Basic Math Examples

$\frac{y}{5} - \frac{y}{10} + 2 = y + 2$

Step 1

Simplify $\frac{y}{5} - \frac{y}{10} + 2$ .

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Step 1.1

To write $\frac{y}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{5} \cdot \frac{2}{2} - \frac{y}{10} + 2 = y + 2$

Step 1.2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{y}{5}$ by $\frac{2}{2}$ .

$\frac{y \cdot 2}{5 \cdot 2} - \frac{y}{10} + 2 = y + 2$

Step 1.2.2

Multiply $5$ by $2$ .

$\frac{y \cdot 2}{10} - \frac{y}{10} + 2 = y + 2$

Step 1.3

Combine the numerators over the common denominator.

$\frac{y \cdot 2 - y}{10} + 2 = y + 2$

Step 1.4

Subtract $y$ from $y \cdot 2$ .

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Step 1.4.1

Reorder $y$ and $2$ .

$\frac{2 \cdot y - y}{10} + 2 = y + 2$

Step 1.4.2

Subtract $y$ from $2 \cdot y$ .

$\frac{y}{10} + 2 = y + 2$

Step 2

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

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Step 2.1

Subtract $y$ from both sides of the equation.

$\frac{y}{10} + 2 - y = 2$

Step 2.2

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

$\frac{y}{10} - y \cdot \frac{10}{10} + 2 = 2$

Step 2.3

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

$\frac{y}{10} + \frac{- y \cdot 10}{10} + 2 = 2$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y - y \cdot 10}{10} + 2 = 2$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

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

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Step 2.5.1.1.1

Raise $y$ to the power of $1$ .

$\frac{y^{1} - y \cdot 10}{10} + 2 = 2$

Step 2.5.1.1.2

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1 - y \cdot 10}{10} + 2 = 2$

Step 2.5.1.1.3

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

$\frac{y \cdot 1 + y (- 1 \cdot 10)}{10} + 2 = 2$

Step 2.5.1.1.4

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

$\frac{y (1 - 1 \cdot 10)}{10} + 2 = 2$

Step 2.5.1.2

Multiply $- 1$ by $10$ .

$\frac{y (1 - 10)}{10} + 2 = 2$

Step 2.5.1.3

Subtract $10$ from $1$ .

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

Step 2.5.2

Move $- 9$ to the left of $y$ .

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

Step 2.5.3

Move the negative in front of the fraction.

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

Step 3

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1

Subtract $2$ from both sides of the equation.

$- \frac{9 y}{10} = 2 - 2$

Step 3.2

Subtract $2$ from $2$ .

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

Step 4

Set the numerator equal to zero.

$9 y = 0$

Step 5

Divide each term in $9 y = 0$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 y = 0$ by $9$ .

$\frac{9 y}{9} = \frac{0}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{0}{9}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $9$ .

$y = 0$