Pre-Algebra Examples

$\frac{7}{18} + \frac{5}{12} - \frac{1}{4}$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{7}{18} \cdot \frac{2}{2} + \frac{5}{12} - \frac{1}{4}$

Step 1.2

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

$\frac{7 \cdot 2}{18 \cdot 2} + \frac{5}{12} - \frac{1}{4}$

Step 1.3

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

$\frac{7 \cdot 2}{18 \cdot 2} + \frac{5}{12} \cdot \frac{3}{3} - \frac{1}{4}$

Step 1.4

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

$\frac{7 \cdot 2}{18 \cdot 2} + \frac{5 \cdot 3}{12 \cdot 3} - \frac{1}{4}$

Step 1.5

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

$\frac{7 \cdot 2}{18 \cdot 2} + \frac{5 \cdot 3}{12 \cdot 3} - (\frac{1}{4} \cdot \frac{9}{9})$

Step 1.6

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

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

Step 1.7

Reorder the factors of $18 \cdot 2$ .

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

Step 1.8

Multiply $2$ by $18$ .

$\frac{7 \cdot 2}{36} + \frac{5 \cdot 3}{12 \cdot 3} - \frac{9}{4 \cdot 9}$

Step 1.9

Reorder the factors of $12 \cdot 3$ .

$\frac{7 \cdot 2}{36} + \frac{5 \cdot 3}{3 \cdot 12} - \frac{9}{4 \cdot 9}$

Step 1.10

Multiply $3$ by $12$ .

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

Step 1.11

Multiply $4$ by $9$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $7$ by $2$ .

$\frac{14 + 5 \cdot 3 - 9}{36}$

Step 3.2

Multiply $5$ by $3$ .

$\frac{14 + 15 - 9}{36}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add $14$ and $15$ .

$\frac{29 - 9}{36}$

Step 4.2

Subtract $9$ from $29$ .

$\frac{20}{36}$

Step 4.3

Cancel the common factor of $20$ and $36$ .

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Step 4.3.1

Factor $4$ out of $20$ .

$\frac{4 (5)}{36}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $4$ out of $36$ .

$\frac{4 \cdot 5}{4 \cdot 9}$

Step 4.3.2.2

Cancel the common factor.

$\frac{4 \cdot 5}{4 \cdot 9}$

Step 4.3.2.3

Rewrite the expression.

$\frac{5}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{9}$

Decimal Form:

$0.\overline{5}$