Pre-Algebra Examples

\frac{1}{6} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}

$\frac{1}{6} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{81}{81}

$\frac{81}{81}$ .

\frac{1}{6} \cdot \frac{81}{81} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}

$\frac{1}{6} \cdot \frac{81}{81} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Step 1.2

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{81}{81}

$\frac{81}{81}$ .

\frac{81}{6 \cdot 81} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}

$\frac{81}{6 \cdot 81} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Step 1.3

Multiply

\frac{1}{18}

$\frac{1}{18}$ by

\frac{27}{27}

$\frac{27}{27}$ .

\frac{81}{6 \cdot 81} + \frac{1}{18} \cdot \frac{27}{27} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}

$\frac{81}{6 \cdot 81} + \frac{1}{18} \cdot \frac{27}{27} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Step 1.4

Multiply

\frac{1}{18}

$\frac{1}{18}$ by

\frac{27}{27}

$\frac{27}{27}$ .

\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Step 1.5

Multiply

\frac{1}{54}

$\frac{1}{54}$ by

\frac{9}{9}

$\frac{9}{9}$ .

\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{1}{54} \cdot \frac{9}{9} + \frac{1}{162} + \frac{1}{486}

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{1}{54} \cdot \frac{9}{9} + \frac{1}{162} + \frac{1}{486}$

Step 1.6

Multiply

\frac{1}{54}

$\frac{1}{54}$ by

\frac{9}{9}

$\frac{9}{9}$ .

\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{1}{162} + \frac{1}{486}

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{1}{162} + \frac{1}{486}$

Step 1.7

Multiply

\frac{1}{162}

$\frac{1}{162}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{1}{162} \cdot \frac{3}{3} + \frac{1}{486}

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{1}{162} \cdot \frac{3}{3} + \frac{1}{486}$

Step 1.8

Multiply

\frac{1}{162}

$\frac{1}{162}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Step 1.9

Multiply

6

$6$ by

81

$81$ .

\frac{81}{486} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}

$\frac{81}{486} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Step 1.10

Multiply

18

$18$ by

27

$27$ .

\frac{81}{486} + \frac{27}{486} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}

$\frac{81}{486} + \frac{27}{486} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Step 1.11

Reorder the factors of

54 \cdot 9

$54 \cdot 9$ .

\frac{81}{486} + \frac{27}{486} + \frac{9}{9 \cdot 54} + \frac{3}{162 \cdot 3} + \frac{1}{486}

$\frac{81}{486} + \frac{27}{486} + \frac{9}{9 \cdot 54} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Step 1.12

Multiply

9

$9$ by

54

$54$ .

\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{162 \cdot 3} + \frac{1}{486}

$\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Step 1.13

Reorder the factors of

162 \cdot 3

$162 \cdot 3$ .

\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{3 \cdot 162} + \frac{1}{486}

$\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{3 \cdot 162} + \frac{1}{486}$

Step 1.14

Multiply

3

$3$ by

162

$162$ .

\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{486} + \frac{1}{486}

$\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{486} + \frac{1}{486}$

\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{486} + \frac{1}{486}

$\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{486} + \frac{1}{486}$

Step 2

Combine the numerators over the common denominator.

\frac{81 + 27 + 9 + 3 + 1}{486}

$\frac{81 + 27 + 9 + 3 + 1}{486}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add

81

$81$ and

27

$27$ .

\frac{108 + 9 + 3 + 1}{486}

$\frac{108 + 9 + 3 + 1}{486}$

Step 3.2

Add

108

$108$ and

9

$9$ .

\frac{117 + 3 + 1}{486}

$\frac{117 + 3 + 1}{486}$

Step 3.3

Add

117

$117$ and

3

$3$ .

\frac{120 + 1}{486}

$\frac{120 + 1}{486}$

Step 3.4

Add

120

$120$ and

1

$1$ .

\frac{121}{486}

$\frac{121}{486}$

\frac{121}{486}

$\frac{121}{486}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{121}{486}

$\frac{121}{486}$

Decimal Form:

0.24897119 \dots

$0.24897119 \dots$