Basic Math Examples

$\frac{1}{54} + \frac{35}{36} + \frac{319}{162}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{54}$ by $\frac{6}{6}$ .

$\frac{1}{54} \cdot \frac{6}{6} + \frac{35}{36} + \frac{319}{162}$

Step 1.2

Multiply $\frac{1}{54}$ by $\frac{6}{6}$ .

$\frac{6}{54 \cdot 6} + \frac{35}{36} + \frac{319}{162}$

Step 1.3

Multiply $\frac{35}{36}$ by $\frac{9}{9}$ .

$\frac{6}{54 \cdot 6} + \frac{35}{36} \cdot \frac{9}{9} + \frac{319}{162}$

Step 1.4

Multiply $\frac{35}{36}$ by $\frac{9}{9}$ .

$\frac{6}{54 \cdot 6} + \frac{35 \cdot 9}{36 \cdot 9} + \frac{319}{162}$

Step 1.5

Multiply $\frac{319}{162}$ by $\frac{2}{2}$ .

$\frac{6}{54 \cdot 6} + \frac{35 \cdot 9}{36 \cdot 9} + \frac{319}{162} \cdot \frac{2}{2}$

Step 1.6

Multiply $\frac{319}{162}$ by $\frac{2}{2}$ .

$\frac{6}{54 \cdot 6} + \frac{35 \cdot 9}{36 \cdot 9} + \frac{319 \cdot 2}{162 \cdot 2}$

Step 1.7

Reorder the factors of $54 \cdot 6$ .

$\frac{6}{6 \cdot 54} + \frac{35 \cdot 9}{36 \cdot 9} + \frac{319 \cdot 2}{162 \cdot 2}$

Step 1.8

Multiply $6$ by $54$ .

$\frac{6}{324} + \frac{35 \cdot 9}{36 \cdot 9} + \frac{319 \cdot 2}{162 \cdot 2}$

Step 1.9

Reorder the factors of $36 \cdot 9$ .

$\frac{6}{324} + \frac{35 \cdot 9}{9 \cdot 36} + \frac{319 \cdot 2}{162 \cdot 2}$

Step 1.10

Multiply $9$ by $36$ .

$\frac{6}{324} + \frac{35 \cdot 9}{324} + \frac{319 \cdot 2}{162 \cdot 2}$

Step 1.11

Reorder the factors of $162 \cdot 2$ .

$\frac{6}{324} + \frac{35 \cdot 9}{324} + \frac{319 \cdot 2}{2 \cdot 162}$

Step 1.12

Multiply $2$ by $162$ .

$\frac{6}{324} + \frac{35 \cdot 9}{324} + \frac{319 \cdot 2}{324}$

Step 2

Combine the numerators over the common denominator.

$\frac{6 + 35 \cdot 9 + 319 \cdot 2}{324}$

Step 3

Simplify each term.

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Step 3.1

Multiply $35$ by $9$ .

$\frac{6 + 315 + 319 \cdot 2}{324}$

Step 3.2

Multiply $319$ by $2$ .

$\frac{6 + 315 + 638}{324}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $6$ and $315$ .

$\frac{321 + 638}{324}$

Step 4.2

Add $321$ and $638$ .

$\frac{959}{324}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{959}{324}$

Decimal Form:

$2.95987654 \dots$

Mixed Number Form:

$2 \frac{311}{324}$