Evaluate (-1+3/4-1/3)/(2-1/4)

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $3$ .

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $4$ by $- 1$ .

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Factor $4$ out of $12$ .

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

Cancel the common factor.

$\frac{12 \cdot - 1 + 9 - 4}{12 \cdot 2 + 4 \cdot 3 \frac{- 1}{4}}$

Rewrite the expression.

$\frac{12 \cdot - 1 + 9 - 4}{12 \cdot 2 + 3 \cdot - 1}$

Multiply $3$ by $- 1$ .

$\frac{12 \cdot - 1 + 9 - 4}{12 \cdot 2 - 3}$

Step 4

Simplify the numerator.

Multiply $12$ by $- 1$ .

$\frac{- 12 + 9 - 4}{12 \cdot 2 - 3}$

Add $- 12$ and $9$ .

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

Subtract $4$ from $- 3$ .

$\frac{- 7}{12 \cdot 2 - 3}$

Step 5

Simplify the denominator.

Multiply $12$ by $2$ .

$\frac{- 7}{24 - 3}$

Subtract $3$ from $24$ .

$\frac{- 7}{21}$

Step 6

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 7$ and $21$ .

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{21}$

Cancel the common factors.

Factor $7$ out of $21$ .

$\frac{7 \cdot - 1}{7 \cdot 3}$

Cancel the common factor.

$\frac{7 \cdot - 1}{7 \cdot 3}$

Rewrite the expression.

$\frac{- 1}{3}$

Move the negative in front of the fraction.

$- \frac{1}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$

Evaluate (-1+3/4-1/3)/(2-1/4)

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