Finite Math Examples

$0 = \frac{- 7}{9} + \frac{9}{6} + \frac{13}{18} y$

Step 1

Rewrite the equation as $\frac{- 7}{9} + \frac{9}{6} + \frac{13}{18} y = 0$ .

$\frac{- 7}{9} + \frac{9}{6} + \frac{13}{18} y = 0$

Step 2

Simplify $\frac{- 7}{9} + \frac{9}{6} + \frac{13}{18} y$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Move the negative in front of the fraction.

$- \frac{7}{9} + \frac{9}{6} + \frac{13}{18} y = 0$

Step 2.1.2

Cancel the common factor of $9$ and $6$ .

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Step 2.1.2.1

Factor $3$ out of $9$ .

$- \frac{7}{9} + \frac{3 (3)}{6} + \frac{13}{18} y = 0$

Step 2.1.2.2

Cancel the common factors.

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Step 2.1.2.2.1

Factor $3$ out of $6$ .

$- \frac{7}{9} + \frac{3 \cdot 3}{3 \cdot 2} + \frac{13}{18} y = 0$

Step 2.1.2.2.2

Cancel the common factor.

$- \frac{7}{9} + \frac{3 \cdot 3}{3 \cdot 2} + \frac{13}{18} y = 0$

Step 2.1.2.2.3

Rewrite the expression.

$- \frac{7}{9} + \frac{3}{2} + \frac{13}{18} y = 0$

Step 2.1.3

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

$- \frac{7}{9} + \frac{3}{2} + \frac{13 y}{18} = 0$

Step 2.2

To write $- \frac{7}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{7}{9} \cdot \frac{2}{2} + \frac{3}{2} + \frac{13 y}{18} = 0$

Step 2.3

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{7}{9} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{9}{9} + \frac{13 y}{18} = 0$

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 $\frac{7}{9}$ by $\frac{2}{2}$ .

$- \frac{7 \cdot 2}{9 \cdot 2} + \frac{3}{2} \cdot \frac{9}{9} + \frac{13 y}{18} = 0$

Step 2.4.2

Multiply $9$ by $2$ .

$- \frac{7 \cdot 2}{18} + \frac{3}{2} \cdot \frac{9}{9} + \frac{13 y}{18} = 0$

Step 2.4.3

Multiply $\frac{3}{2}$ by $\frac{9}{9}$ .

$- \frac{7 \cdot 2}{18} + \frac{3 \cdot 9}{2 \cdot 9} + \frac{13 y}{18} = 0$

Step 2.4.4

Multiply $2$ by $9$ .

$- \frac{7 \cdot 2}{18} + \frac{3 \cdot 9}{18} + \frac{13 y}{18} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 2 + 3 \cdot 9}{18} + \frac{13 y}{18} = 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 7$ by $2$ .

$\frac{- 14 + 3 \cdot 9}{18} + \frac{13 y}{18} = 0$

Step 2.6.2

Multiply $3$ by $9$ .

$\frac{- 14 + 27}{18} + \frac{13 y}{18} = 0$

Step 2.6.3

Add $- 14$ and $27$ .

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

Step 3

Subtract $\frac{13}{18}$ from both sides of the equation.

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

Step 4

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

$13 y = - 13$

Step 5

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

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Step 5.1

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

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

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.

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

Step 5.2.1.2

Divide $y$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 13$ by $13$ .

$y = - 1$