Basic Math Examples

$(\frac{3}{4} + \frac{1}{2}) \div (\frac{5}{3} + \frac{1}{6})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{3}{4} + \frac{1}{2}}{\frac{5}{3} + \frac{1}{6}}$

Step 2

Multiply the numerator and denominator of the fraction by $12$ .

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Step 2.1

Multiply $\frac{\frac{3}{4} + \frac{1}{2}}{\frac{5}{3} + \frac{1}{6}}$ by $\frac{12}{12}$ .

$\frac{12}{12} \cdot \frac{\frac{3}{4} + \frac{1}{2}}{\frac{5}{3} + \frac{1}{6}}$

Step 2.2

Combine.

$\frac{12 (\frac{3}{4} + \frac{1}{2})}{12 (\frac{5}{3} + \frac{1}{6})}$

Step 3

Apply the distributive property.

$\frac{12 (\frac{3}{4}) + 12 (\frac{1}{2})}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $4$ .

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Step 4.1.1

Factor $4$ out of $12$ .

$\frac{4 (3) \frac{3}{4} + 12 (\frac{1}{2})}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4.1.2

Cancel the common factor.

$\frac{4 \cdot 3 \frac{3}{4} + 12 (\frac{1}{2})}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4.1.3

Rewrite the expression.

$\frac{3 \cdot 3 + 12 (\frac{1}{2})}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4.2

Multiply $3$ by $3$ .

$\frac{9 + 12 (\frac{1}{2})}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Factor $2$ out of $12$ .

$\frac{9 + 2 (6) \frac{1}{2}}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4.3.2

Cancel the common factor.

$\frac{9 + 2 \cdot 6 \frac{1}{2}}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4.3.3

Rewrite the expression.

$\frac{9 + 6}{12 (\frac{5}{3}) + 12 (\frac{1}{6})}$

Step 4.4

Cancel the common factor of $3$ .

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Step 4.4.1

Factor $3$ out of $12$ .

$\frac{9 + 6}{3 (4) \frac{5}{3} + 12 (\frac{1}{6})}$

Step 4.4.2

Cancel the common factor.

$\frac{9 + 6}{3 \cdot 4 \frac{5}{3} + 12 (\frac{1}{6})}$

Step 4.4.3

Rewrite the expression.

$\frac{9 + 6}{4 \cdot 5 + 12 (\frac{1}{6})}$

Step 4.5

Multiply $4$ by $5$ .

$\frac{9 + 6}{20 + 12 (\frac{1}{6})}$

Step 4.6

Cancel the common factor of $6$ .

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Step 4.6.1

Factor $6$ out of $12$ .

$\frac{9 + 6}{20 + 6 (2) \frac{1}{6}}$

Step 4.6.2

Cancel the common factor.

$\frac{9 + 6}{20 + 6 \cdot 2 \frac{1}{6}}$

Step 4.6.3

Rewrite the expression.

$\frac{9 + 6}{20 + 2}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $9$ and $6$ .

$\frac{15}{20 + 2}$

Step 5.2

Add $20$ and $2$ .

$\frac{15}{22}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{22}$

Decimal Form:

$0.6\overline{81}$