Evaluate -4/9+5/6-7/12

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

Step 1

Find the common denominator.

Multiply $\frac{4}{9}$ by $\frac{4}{4}$ .

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

Multiply $\frac{4}{9}$ by $\frac{4}{4}$ .

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

Multiply $\frac{5}{6}$ by $\frac{6}{6}$ .

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

Multiply $\frac{5}{6}$ by $\frac{6}{6}$ .

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

Multiply $\frac{7}{12}$ by $\frac{3}{3}$ .

$- \frac{4 \cdot 4}{9 \cdot 4} + \frac{5 \cdot 6}{6 \cdot 6} - (\frac{7}{12} \cdot \frac{3}{3})$

Multiply $\frac{7}{12}$ by $\frac{3}{3}$ .

$- \frac{4 \cdot 4}{9 \cdot 4} + \frac{5 \cdot 6}{6 \cdot 6} - \frac{7 \cdot 3}{12 \cdot 3}$

Reorder the factors of $9 \cdot 4$ .

$- \frac{4 \cdot 4}{4 \cdot 9} + \frac{5 \cdot 6}{6 \cdot 6} - \frac{7 \cdot 3}{12 \cdot 3}$

Multiply $4$ by $9$ .

$- \frac{4 \cdot 4}{36} + \frac{5 \cdot 6}{6 \cdot 6} - \frac{7 \cdot 3}{12 \cdot 3}$

Multiply $6$ by $6$ .

$- \frac{4 \cdot 4}{36} + \frac{5 \cdot 6}{36} - \frac{7 \cdot 3}{12 \cdot 3}$

Reorder the factors of $12 \cdot 3$ .

$- \frac{4 \cdot 4}{36} + \frac{5 \cdot 6}{36} - \frac{7 \cdot 3}{3 \cdot 12}$

Multiply $3$ by $12$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

Multiply $- 4$ by $4$ .

$\frac{- 16 + 5 \cdot 6 - 7 \cdot 3}{36}$

Multiply $5$ by $6$ .

$\frac{- 16 + 30 - 7 \cdot 3}{36}$

Multiply $- 7$ by $3$ .

$\frac{- 16 + 30 - 21}{36}$

Step 4

Simplify the expression.

Add $- 16$ and $30$ .

$\frac{14 - 21}{36}$

Subtract $21$ from $14$ .

$\frac{- 7}{36}$

Move the negative in front of the fraction.

$- \frac{7}{36}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{36}$

Decimal Form:

$- 0.19\overline{4}$

Evaluate -4/9+5/6-7/12

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