Pre-Algebra Examples

$\frac{- 5}{12} + \frac{4}{9} - \frac{7}{18}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{- 5}{12}$ by $\frac{3}{3}$ .

$\frac{- 5}{12} \cdot \frac{3}{3} + \frac{4}{9} - \frac{7}{18}$

Step 1.2

Multiply $\frac{- 5}{12}$ by $\frac{3}{3}$ .

$\frac{- 5 \cdot 3}{12 \cdot 3} + \frac{4}{9} - \frac{7}{18}$

Step 1.3

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

$\frac{- 5 \cdot 3}{12 \cdot 3} + \frac{4}{9} \cdot \frac{4}{4} - \frac{7}{18}$

Step 1.4

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

$\frac{- 5 \cdot 3}{12 \cdot 3} + \frac{4 \cdot 4}{9 \cdot 4} - \frac{7}{18}$

Step 1.5

Multiply $\frac{7}{18}$ by $\frac{2}{2}$ .

$\frac{- 5 \cdot 3}{12 \cdot 3} + \frac{4 \cdot 4}{9 \cdot 4} - (\frac{7}{18} \cdot \frac{2}{2})$

Step 1.6

Multiply $\frac{7}{18}$ by $\frac{2}{2}$ .

$\frac{- 5 \cdot 3}{12 \cdot 3} + \frac{4 \cdot 4}{9 \cdot 4} - \frac{7 \cdot 2}{18 \cdot 2}$

Step 1.7

Reorder the factors of $12 \cdot 3$ .

$\frac{- 5 \cdot 3}{3 \cdot 12} + \frac{4 \cdot 4}{9 \cdot 4} - \frac{7 \cdot 2}{18 \cdot 2}$

Step 1.8

Multiply $3$ by $12$ .

$\frac{- 5 \cdot 3}{36} + \frac{4 \cdot 4}{9 \cdot 4} - \frac{7 \cdot 2}{18 \cdot 2}$

Step 1.9

Reorder the factors of $9 \cdot 4$ .

$\frac{- 5 \cdot 3}{36} + \frac{4 \cdot 4}{4 \cdot 9} - \frac{7 \cdot 2}{18 \cdot 2}$

Step 1.10

Multiply $4$ by $9$ .

$\frac{- 5 \cdot 3}{36} + \frac{4 \cdot 4}{36} - \frac{7 \cdot 2}{18 \cdot 2}$

Step 1.11

Reorder the factors of $18 \cdot 2$ .

$\frac{- 5 \cdot 3}{36} + \frac{4 \cdot 4}{36} - \frac{7 \cdot 2}{2 \cdot 18}$

Step 1.12

Multiply $2$ by $18$ .

$\frac{- 5 \cdot 3}{36} + \frac{4 \cdot 4}{36} - \frac{7 \cdot 2}{36}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 3 + 4 \cdot 4 - 7 \cdot 2}{36}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 5$ by $3$ .

$\frac{- 15 + 4 \cdot 4 - 7 \cdot 2}{36}$

Step 3.2

Multiply $4$ by $4$ .

$\frac{- 15 + 16 - 7 \cdot 2}{36}$

Step 3.3

Multiply $- 7$ by $2$ .

$\frac{- 15 + 16 - 14}{36}$

Step 4

Simplify the expression.

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Step 4.1

Add $- 15$ and $16$ .

$\frac{1 - 14}{36}$

Step 4.2

Subtract $14$ from $1$ .

$\frac{- 13}{36}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{13}{36}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{13}{36}$

Decimal Form:

$- 0.36\overline{1}$