Finite Math Examples

$0 = - 9 (\frac{2}{36}) + 13 (\frac{8}{36}) + y (\frac{13}{18})$

Step 1

Rewrite the equation as $- 9 (\frac{2}{36}) + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$ .

$- 9 (\frac{2}{36}) + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2

Simplify $- 9 (\frac{2}{36}) + 13 (\frac{8}{36}) + y (\frac{13}{18})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $9$ .

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Step 2.1.1.1

Factor $9$ out of $- 9$ .

$9 (- 1) \frac{2}{36} + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.1.2

Factor $9$ out of $36$ .

$9 \cdot - 1 \frac{2}{9 \cdot 4} + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.1.3

Cancel the common factor.

$9 \cdot - 1 \frac{2}{9 \cdot 4} + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.1.4

Rewrite the expression.

$- 1 (\frac{2}{4}) + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.2

Cancel the common factor of $2$ and $4$ .

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Step 2.1.2.1

Factor $2$ out of $2$ .

$- 1 \frac{2 (1)}{4} + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.2.2

Cancel the common factors.

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Step 2.1.2.2.1

Factor $2$ out of $4$ .

$- 1 \frac{2 \cdot 1}{2 \cdot 2} + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.2.2.2

Cancel the common factor.

$- 1 \frac{2 \cdot 1}{2 \cdot 2} + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.2.2.3

Rewrite the expression.

$- 1 (\frac{1}{2}) + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.3

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

$- (\frac{1}{2}) + 13 (\frac{8}{36}) + y (\frac{13}{18}) = 0$

Step 2.1.4

Cancel the common factor of $8$ and $36$ .

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Step 2.1.4.1

Factor $4$ out of $8$ .

$- \frac{1}{2} + 13 \frac{4 (2)}{36} + y (\frac{13}{18}) = 0$

Step 2.1.4.2

Cancel the common factors.

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Step 2.1.4.2.1

Factor $4$ out of $36$ .

$- \frac{1}{2} + 13 \frac{4 \cdot 2}{4 \cdot 9} + y (\frac{13}{18}) = 0$

Step 2.1.4.2.2

Cancel the common factor.

$- \frac{1}{2} + 13 \frac{4 \cdot 2}{4 \cdot 9} + y (\frac{13}{18}) = 0$

Step 2.1.4.2.3

Rewrite the expression.

$- \frac{1}{2} + 13 (\frac{2}{9}) + y (\frac{13}{18}) = 0$

Step 2.1.5

Multiply $13 (\frac{2}{9})$ .

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Step 2.1.5.1

Combine $13$ and $\frac{2}{9}$ .

$- \frac{1}{2} + \frac{13 \cdot 2}{9} + y (\frac{13}{18}) = 0$

Step 2.1.5.2

Multiply $13$ by $2$ .

$- \frac{1}{2} + \frac{26}{9} + y (\frac{13}{18}) = 0$

Step 2.1.6

Combine $y$ and $\frac{13}{18}$ .

$- \frac{1}{2} + \frac{26}{9} + \frac{y \cdot 13}{18} = 0$

Step 2.1.7

Move $13$ to the left of $y$ .

$- \frac{1}{2} + \frac{26}{9} + \frac{13 y}{18} = 0$

Step 2.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{1}{2} \cdot \frac{9}{9} + \frac{26}{9} + \frac{13 y}{18} = 0$

Step 2.3

To write $\frac{26}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{2} \cdot \frac{9}{9} + \frac{26}{9} \cdot \frac{2}{2} + \frac{13 y}{18} = 0$

Step 2.4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$- \frac{9}{2 \cdot 9} + \frac{26}{9} \cdot \frac{2}{2} + \frac{13 y}{18} = 0$

Step 2.4.2

Multiply $2$ by $9$ .

$- \frac{9}{18} + \frac{26}{9} \cdot \frac{2}{2} + \frac{13 y}{18} = 0$

Step 2.4.3

Multiply $\frac{26}{9}$ by $\frac{2}{2}$ .

$- \frac{9}{18} + \frac{26 \cdot 2}{9 \cdot 2} + \frac{13 y}{18} = 0$

Step 2.4.4

Multiply $9$ by $2$ .

$- \frac{9}{18} + \frac{26 \cdot 2}{18} + \frac{13 y}{18} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 9 + 26 \cdot 2}{18} + \frac{13 y}{18} = 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $26$ by $2$ .

$\frac{- 9 + 52}{18} + \frac{13 y}{18} = 0$

Step 2.6.2

Add $- 9$ and $52$ .

$\frac{43}{18} + \frac{13 y}{18} = 0$

Step 3

Subtract $\frac{43}{18}$ from both sides of the equation.

$\frac{13 y}{18} = - \frac{43}{18}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$13 y = - 43$

Step 5

Divide each term in $13 y = - 43$ by $13$ and simplify.

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Step 5.1

Divide each term in $13 y = - 43$ by $13$ .

$\frac{13 y}{13} = \frac{- 43}{13}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $13$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{13 y}{13} = \frac{- 43}{13}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 43}{13}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$y = - \frac{43}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{43}{13}$

Decimal Form:

$y = - 3.\overline{307692}$

Mixed Number Form:

$y = - 3 \frac{4}{13}$