Basic Math Examples

$\frac{\frac{1}{4} + \frac{1}{3}}{\frac{7}{9} - \frac{5}{6}}$

Step 1

Multiply the numerator and denominator of the fraction by $36$ .

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Step 1.1

Multiply $\frac{\frac{1}{4} + \frac{1}{3}}{\frac{7}{9} - \frac{5}{6}}$ by $\frac{36}{36}$ .

$\frac{36}{36} \cdot \frac{\frac{1}{4} + \frac{1}{3}}{\frac{7}{9} - \frac{5}{6}}$

Step 1.2

Combine.

$\frac{36 (\frac{1}{4} + \frac{1}{3})}{36 (\frac{7}{9} - \frac{5}{6})}$

Step 2

Apply the distributive property.

$\frac{36 (\frac{1}{4}) + 36 (\frac{1}{3})}{36 (\frac{7}{9}) + 36 (- \frac{5}{6})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $36$ .

$\frac{4 (9) \frac{1}{4} + 36 (\frac{1}{3})}{36 (\frac{7}{9}) + 36 (- \frac{5}{6})}$

Step 3.1.2

Cancel the common factor.

$\frac{4 \cdot 9 \frac{1}{4} + 36 (\frac{1}{3})}{36 (\frac{7}{9}) + 36 (- \frac{5}{6})}$

Step 3.1.3

Rewrite the expression.

$\frac{9 + 36 (\frac{1}{3})}{36 (\frac{7}{9}) + 36 (- \frac{5}{6})}$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $36$ .

$\frac{9 + 3 (12) \frac{1}{3}}{36 (\frac{7}{9}) + 36 (- \frac{5}{6})}$

Step 3.2.2

Cancel the common factor.

$\frac{9 + 3 \cdot 12 \frac{1}{3}}{36 (\frac{7}{9}) + 36 (- \frac{5}{6})}$

Step 3.2.3

Rewrite the expression.

$\frac{9 + 12}{36 (\frac{7}{9}) + 36 (- \frac{5}{6})}$

Step 3.3

Cancel the common factor of $9$ .

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Step 3.3.1

Factor $9$ out of $36$ .

$\frac{9 + 12}{9 (4) \frac{7}{9} + 36 (- \frac{5}{6})}$

Step 3.3.2

Cancel the common factor.

$\frac{9 + 12}{9 \cdot 4 \frac{7}{9} + 36 (- \frac{5}{6})}$

Step 3.3.3

Rewrite the expression.

$\frac{9 + 12}{4 \cdot 7 + 36 (- \frac{5}{6})}$

Step 3.4

Multiply $4$ by $7$ .

$\frac{9 + 12}{28 + 36 (- \frac{5}{6})}$

Step 3.5

Cancel the common factor of $6$ .

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Step 3.5.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{9 + 12}{28 + 36 (\frac{- 5}{6})}$

Step 3.5.2

Factor $6$ out of $36$ .

$\frac{9 + 12}{28 + 6 (6) \frac{- 5}{6}}$

Step 3.5.3

Cancel the common factor.

$\frac{9 + 12}{28 + 6 \cdot 6 \frac{- 5}{6}}$

Step 3.5.4

Rewrite the expression.

$\frac{9 + 12}{28 + 6 \cdot - 5}$

Step 3.6

Multiply $6$ by $- 5$ .

$\frac{9 + 12}{28 - 30}$

Step 4

Simplify the expression.

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Step 4.1

Add $9$ and $12$ .

$\frac{21}{28 - 30}$

Step 4.2

Subtract $30$ from $28$ .

$\frac{21}{- 2}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{21}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{21}{2}$

Decimal Form:

$- 10.5$

Mixed Number Form:

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