Finite Math Examples

$\frac{18}{81} + \frac{19}{81} + \frac{36}{81} + \frac{n}{n} = 1$

Step 1

Factor each term.

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Step 1.1

Cancel the common factor of $18$ and $81$ .

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Step 1.1.1

Factor $9$ out of $18$ .

$\frac{9 (2)}{81} + \frac{19}{81} + \frac{36}{81} + \frac{n}{n} = 1$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $9$ out of $81$ .

$\frac{9 \cdot 2}{9 \cdot 9} + \frac{19}{81} + \frac{36}{81} + \frac{n}{n} = 1$

Step 1.1.2.2

Cancel the common factor.

$\frac{9 \cdot 2}{9 \cdot 9} + \frac{19}{81} + \frac{36}{81} + \frac{n}{n} = 1$

Step 1.1.2.3

Rewrite the expression.

$\frac{2}{9} + \frac{19}{81} + \frac{36}{81} + \frac{n}{n} = 1$

Step 1.2

Cancel the common factor of $36$ and $81$ .

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Step 1.2.1

Factor $9$ out of $36$ .

$\frac{2}{9} + \frac{19}{81} + \frac{9 (4)}{81} + \frac{n}{n} = 1$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $9$ out of $81$ .

$\frac{2}{9} + \frac{19}{81} + \frac{9 \cdot 4}{9 \cdot 9} + \frac{n}{n} = 1$

Step 1.2.2.2

Cancel the common factor.

$\frac{2}{9} + \frac{19}{81} + \frac{9 \cdot 4}{9 \cdot 9} + \frac{n}{n} = 1$

Step 1.2.2.3

Rewrite the expression.

$\frac{2}{9} + \frac{19}{81} + \frac{4}{9} + \frac{n}{n} = 1$

Step 1.3

Reduce the expression by cancelling the common factors.

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Step 1.3.1

Reduce the expression $\frac{n}{n}$ by cancelling the common factors.

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Step 1.3.1.1

Cancel the common factor.

$\frac{2}{9} + \frac{19}{81} + \frac{4}{9} + \frac{n}{n} = 1$

Step 1.3.1.2

Rewrite the expression.

$\frac{2}{9} + \frac{19}{81} + \frac{4}{9} + \frac{1}{1} = 1$

Step 1.3.2

Rewrite the expression.

$\frac{2}{9} + \frac{19}{81} + \frac{4}{9} + 1 = 1$

Step 1.4

To write $\frac{2}{9}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2}{9} \cdot \frac{9}{9} + \frac{19}{81} + \frac{4}{9} + 1 = 1$

Step 1.5

Write each expression with a common denominator of $81$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.5.1

Multiply $\frac{2}{9}$ by $\frac{9}{9}$ .

$\frac{2 \cdot 9}{9 \cdot 9} + \frac{19}{81} + \frac{4}{9} + 1 = 1$

Step 1.5.2

Multiply $9$ by $9$ .

$\frac{2 \cdot 9}{81} + \frac{19}{81} + \frac{4}{9} + 1 = 1$

Step 1.6

Combine the numerators over the common denominator.

$\frac{2 \cdot 9 + 19}{81} + \frac{4}{9} + 1 = 1$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Multiply $2$ by $9$ .

$\frac{18 + 19}{81} + \frac{4}{9} + 1 = 1$

Step 1.7.2

Add $18$ and $19$ .

$\frac{37}{81} + \frac{4}{9} + 1 = 1$

Step 1.8

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{37}{81} + \frac{4}{9} \cdot \frac{9}{9} + 1 = 1$

Step 1.9

Write each expression with a common denominator of $81$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.9.1

Multiply $\frac{4}{9}$ by $\frac{9}{9}$ .

$\frac{37}{81} + \frac{4 \cdot 9}{9 \cdot 9} + 1 = 1$

Step 1.9.2

Multiply $9$ by $9$ .

$\frac{37}{81} + \frac{4 \cdot 9}{81} + 1 = 1$

Step 1.10

Combine the numerators over the common denominator.

$\frac{37 + 4 \cdot 9}{81} + 1 = 1$

Step 1.11

Simplify the numerator.

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Step 1.11.1

Multiply $4$ by $9$ .

$\frac{37 + 36}{81} + 1 = 1$

Step 1.11.2

Add $37$ and $36$ .

$\frac{73}{81} + 1 = 1$

Step 1.12

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

$\frac{73}{81} + \frac{81}{81} = 1$

Step 1.13

Combine the numerators over the common denominator.

$\frac{73 + 81}{81} = 1$

Step 1.14

Add $73$ and $81$ .

$\frac{154}{81} = 1$

Step 2

Since $\frac{154}{81} \neq 1$ , there are no solutions.

No solution