Finite Math Examples

$\frac{1}{7} + \frac{1}{21} + \frac{1}{63} + \frac{1}{189}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{7}$ by $\frac{27}{27}$ .

$\frac{1}{7} \cdot \frac{27}{27} + \frac{1}{21} + \frac{1}{63} + \frac{1}{189}$

Step 1.2

Multiply $\frac{1}{7}$ by $\frac{27}{27}$ .

$\frac{27}{7 \cdot 27} + \frac{1}{21} + \frac{1}{63} + \frac{1}{189}$

Step 1.3

Multiply $\frac{1}{21}$ by $\frac{9}{9}$ .

$\frac{27}{7 \cdot 27} + \frac{1}{21} \cdot \frac{9}{9} + \frac{1}{63} + \frac{1}{189}$

Step 1.4

Multiply $\frac{1}{21}$ by $\frac{9}{9}$ .

$\frac{27}{7 \cdot 27} + \frac{9}{21 \cdot 9} + \frac{1}{63} + \frac{1}{189}$

Step 1.5

Multiply $\frac{1}{63}$ by $\frac{3}{3}$ .

$\frac{27}{7 \cdot 27} + \frac{9}{21 \cdot 9} + \frac{1}{63} \cdot \frac{3}{3} + \frac{1}{189}$

Step 1.6

Multiply $\frac{1}{63}$ by $\frac{3}{3}$ .

$\frac{27}{7 \cdot 27} + \frac{9}{21 \cdot 9} + \frac{3}{63 \cdot 3} + \frac{1}{189}$

Step 1.7

Multiply $7$ by $27$ .

$\frac{27}{189} + \frac{9}{21 \cdot 9} + \frac{3}{63 \cdot 3} + \frac{1}{189}$

Step 1.8

Reorder the factors of $21 \cdot 9$ .

$\frac{27}{189} + \frac{9}{9 \cdot 21} + \frac{3}{63 \cdot 3} + \frac{1}{189}$

Step 1.9

Multiply $9$ by $21$ .

$\frac{27}{189} + \frac{9}{189} + \frac{3}{63 \cdot 3} + \frac{1}{189}$

Step 1.10

Reorder the factors of $63 \cdot 3$ .

$\frac{27}{189} + \frac{9}{189} + \frac{3}{3 \cdot 63} + \frac{1}{189}$

Step 1.11

Multiply $3$ by $63$ .

$\frac{27}{189} + \frac{9}{189} + \frac{3}{189} + \frac{1}{189}$

Step 2

Combine the numerators over the common denominator.

$\frac{27 + 9 + 3 + 1}{189}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add $27$ and $9$ .

$\frac{36 + 3 + 1}{189}$

Step 3.2

Add $36$ and $3$ .

$\frac{39 + 1}{189}$

Step 3.3

Add $39$ and $1$ .

$\frac{40}{189}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{40}{189}$

Decimal Form:

$0.\overline{211640}$