Pre-Algebra Examples

$\frac{1}{3} y + 9 = \frac{1}{10} y$

Step 1

Combine $\frac{1}{3}$ and $y$ .

$\frac{y}{3} + 9 = \frac{1}{10} y$

Step 2

Combine $\frac{1}{10}$ and $y$ .

$\frac{y}{3} + 9 = \frac{y}{10}$

Step 3

Move all terms containing $y$ to the left side of the equation.

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Step 3.1

Subtract $\frac{y}{10}$ from both sides of the equation.

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

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

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

Step 3.4.2

Multiply $3$ by $10$ .

$\frac{y \cdot 10}{30} - \frac{y}{10} \cdot \frac{3}{3} + 9 = 0$

Step 3.4.3

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

$\frac{y \cdot 10}{30} - \frac{y \cdot 3}{10 \cdot 3} + 9 = 0$

Step 3.4.4

Multiply $10$ by $3$ .

$\frac{y \cdot 10}{30} - \frac{y \cdot 3}{30} + 9 = 0$

Step 3.5

Combine the numerators over the common denominator.

$\frac{y \cdot 10 - y \cdot 3}{30} + 9 = 0$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $y$ out of $y \cdot 10 - y \cdot 3$ .

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Step 3.6.1.1.1

Factor $y$ out of $y \cdot 10$ .

$\frac{y (10) - y \cdot 3}{30} + 9 = 0$

Step 3.6.1.1.2

Factor $y$ out of $- y \cdot 3$ .

$\frac{y (10) + y (- 1 \cdot 3)}{30} + 9 = 0$

Step 3.6.1.1.3

Factor $y$ out of $y (10) + y (- 1 \cdot 3)$ .

$\frac{y (10 - 1 \cdot 3)}{30} + 9 = 0$

Step 3.6.1.2

Multiply $- 1$ by $3$ .

$\frac{y (10 - 3)}{30} + 9 = 0$

Step 3.6.1.3

Subtract $3$ from $10$ .

$\frac{y \cdot 7}{30} + 9 = 0$

Step 3.6.2

Move $7$ to the left of $y$ .

$\frac{7 y}{30} + 9 = 0$

Step 4

Subtract $9$ from both sides of the equation.

$\frac{7 y}{30} = - 9$

Step 5

Multiply both sides of the equation by $\frac{30}{7}$ .

$\frac{30}{7} \cdot \frac{7 y}{30} = \frac{30}{7} \cdot - 9$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{30}{7} \cdot \frac{7 y}{30}$ .

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Step 6.1.1.1

Cancel the common factor of $30$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{30}{7} \cdot \frac{7 y}{30} = \frac{30}{7} \cdot - 9$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 y) = \frac{30}{7} \cdot - 9$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

Factor $7$ out of $7 y$ .

$\frac{1}{7} (7 (y)) = \frac{30}{7} \cdot - 9$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 y) = \frac{30}{7} \cdot - 9$

Step 6.1.1.2.3

Rewrite the expression.

$y = \frac{30}{7} \cdot - 9$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{30}{7} \cdot - 9$ .

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Step 6.2.1.1

Multiply $\frac{30}{7} \cdot - 9$ .

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Step 6.2.1.1.1

Combine $\frac{30}{7}$ and $- 9$ .

$y = \frac{30 \cdot - 9}{7}$

Step 6.2.1.1.2

Multiply $30$ by $- 9$ .

$y = \frac{- 270}{7}$

Step 6.2.1.2

Move the negative in front of the fraction.

$y = - \frac{270}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{270}{7}$

Decimal Form:

$y = - 38.57142857 \dots$

Mixed Number Form:

$y = - 38 \frac{4}{7}$