Basic Math Examples

$0 = - 8 (\frac{1}{18}) + 12 (\frac{5}{18}) + y (\frac{2}{3})$

Step 1

Rewrite the equation as $- 8 (\frac{1}{18}) + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$ .

$- 8 (\frac{1}{18}) + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$

Step 2

Simplify $- 8 (\frac{1}{18}) + 12 (\frac{5}{18}) + y (\frac{2}{3})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Factor $2$ out of $- 8$ .

$2 (- 4) \frac{1}{18} + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$

Step 2.1.1.2

Factor $2$ out of $18$ .

$2 \cdot - 4 \frac{1}{2 \cdot 9} + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$

Step 2.1.1.3

Cancel the common factor.

$2 \cdot - 4 \frac{1}{2 \cdot 9} + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$

Step 2.1.1.4

Rewrite the expression.

$- 4 (\frac{1}{9}) + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$

Step 2.1.2

Combine $- 4$ and $\frac{1}{9}$ .

$\frac{- 4}{9} + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$

Step 2.1.3

Move the negative in front of the fraction.

$- \frac{4}{9} + 12 (\frac{5}{18}) + y (\frac{2}{3}) = 0$

Step 2.1.4

Cancel the common factor of $6$ .

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Step 2.1.4.1

Factor $6$ out of $12$ .

$- \frac{4}{9} + 6 (2) \frac{5}{18} + y (\frac{2}{3}) = 0$

Step 2.1.4.2

Factor $6$ out of $18$ .

$- \frac{4}{9} + 6 \cdot 2 \frac{5}{6 \cdot 3} + y (\frac{2}{3}) = 0$

Step 2.1.4.3

Cancel the common factor.

$- \frac{4}{9} + 6 \cdot 2 \frac{5}{6 \cdot 3} + y (\frac{2}{3}) = 0$

Step 2.1.4.4

Rewrite the expression.

$- \frac{4}{9} + 2 (\frac{5}{3}) + y (\frac{2}{3}) = 0$

Step 2.1.5

Combine $2$ and $\frac{5}{3}$ .

$- \frac{4}{9} + \frac{2 \cdot 5}{3} + y (\frac{2}{3}) = 0$

Step 2.1.6

Multiply $2$ by $5$ .

$- \frac{4}{9} + \frac{10}{3} + y (\frac{2}{3}) = 0$

Step 2.1.7

Combine $y$ and $\frac{2}{3}$ .

$- \frac{4}{9} + \frac{10}{3} + \frac{y \cdot 2}{3} = 0$

Step 2.1.8

Move $2$ to the left of $y$ .

$- \frac{4}{9} + \frac{10}{3} + \frac{2 y}{3} = 0$

Step 2.2

To write $\frac{10}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4}{9} + \frac{10}{3} \cdot \frac{3}{3} + \frac{2 y}{3} = 0$

Step 2.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{10}{3}$ by $\frac{3}{3}$ .

$- \frac{4}{9} + \frac{10 \cdot 3}{3 \cdot 3} + \frac{2 y}{3} = 0$

Step 2.3.2

Multiply $3$ by $3$ .

$- \frac{4}{9} + \frac{10 \cdot 3}{9} + \frac{2 y}{3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 4 + 10 \cdot 3}{9} + \frac{2 y}{3} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $10$ by $3$ .

$\frac{- 4 + 30}{9} + \frac{2 y}{3} = 0$

Step 2.5.2

Add $- 4$ and $30$ .

$\frac{26}{9} + \frac{2 y}{3} = 0$

Step 3

Subtract $\frac{26}{9}$ from both sides of the equation.

$\frac{2 y}{3} = - \frac{26}{9}$

Step 4

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{26}{9})$

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

Simplify $\frac{3}{2} \cdot \frac{2 y}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{26}{9})$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{26}{9})$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{3}{2} (- \frac{26}{9})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{26}{9})$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} (- \frac{26}{9})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3}{2} (- \frac{26}{9})$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{26}{9}$ into the numerator.

$y = \frac{3}{2} \cdot \frac{- 26}{9}$

Step 5.2.1.1.2

Factor $3$ out of $9$ .

$y = \frac{3}{2} \cdot \frac{- 26}{3 (3)}$

Step 5.2.1.1.3

Cancel the common factor.

$y = \frac{3}{2} \cdot \frac{- 26}{3 \cdot 3}$

Step 5.2.1.1.4

Rewrite the expression.

$y = \frac{1}{2} \cdot \frac{- 26}{3}$

Step 5.2.1.2

Cancel the common factor of $2$ .

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Step 5.2.1.2.1

Factor $2$ out of $- 26$ .

$y = \frac{1}{2} \cdot \frac{2 (- 13)}{3}$

Step 5.2.1.2.2

Cancel the common factor.

$y = \frac{1}{2} \cdot \frac{2 \cdot - 13}{3}$

Step 5.2.1.2.3

Rewrite the expression.

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

Step 5.2.1.3

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 4.\overline{3}$

Mixed Number Form:

$y = - 4 \frac{1}{3}$