Basic Math Examples

$- \frac{1}{5} = - \frac{1}{4} - \frac{1}{8} y$

Step 1

Rewrite the equation as $- \frac{1}{4} - \frac{1}{8} y = - \frac{1}{5}$ .

$- \frac{1}{4} - \frac{1}{8} y = - \frac{1}{5}$

Step 2

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

$- \frac{1}{4} - \frac{y}{8} = - \frac{1}{5}$

Step 3

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

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Step 3.1

Add $\frac{1}{4}$ to both sides of the equation.

$- \frac{y}{8} = - \frac{1}{5} + \frac{1}{4}$

Step 3.2

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{y}{8} = - \frac{1}{5} \cdot \frac{4}{4} + \frac{1}{4}$

Step 3.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{y}{8} = - \frac{1}{5} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{5}{5}$

Step 3.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$- \frac{y}{8} = - \frac{4}{5 \cdot 4} + \frac{1}{4} \cdot \frac{5}{5}$

Step 3.4.2

Multiply $5$ by $4$ .

$- \frac{y}{8} = - \frac{4}{20} + \frac{1}{4} \cdot \frac{5}{5}$

Step 3.4.3

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$- \frac{y}{8} = - \frac{4}{20} + \frac{5}{4 \cdot 5}$

Step 3.4.4

Multiply $4$ by $5$ .

$- \frac{y}{8} = - \frac{4}{20} + \frac{5}{20}$

Step 3.5

Combine the numerators over the common denominator.

$- \frac{y}{8} = \frac{- 4 + 5}{20}$

Step 3.6

Add $- 4$ and $5$ .

$- \frac{y}{8} = \frac{1}{20}$

Step 4

Multiply both sides of the equation by $- 8$ .

$- 8 (- \frac{y}{8}) = - 8 (\frac{1}{20})$

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 $- 8 (- \frac{y}{8})$ .

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Step 5.1.1.1

Cancel the common factor of $8$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{y}{8}$ into the numerator.

$- 8 \frac{- y}{8} = - 8 (\frac{1}{20})$

Step 5.1.1.1.2

Factor $8$ out of $- 8$ .

$8 (- 1) \frac{- y}{8} = - 8 (\frac{1}{20})$

Step 5.1.1.1.3

Cancel the common factor.

$8 \cdot - 1 \frac{- y}{8} = - 8 (\frac{1}{20})$

Step 5.1.1.1.4

Rewrite the expression.

$- - y = - 8 (\frac{1}{20})$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 8 (\frac{1}{20})$

Step 5.1.1.2.2

Multiply $y$ by $1$ .

$y = - 8 (\frac{1}{20})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 8 (\frac{1}{20})$ .

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Step 5.2.1.1

Cancel the common factor of $4$ .

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Step 5.2.1.1.1

Factor $4$ out of $- 8$ .

$y = 4 (- 2) \frac{1}{20}$

Step 5.2.1.1.2

Factor $4$ out of $20$ .

$y = 4 \cdot - 2 \frac{1}{4 \cdot 5}$

Step 5.2.1.1.3

Cancel the common factor.

$y = 4 \cdot - 2 \frac{1}{4 \cdot 5}$

Step 5.2.1.1.4

Rewrite the expression.

$y = - 2 (\frac{1}{5})$

Step 5.2.1.2

Combine $- 2$ and $\frac{1}{5}$ .

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

Step 5.2.1.3

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 0.4$