Finite Math Examples

$0 = (- 9 \cdot \frac{1}{18}) + (14 \cdot \frac{8}{36}) + (y \cdot \frac{9}{36})$

Step 1

Rewrite the equation as $- 9 \cdot \frac{1}{18} + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$ .

$- 9 \cdot \frac{1}{18} + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$

Step 2

Simplify $- 9 \cdot \frac{1}{18} + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36}$ .

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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 $- 9$ .

$9 (- 1) \cdot \frac{1}{18} + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$

Step 2.1.1.2

Factor $9$ out of $18$ .

$9 \cdot - 1 \cdot \frac{1}{9 \cdot 2} + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$

Step 2.1.1.3

Cancel the common factor.

$9 \cdot - 1 \cdot \frac{1}{9 \cdot 2} + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$

Step 2.1.1.4

Rewrite the expression.

$- 1 \cdot \frac{1}{2} + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$

Step 2.1.2

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

$- (\frac{1}{2}) + 14 \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Factor $2$ out of $14$ .

$- \frac{1}{2} + 2 (7) \cdot \frac{8}{36} + y \cdot \frac{9}{36} = 0$

Step 2.1.3.2

Factor $2$ out of $36$ .

$- \frac{1}{2} + 2 \cdot 7 \cdot \frac{8}{2 \cdot 18} + y \cdot \frac{9}{36} = 0$

Step 2.1.3.3

Cancel the common factor.

$- \frac{1}{2} + 2 \cdot 7 \cdot \frac{8}{2 \cdot 18} + y \cdot \frac{9}{36} = 0$

Step 2.1.3.4

Rewrite the expression.

$- \frac{1}{2} + 7 \cdot \frac{8}{18} + y \cdot \frac{9}{36} = 0$

Step 2.1.4

Combine $7$ and $\frac{8}{18}$ .

$- \frac{1}{2} + \frac{7 \cdot 8}{18} + y \cdot \frac{9}{36} = 0$

Step 2.1.5

Multiply $7$ by $8$ .

$- \frac{1}{2} + \frac{56}{18} + y \cdot \frac{9}{36} = 0$

Step 2.1.6

Cancel the common factor of $56$ and $18$ .

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Step 2.1.6.1

Factor $2$ out of $56$ .

$- \frac{1}{2} + \frac{2 (28)}{18} + y \cdot \frac{9}{36} = 0$

Step 2.1.6.2

Cancel the common factors.

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Step 2.1.6.2.1

Factor $2$ out of $18$ .

$- \frac{1}{2} + \frac{2 \cdot 28}{2 \cdot 9} + y \cdot \frac{9}{36} = 0$

Step 2.1.6.2.2

Cancel the common factor.

$- \frac{1}{2} + \frac{2 \cdot 28}{2 \cdot 9} + y \cdot \frac{9}{36} = 0$

Step 2.1.6.2.3

Rewrite the expression.

$- \frac{1}{2} + \frac{28}{9} + y \cdot \frac{9}{36} = 0$

Step 2.1.7

Cancel the common factor of $9$ and $36$ .

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Step 2.1.7.1

Factor $9$ out of $9$ .

$- \frac{1}{2} + \frac{28}{9} + y \cdot \frac{9 (1)}{36} = 0$

Step 2.1.7.2

Cancel the common factors.

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Step 2.1.7.2.1

Factor $9$ out of $36$ .

$- \frac{1}{2} + \frac{28}{9} + y \cdot \frac{9 \cdot 1}{9 \cdot 4} = 0$

Step 2.1.7.2.2

Cancel the common factor.

$- \frac{1}{2} + \frac{28}{9} + y \cdot \frac{9 \cdot 1}{9 \cdot 4} = 0$

Step 2.1.7.2.3

Rewrite the expression.

$- \frac{1}{2} + \frac{28}{9} + y \cdot \frac{1}{4} = 0$

Step 2.1.8

Combine $y$ and $\frac{1}{4}$ .

$- \frac{1}{2} + \frac{28}{9} + \frac{y}{4} = 0$

Step 2.2

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

$- \frac{1}{2} \cdot \frac{9}{9} + \frac{28}{9} + \frac{y}{4} = 0$

Step 2.3

To write $\frac{28}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{2} \cdot \frac{9}{9} + \frac{28}{9} \cdot \frac{2}{2} + \frac{y}{4} = 0$

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 $\frac{9}{9}$ .

$- \frac{9}{2 \cdot 9} + \frac{28}{9} \cdot \frac{2}{2} + \frac{y}{4} = 0$

Step 2.4.2

Multiply $2$ by $9$ .

$- \frac{9}{18} + \frac{28}{9} \cdot \frac{2}{2} + \frac{y}{4} = 0$

Step 2.4.3

Multiply $\frac{28}{9}$ by $\frac{2}{2}$ .

$- \frac{9}{18} + \frac{28 \cdot 2}{9 \cdot 2} + \frac{y}{4} = 0$

Step 2.4.4

Multiply $9$ by $2$ .

$- \frac{9}{18} + \frac{28 \cdot 2}{18} + \frac{y}{4} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 9 + 28 \cdot 2}{18} + \frac{y}{4} = 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $28$ by $2$ .

$\frac{- 9 + 56}{18} + \frac{y}{4} = 0$

Step 2.6.2

Add $- 9$ and $56$ .

$\frac{47}{18} + \frac{y}{4} = 0$

Step 3

Subtract $\frac{47}{18}$ from both sides of the equation.

$\frac{y}{4} = - \frac{47}{18}$

Step 4

Multiply both sides of the equation by $4$ .

$4 \frac{y}{4} = 4 (- \frac{47}{18})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$4 \frac{y}{4} = 4 (- \frac{47}{18})$

Step 5.1.1.2

Rewrite the expression.

$y = 4 (- \frac{47}{18})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $4 (- \frac{47}{18})$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{47}{18}$ into the numerator.

$y = 4 (\frac{- 47}{18})$

Step 5.2.1.1.2

Factor $2$ out of $4$ .

$y = 2 (2) \frac{- 47}{18}$

Step 5.2.1.1.3

Factor $2$ out of $18$ .

$y = 2 \cdot 2 \frac{- 47}{2 \cdot 9}$

Step 5.2.1.1.4

Cancel the common factor.

$y = 2 \cdot 2 \frac{- 47}{2 \cdot 9}$

Step 5.2.1.1.5

Rewrite the expression.

$y = 2 (\frac{- 47}{9})$

Step 5.2.1.2

Combine $2$ and $\frac{- 47}{9}$ .

$y = \frac{2 \cdot - 47}{9}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $2$ by $- 47$ .

$y = \frac{- 94}{9}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$y = - \frac{94}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{94}{9}$

Decimal Form:

$y = - 10.\overline{4}$

Mixed Number Form:

$y = - 10 \frac{4}{9}$