Basic Math Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $30$ .

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Step 1.1

Multiply $\frac{\frac{3}{10} + \frac{2}{3}}{\frac{1}{5} + \frac{1}{3}}$ by $\frac{30}{30}$ .

$\frac{30}{30} \cdot \frac{\frac{3}{10} + \frac{2}{3}}{\frac{1}{5} + \frac{1}{3}}$

Step 1.2

Combine.

$\frac{30 (\frac{3}{10} + \frac{2}{3})}{30 (\frac{1}{5} + \frac{1}{3})}$

Step 2

Apply the distributive property.

$\frac{30 (\frac{3}{10}) + 30 (\frac{2}{3})}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $10$ .

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Step 3.1.1

Factor $10$ out of $30$ .

$\frac{10 (3) \frac{3}{10} + 30 (\frac{2}{3})}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.1.2

Cancel the common factor.

$\frac{10 \cdot 3 \frac{3}{10} + 30 (\frac{2}{3})}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.1.3

Rewrite the expression.

$\frac{3 \cdot 3 + 30 (\frac{2}{3})}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.2

Multiply $3$ by $3$ .

$\frac{9 + 30 (\frac{2}{3})}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Factor $3$ out of $30$ .

$\frac{9 + 3 (10) \frac{2}{3}}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.3.2

Cancel the common factor.

$\frac{9 + 3 \cdot 10 \frac{2}{3}}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.3.3

Rewrite the expression.

$\frac{9 + 10 \cdot 2}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.4

Multiply $10$ by $2$ .

$\frac{9 + 20}{30 (\frac{1}{5}) + 30 (\frac{1}{3})}$

Step 3.5

Cancel the common factor of $5$ .

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Step 3.5.1

Factor $5$ out of $30$ .

$\frac{9 + 20}{5 (6) \frac{1}{5} + 30 (\frac{1}{3})}$

Step 3.5.2

Cancel the common factor.

$\frac{9 + 20}{5 \cdot 6 \frac{1}{5} + 30 (\frac{1}{3})}$

Step 3.5.3

Rewrite the expression.

$\frac{9 + 20}{6 + 30 (\frac{1}{3})}$

Step 3.6

Cancel the common factor of $3$ .

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Step 3.6.1

Factor $3$ out of $30$ .

$\frac{9 + 20}{6 + 3 (10) \frac{1}{3}}$

Step 3.6.2

Cancel the common factor.

$\frac{9 + 20}{6 + 3 \cdot 10 \frac{1}{3}}$

Step 3.6.3

Rewrite the expression.

$\frac{9 + 20}{6 + 10}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $9$ and $20$ .

$\frac{29}{6 + 10}$

Step 4.2

Add $6$ and $10$ .

$\frac{29}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{16}$

Decimal Form:

$1.8125$

Mixed Number Form:

$1 \frac{13}{16}$