Algebra Examples

$(1 + \frac{2}{3}) \cdot (1 + \frac{2}{5}) \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 1

Simplify the expression.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$(\frac{3}{3} + \frac{2}{3}) \cdot (1 + \frac{2}{5}) \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 + 2}{3} \cdot (1 + \frac{2}{5}) \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 1.3

Add $3$ and $2$ .

$\frac{5}{3} \cdot (1 + \frac{2}{5}) \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 1.4

Write $1$ as a fraction with a common denominator.

$\frac{5}{3} \cdot (\frac{5}{5} + \frac{2}{5}) \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 1.5

Combine the numerators over the common denominator.

$\frac{5}{3} \cdot \frac{5 + 2}{5} \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 1.6

Add $5$ and $2$ .

$\frac{5}{3} \cdot \frac{7}{5} \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{7}{5} \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 2.2

Rewrite the expression.

$\frac{1}{3} \cdot 7 \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 3

Combine $\frac{1}{3}$ and $7$ .

$\frac{7}{3} \cdot (1 + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 4

Simplify the expression.

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Step 4.1

Write $1$ as a fraction with a common denominator.

$\frac{7}{3} \cdot (\frac{7}{7} + \frac{2}{7}) \cdot (1 + \frac{2}{9})$

Step 4.2

Combine the numerators over the common denominator.

$\frac{7}{3} \cdot \frac{7 + 2}{7} \cdot (1 + \frac{2}{9})$

Step 4.3

Add $7$ and $2$ .

$\frac{7}{3} \cdot \frac{9}{7} \cdot (1 + \frac{2}{9})$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Cancel the common factor.

$\frac{7}{3} \cdot \frac{9}{7} \cdot (1 + \frac{2}{9})$

Step 5.2

Rewrite the expression.

$\frac{1}{3} \cdot 9 \cdot (1 + \frac{2}{9})$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Factor $3$ out of $9$ .

$\frac{1}{3} \cdot (3 (3)) \cdot (1 + \frac{2}{9})$

Step 6.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 3) \cdot (1 + \frac{2}{9})$

Step 6.3

Rewrite the expression.

$3 \cdot (1 + \frac{2}{9})$

Step 7

Simplify the expression.

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Step 7.1

Write $1$ as a fraction with a common denominator.

$3 \cdot (\frac{9}{9} + \frac{2}{9})$

Step 7.2

Combine the numerators over the common denominator.

$3 \cdot \frac{9 + 2}{9}$

Step 7.3

Add $9$ and $2$ .

$3 \cdot \frac{11}{9}$

Step 8

Cancel the common factor of $3$ .

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Step 8.1

Factor $3$ out of $9$ .

$3 \cdot \frac{11}{3 (3)}$

Step 8.2

Cancel the common factor.

$3 \cdot \frac{11}{3 \cdot 3}$

Step 8.3

Rewrite the expression.

$\frac{11}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{3}$

Decimal Form:

$3.\overline{6}$

Mixed Number Form:

$3 \frac{2}{3}$