Basic Math Examples

$\frac{\frac{1}{2} + \frac{2}{3} + \frac{3}{4}}{\frac{1}{2} - \frac{2}{3} - \frac{3}{4}}$

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $12$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $12$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.3

Multiply $4$ by $2$ .

$\frac{6 + 8 + 12 (\frac{3}{4})}{12 (\frac{1}{2}) + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.4

Cancel the common factor of $4$ .

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Step 3.4.1

Factor $4$ out of $12$ .

$\frac{6 + 8 + 4 (3) \frac{3}{4}}{12 (\frac{1}{2}) + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.4.2

Cancel the common factor.

$\frac{6 + 8 + 4 \cdot 3 \frac{3}{4}}{12 (\frac{1}{2}) + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.4.3

Rewrite the expression.

$\frac{6 + 8 + 3 \cdot 3}{12 (\frac{1}{2}) + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.5

Multiply $3$ by $3$ .

$\frac{6 + 8 + 9}{12 (\frac{1}{2}) + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.6

Cancel the common factor of $2$ .

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Step 3.6.1

Factor $2$ out of $12$ .

$\frac{6 + 8 + 9}{2 (6) \frac{1}{2} + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.6.2

Cancel the common factor.

$\frac{6 + 8 + 9}{2 \cdot 6 \frac{1}{2} + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.6.3

Rewrite the expression.

$\frac{6 + 8 + 9}{6 + 12 (- \frac{2}{3}) + 12 (- \frac{3}{4})}$

Step 3.7

Cancel the common factor of $3$ .

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Step 3.7.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{6 + 8 + 9}{6 + 12 (\frac{- 2}{3}) + 12 (- \frac{3}{4})}$

Step 3.7.2

Factor $3$ out of $12$ .

$\frac{6 + 8 + 9}{6 + 3 (4) \frac{- 2}{3} + 12 (- \frac{3}{4})}$

Step 3.7.3

Cancel the common factor.

$\frac{6 + 8 + 9}{6 + 3 \cdot 4 \frac{- 2}{3} + 12 (- \frac{3}{4})}$

Step 3.7.4

Rewrite the expression.

$\frac{6 + 8 + 9}{6 + 4 \cdot - 2 + 12 (- \frac{3}{4})}$

Step 3.8

Multiply $4$ by $- 2$ .

$\frac{6 + 8 + 9}{6 - 8 + 12 (- \frac{3}{4})}$

Step 3.9

Cancel the common factor of $4$ .

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Step 3.9.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{6 + 8 + 9}{6 - 8 + 12 (\frac{- 3}{4})}$

Step 3.9.2

Factor $4$ out of $12$ .

$\frac{6 + 8 + 9}{6 - 8 + 4 (3) \frac{- 3}{4}}$

Step 3.9.3

Cancel the common factor.

$\frac{6 + 8 + 9}{6 - 8 + 4 \cdot 3 \frac{- 3}{4}}$

Step 3.9.4

Rewrite the expression.

$\frac{6 + 8 + 9}{6 - 8 + 3 \cdot - 3}$

Step 3.10

Multiply $3$ by $- 3$ .

$\frac{6 + 8 + 9}{6 - 8 - 9}$

Step 4

Simplify the numerator.

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Step 4.1

Add $6$ and $8$ .

$\frac{14 + 9}{6 - 8 - 9}$

Step 4.2

Add $14$ and $9$ .

$\frac{23}{6 - 8 - 9}$

Step 5

Simplify the denominator.

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Step 5.1

Subtract $8$ from $6$ .

$\frac{23}{- 2 - 9}$

Step 5.2

Subtract $9$ from $- 2$ .

$\frac{23}{- 11}$

Step 6

Move the negative in front of the fraction.

$- \frac{23}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{23}{11}$

Decimal Form:

$- 2.\overline{09}$

Mixed Number Form:

$- 2 \frac{1}{11}$