Finite Math Examples

$0 = - 9 (\frac{2}{18}) + 13 (\frac{7}{36}) + y (\frac{25}{36})$

Step 1

Rewrite the equation as $- 9 (\frac{2}{18}) + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$ .

$- 9 (\frac{2}{18}) + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2

Simplify $- 9 (\frac{2}{18}) + 13 (\frac{7}{36}) + y (\frac{25}{36})$ .

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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 $- 9$ .

$9 (- 1) \frac{2}{18} + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2.1.1.2

Factor $9$ out of $18$ .

$9 \cdot - 1 \frac{2}{9 \cdot 2} + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2.1.1.3

Cancel the common factor.

$9 \cdot - 1 \frac{2}{9 \cdot 2} + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2.1.1.4

Rewrite the expression.

$- 1 (\frac{2}{2}) + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2.1.2

Cancel the common factor of $2$ .

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Step 2.1.2.1

Cancel the common factor.

$- 1 (\frac{2}{2}) + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2.1.2.2

Rewrite the expression.

$- 1 \cdot 1 + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2.1.3

Multiply $- 1$ by $1$ .

$- 1 + 13 (\frac{7}{36}) + y (\frac{25}{36}) = 0$

Step 2.1.4

Multiply $13 (\frac{7}{36})$ .

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Step 2.1.4.1

Combine $13$ and $\frac{7}{36}$ .

$- 1 + \frac{13 \cdot 7}{36} + y (\frac{25}{36}) = 0$

Step 2.1.4.2

Multiply $13$ by $7$ .

$- 1 + \frac{91}{36} + y (\frac{25}{36}) = 0$

Step 2.1.5

Combine $y$ and $\frac{25}{36}$ .

$- 1 + \frac{91}{36} + \frac{y \cdot 25}{36} = 0$

Step 2.1.6

Move $25$ to the left of $y$ .

$- 1 + \frac{91}{36} + \frac{25 y}{36} = 0$

Step 2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{36}{36}$ .

$- 1 \cdot \frac{36}{36} + \frac{91}{36} + \frac{25 y}{36} = 0$

Step 2.3

Combine $- 1$ and $\frac{36}{36}$ .

$\frac{- 1 \cdot 36}{36} + \frac{91}{36} + \frac{25 y}{36} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 1 \cdot 36 + 91}{36} + \frac{25 y}{36} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 1$ by $36$ .

$\frac{- 36 + 91}{36} + \frac{25 y}{36} = 0$

Step 2.5.2

Add $- 36$ and $91$ .

$\frac{55}{36} + \frac{25 y}{36} = 0$

Step 3

Subtract $\frac{55}{36}$ from both sides of the equation.

$\frac{25 y}{36} = - \frac{55}{36}$

Step 4

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

$25 y = - 55$

Step 5

Divide each term in $25 y = - 55$ by $25$ and simplify.

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Step 5.1

Divide each term in $25 y = - 55$ by $25$ .

$\frac{25 y}{25} = \frac{- 55}{25}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $25$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{25 y}{25} = \frac{- 55}{25}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 55}{25}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 55$ and $25$ .

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Step 5.3.1.1

Factor $5$ out of $- 55$ .

$y = \frac{5 (- 11)}{25}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $5$ out of $25$ .

$y = \frac{5 \cdot - 11}{5 \cdot 5}$

Step 5.3.1.2.2

Cancel the common factor.

$y = \frac{5 \cdot - 11}{5 \cdot 5}$

Step 5.3.1.2.3

Rewrite the expression.

$y = \frac{- 11}{5}$

Step 5.3.2

Move the negative in front of the fraction.

$y = - \frac{11}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{11}{5}$

Decimal Form:

$y = - 2.2$

Mixed Number Form:

$y = - 2 \frac{1}{5}$