Evaluate (1/2-11/12)/(2/3-11/12)

$\frac{\frac{1}{2} - \frac{11}{12}}{\frac{2}{3} - \frac{11}{12}}$

Step 1

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

Multiply $\frac{\frac{1}{2} - \frac{11}{12}}{\frac{2}{3} - \frac{11}{12}}$ by $\frac{12}{12}$ .

$\frac{12}{12} \cdot \frac{\frac{1}{2} - \frac{11}{12}}{\frac{2}{3} - \frac{11}{12}}$

Combine.

$\frac{12 (\frac{1}{2} - \frac{11}{12})}{12 (\frac{2}{3} - \frac{11}{12})}$

Step 2

Apply the distributive property.

$\frac{12 (\frac{1}{2}) + 12 (- \frac{11}{12})}{12 (\frac{2}{3}) + 12 (- \frac{11}{12})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$\frac{2 (6) \frac{1}{2} + 12 (- \frac{11}{12})}{12 (\frac{2}{3}) + 12 (- \frac{11}{12})}$

Cancel the common factor.

$\frac{2 \cdot 6 \frac{1}{2} + 12 (- \frac{11}{12})}{12 (\frac{2}{3}) + 12 (- \frac{11}{12})}$

Rewrite the expression.

$\frac{6 + 12 (- \frac{11}{12})}{12 (\frac{2}{3}) + 12 (- \frac{11}{12})}$

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{11}{12}$ into the numerator.

$\frac{6 + 12 (\frac{- 11}{12})}{12 (\frac{2}{3}) + 12 (- \frac{11}{12})}$

Cancel the common factor.

$\frac{6 + 12 (\frac{- 11}{12})}{12 (\frac{2}{3}) + 12 (- \frac{11}{12})}$

Rewrite the expression.

$\frac{6 - 11}{12 (\frac{2}{3}) + 12 (- \frac{11}{12})}$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$\frac{6 - 11}{3 (4) \frac{2}{3} + 12 (- \frac{11}{12})}$

Cancel the common factor.

$\frac{6 - 11}{3 \cdot 4 \frac{2}{3} + 12 (- \frac{11}{12})}$

Rewrite the expression.

$\frac{6 - 11}{4 \cdot 2 + 12 (- \frac{11}{12})}$

Multiply $4$ by $2$ .

$\frac{6 - 11}{8 + 12 (- \frac{11}{12})}$

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{11}{12}$ into the numerator.

$\frac{6 - 11}{8 + 12 (\frac{- 11}{12})}$

Cancel the common factor.

$\frac{6 - 11}{8 + 12 (\frac{- 11}{12})}$

Rewrite the expression.

$\frac{6 - 11}{8 - 11}$

Step 4

Reduce the expression by cancelling the common factors.

Subtract $11$ from $6$ .

$\frac{- 5}{8 - 11}$

Subtract $11$ from $8$ .

$\frac{- 5}{- 3}$

Dividing two negative values results in a positive value.

$\frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$

Evaluate (1/2-11/12)/(2/3-11/12)

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