Algebra Examples

$\frac{\frac{2}{5} + \frac{1}{2}}{\frac{1}{10} + \frac{3}{15}}$

Step 1

Cancel the common factor of $3$ and $15$ .

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Step 1.1

Factor $3$ out of $3$ .

$\frac{\frac{2}{5} + \frac{1}{2}}{\frac{1}{10} + \frac{3 (1)}{15}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $15$ .

$\frac{\frac{2}{5} + \frac{1}{2}}{\frac{1}{10} + \frac{3 \cdot 1}{3 \cdot 5}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{2}{5} + \frac{1}{2}}{\frac{1}{10} + \frac{3 \cdot 1}{3 \cdot 5}}$

Step 1.2.3

Rewrite the expression.

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

Step 2

Multiply the numerator and denominator of the fraction by $10$ .

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Step 2.1

Multiply $\frac{\frac{2}{5} + \frac{1}{2}}{\frac{1}{10} + \frac{1}{5}}$ by $\frac{10}{10}$ .

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

Step 2.2

Combine.

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

Step 3

Apply the distributive property.

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

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $5$ .

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Step 4.1.1

Factor $5$ out of $10$ .

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Multiply $2$ by $2$ .

$\frac{4 + 10 (\frac{1}{2})}{10 (\frac{1}{10}) + 10 (\frac{1}{5})}$

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Factor $2$ out of $10$ .

$\frac{4 + 2 (5) \frac{1}{2}}{10 (\frac{1}{10}) + 10 (\frac{1}{5})}$

Step 4.3.2

Cancel the common factor.

$\frac{4 + 2 \cdot 5 \frac{1}{2}}{10 (\frac{1}{10}) + 10 (\frac{1}{5})}$

Step 4.3.3

Rewrite the expression.

$\frac{4 + 5}{10 (\frac{1}{10}) + 10 (\frac{1}{5})}$

Step 4.4

Cancel the common factor of $10$ .

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Step 4.4.1

Cancel the common factor.

$\frac{4 + 5}{10 (\frac{1}{10}) + 10 (\frac{1}{5})}$

Step 4.4.2

Rewrite the expression.

$\frac{4 + 5}{1 + 10 (\frac{1}{5})}$

Step 4.5

Cancel the common factor of $5$ .

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Step 4.5.1

Factor $5$ out of $10$ .

$\frac{4 + 5}{1 + 5 (2) \frac{1}{5}}$

Step 4.5.2

Cancel the common factor.

$\frac{4 + 5}{1 + 5 \cdot 2 \frac{1}{5}}$

Step 4.5.3

Rewrite the expression.

$\frac{4 + 5}{1 + 2}$

Step 5

Simplify the expression.

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Step 5.1

Add $4$ and $5$ .

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

Step 5.2

Add $1$ and $2$ .

$\frac{9}{3}$

Step 5.3

Divide $9$ by $3$ .

$3$