Basic Math Examples

$\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \frac{1}{7 \cdot 9} + \frac{1}{9 \cdot 11}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $3$ by $1$ .

$\frac{1}{3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \frac{1}{7 \cdot 9} + \frac{1}{9 \cdot 11}$

Step 1.2

Multiply $3$ by $5$ .

$\frac{1}{3} + \frac{1}{15} + \frac{1}{5 \cdot 7} + \frac{1}{7 \cdot 9} + \frac{1}{9 \cdot 11}$

Step 1.3

Multiply $5$ by $7$ .

$\frac{1}{3} + \frac{1}{15} + \frac{1}{35} + \frac{1}{7 \cdot 9} + \frac{1}{9 \cdot 11}$

Step 1.4

Multiply $7$ by $9$ .

$\frac{1}{3} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{9 \cdot 11}$

Step 1.5

Multiply $9$ by $11$ .

$\frac{1}{3} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99}$

Step 1.6

Multiply $\frac{1}{3}$ by $\frac{1155}{1155}$ .

$\frac{1}{3} \cdot \frac{1155}{1155} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99}$

Step 1.7

Multiply $\frac{1}{3}$ by $\frac{1155}{1155}$ .

$\frac{1155}{3 \cdot 1155} + \frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99}$

Step 1.8

Multiply $\frac{1}{15}$ by $\frac{231}{231}$ .

$\frac{1155}{3 \cdot 1155} + \frac{1}{15} \cdot \frac{231}{231} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99}$

Step 1.9

Multiply $\frac{1}{15}$ by $\frac{231}{231}$ .

$\frac{1155}{3 \cdot 1155} + \frac{231}{15 \cdot 231} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99}$

Step 1.10

Multiply $\frac{1}{35}$ by $\frac{99}{99}$ .

$\frac{1155}{3 \cdot 1155} + \frac{231}{15 \cdot 231} + \frac{1}{35} \cdot \frac{99}{99} + \frac{1}{63} + \frac{1}{99}$

Step 1.11

Multiply $\frac{1}{35}$ by $\frac{99}{99}$ .

$\frac{1155}{3 \cdot 1155} + \frac{231}{15 \cdot 231} + \frac{99}{35 \cdot 99} + \frac{1}{63} + \frac{1}{99}$

Step 1.12

Multiply $\frac{1}{63}$ by $\frac{55}{55}$ .

$\frac{1155}{3 \cdot 1155} + \frac{231}{15 \cdot 231} + \frac{99}{35 \cdot 99} + \frac{1}{63} \cdot \frac{55}{55} + \frac{1}{99}$

Step 1.13

Multiply $\frac{1}{63}$ by $\frac{55}{55}$ .

$\frac{1155}{3 \cdot 1155} + \frac{231}{15 \cdot 231} + \frac{99}{35 \cdot 99} + \frac{55}{63 \cdot 55} + \frac{1}{99}$

Step 1.14

Multiply $\frac{1}{99}$ by $\frac{35}{35}$ .

$\frac{1155}{3 \cdot 1155} + \frac{231}{15 \cdot 231} + \frac{99}{35 \cdot 99} + \frac{55}{63 \cdot 55} + \frac{1}{99} \cdot \frac{35}{35}$

Step 1.15

Multiply $\frac{1}{99}$ by $\frac{35}{35}$ .

$\frac{1155}{3 \cdot 1155} + \frac{231}{15 \cdot 231} + \frac{99}{35 \cdot 99} + \frac{55}{63 \cdot 55} + \frac{35}{99 \cdot 35}$

Step 1.16

Multiply $3$ by $1155$ .

$\frac{1155}{3465} + \frac{231}{15 \cdot 231} + \frac{99}{35 \cdot 99} + \frac{55}{63 \cdot 55} + \frac{35}{99 \cdot 35}$

Step 1.17

Multiply $15$ by $231$ .

$\frac{1155}{3465} + \frac{231}{3465} + \frac{99}{35 \cdot 99} + \frac{55}{63 \cdot 55} + \frac{35}{99 \cdot 35}$

Step 1.18

Multiply $35$ by $99$ .

$\frac{1155}{3465} + \frac{231}{3465} + \frac{99}{3465} + \frac{55}{63 \cdot 55} + \frac{35}{99 \cdot 35}$

Step 1.19

Reorder the factors of $63 \cdot 55$ .

$\frac{1155}{3465} + \frac{231}{3465} + \frac{99}{3465} + \frac{55}{55 \cdot 63} + \frac{35}{99 \cdot 35}$

Step 1.20

Multiply $55$ by $63$ .

$\frac{1155}{3465} + \frac{231}{3465} + \frac{99}{3465} + \frac{55}{3465} + \frac{35}{99 \cdot 35}$

Step 1.21

Reorder the factors of $99 \cdot 35$ .

$\frac{1155}{3465} + \frac{231}{3465} + \frac{99}{3465} + \frac{55}{3465} + \frac{35}{35 \cdot 99}$

Step 1.22

Multiply $35$ by $99$ .

$\frac{1155}{3465} + \frac{231}{3465} + \frac{99}{3465} + \frac{55}{3465} + \frac{35}{3465}$

Step 2

Combine the numerators over the common denominator.

$\frac{1155 + 231 + 99 + 55 + 35}{3465}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add $1155$ and $231$ .

$\frac{1386 + 99 + 55 + 35}{3465}$

Step 3.2

Add $1386$ and $99$ .

$\frac{1485 + 55 + 35}{3465}$

Step 3.3

Add $1485$ and $55$ .

$\frac{1540 + 35}{3465}$

Step 3.4

Add $1540$ and $35$ .

$\frac{1575}{3465}$

Step 4

Cancel the common factor of $1575$ and $3465$ .

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Step 4.1

Factor $315$ out of $1575$ .

$\frac{315 (5)}{3465}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $315$ out of $3465$ .

$\frac{315 \cdot 5}{315 \cdot 11}$

Step 4.2.2

Cancel the common factor.

$\frac{315 \cdot 5}{315 \cdot 11}$

Step 4.2.3

Rewrite the expression.

$\frac{5}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{11}$

Decimal Form:

$0.\overline{45}$