}{10}}$

Step 1.2

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

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 \cdot \frac{5}{5} + \frac{2}{5}}{2 \frac{1}{10}}$

Step 1.2.2

Combine $2$ and $\frac{5}{5}$ .

$\frac{\frac{2 \cdot 5}{5} + \frac{2}{5}}{2 \frac{1}{10}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 5 + 2}{5}}{2 \frac{1}{10}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$\frac{\frac{10 + 2}{5}}{2 \frac{1}{10}}$

Step 1.2.4.2

Add $10$ and $2$ .

$\frac{\frac{12}{5}}{2 \frac{1}{10}}$

Step 2

Convert $2 \frac{1}{10}$ to an improper fraction.

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Step 2.1

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

$\frac{\frac{12}{5}}{2 + \frac{1}{10}}$

Step 2.2

Add $2$ and $\frac{1}{10}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{\frac{12}{5}}{2 \cdot \frac{10}{10} + \frac{1}{10}}$

Step 2.2.2

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

$\frac{\frac{12}{5}}{\frac{2 \cdot 10}{10} + \frac{1}{10}}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{\frac{12}{5}}{\frac{2 \cdot 10 + 1}{10}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $10$ .

$\frac{\frac{12}{5}}{\frac{20 + 1}{10}}$

Step 2.2.4.2

Add $20$ and $1$ .

$\frac{\frac{12}{5}}{\frac{21}{10}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{12}{5} \cdot \frac{10}{21}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $12$ .

$\frac{3 (4)}{5} \cdot \frac{10}{21}$

Step 4.2

Factor $3$ out of $21$ .

$\frac{3 \cdot 4}{5} \cdot \frac{10}{3 \cdot 7}$

Step 4.3

Cancel the common factor.

$\frac{3 \cdot 4}{5} \cdot \frac{10}{3 \cdot 7}$

Step 4.4

Rewrite the expression.

$\frac{4}{5} \cdot \frac{10}{7}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Factor $5$ out of $10$ .

$\frac{4}{5} \cdot \frac{5 (2)}{7}$

Step 5.2

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 \cdot 2}{7}$

Step 5.3

Rewrite the expression.

$4 (\frac{2}{7})$

Step 6

Combine $4$ and $\frac{2}{7}$ .

$\frac{4 \cdot 2}{7}$

Step 7

Multiply $4$ by $2$ .

$\frac{8}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{7}$

Decimal Form:

$1.\overline{142857}$

Mixed Number Form:

$1 \frac{1}{7}$