Basic Math Examples

$\frac{1}{2} y + 5 = \frac{1}{8} y$

Step 1

Combine $\frac{1}{2}$ and $y$ .

$\frac{y}{2} + 5 = \frac{1}{8} y$

Step 2

Combine $\frac{1}{8}$ and $y$ .

$\frac{y}{2} + 5 = \frac{y}{8}$

Step 3

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

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Step 3.1

Subtract $\frac{y}{8}$ from both sides of the equation.

$\frac{y}{2} + 5 - \frac{y}{8} = 0$

Step 3.2

To write $\frac{y}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{y}{2} \cdot \frac{4}{4} - \frac{y}{8} + 5 = 0$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{y}{2}$ by $\frac{4}{4}$ .

$\frac{y \cdot 4}{2 \cdot 4} - \frac{y}{8} + 5 = 0$

Step 3.3.2

Multiply $2$ by $4$ .

$\frac{y \cdot 4}{8} - \frac{y}{8} + 5 = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{y \cdot 4 - y}{8} + 5 = 0$

Step 3.5

Subtract $y$ from $y \cdot 4$ .

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Step 3.5.1

Reorder $y$ and $4$ .

$\frac{4 \cdot y - y}{8} + 5 = 0$

Step 3.5.2

Subtract $y$ from $4 \cdot y$ .

$\frac{3 \cdot y}{8} + 5 = 0$

$\frac{3 y}{8} + 5 = 0$

Step 4

Subtract $5$ from both sides of the equation.

$\frac{3 y}{8} = - 5$

Step 5

Multiply both sides of the equation by $\frac{8}{3}$ .

$\frac{8}{3} \cdot \frac{3 y}{8} = \frac{8}{3} \cdot - 5$

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 $\frac{8}{3} \cdot \frac{3 y}{8}$ .

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Step 6.1.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{8}{3} \cdot \frac{3 y}{8} = \frac{8}{3} \cdot - 5$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 y) = \frac{8}{3} \cdot - 5$

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) = \frac{8}{3} \cdot - 5$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 y) = \frac{8}{3} \cdot - 5$

Step 6.1.1.2.3

Rewrite the expression.

$y = \frac{8}{3} \cdot - 5$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{8}{3} \cdot - 5$ .

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Step 6.2.1.1

Multiply $\frac{8}{3} \cdot - 5$ .

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Step 6.2.1.1.1

Combine $\frac{8}{3}$ and $- 5$ .

$y = \frac{8 \cdot - 5}{3}$

Step 6.2.1.1.2

Multiply $8$ by $- 5$ .

$y = \frac{- 40}{3}$

Step 6.2.1.2

Move the negative in front of the fraction.

$y = - \frac{40}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{40}{3}$

Decimal Form:

$y = - 13.\overline{3}$

Mixed Number Form:

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