Basic Math Examples

$y - \frac{1}{2 y} - \frac{1}{4 y} - \frac{1}{8 y}$

Step 1

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

$y \cdot \frac{2 y}{2 y} - \frac{1}{2 y} - \frac{1}{4 y} - \frac{1}{8 y}$

Step 2

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

$\frac{y (2 y)}{2 y} - \frac{1}{2 y} - \frac{1}{4 y} - \frac{1}{8 y}$

Step 3

Combine the numerators over the common denominator.

$\frac{y (2 y) - 1}{2 y} - \frac{1}{4 y} - \frac{1}{8 y}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{y (2 y) - 1}{2 y}$ by $\frac{4}{4}$ .

$\frac{y (2 y) - 1}{2 y} \cdot \frac{4}{4} - \frac{1}{4 y} - \frac{1}{8 y}$

Step 4.2

Multiply $\frac{y (2 y) - 1}{2 y}$ by $\frac{4}{4}$ .

$\frac{(y (2 y) - 1) \cdot 4}{2 y \cdot 4} - \frac{1}{4 y} - \frac{1}{8 y}$

Step 4.3

Multiply $\frac{1}{4 y}$ by $\frac{2}{2}$ .

$\frac{(y (2 y) - 1) \cdot 4}{2 y \cdot 4} - (\frac{1}{4 y} \cdot \frac{2}{2}) - \frac{1}{8 y}$

Step 4.4

Multiply $\frac{1}{4 y}$ by $\frac{2}{2}$ .

$\frac{(y (2 y) - 1) \cdot 4}{2 y \cdot 4} - \frac{2}{4 y \cdot 2} - \frac{1}{8 y}$

Step 4.5

Reorder the factors of $2 y \cdot 4$ .

$\frac{(y (2 y) - 1) \cdot 4}{2 \cdot 4 y} - \frac{2}{4 y \cdot 2} - \frac{1}{8 y}$

Step 4.6

Multiply $2$ by $4$ .

$\frac{(y (2 y) - 1) \cdot 4}{8 y} - \frac{2}{4 y \cdot 2} - \frac{1}{8 y}$

Step 4.7

Reorder the factors of $4 y \cdot 2$ .

$\frac{(y (2 y) - 1) \cdot 4}{8 y} - \frac{2}{2 \cdot 4 y} - \frac{1}{8 y}$

Step 4.8

Multiply $2$ by $4$ .

$\frac{(y (2 y) - 1) \cdot 4}{8 y} - \frac{2}{8 y} - \frac{1}{8 y}$

Step 5

Combine the numerators over the common denominator.

$\frac{(y (2 y) - 1) \cdot 4 - 2}{8 y} + \frac{- 1}{8 y}$

Step 6

Simplify each term.

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Step 6.1

Simplify each term.

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Step 6.1.1

Rewrite using the commutative property of multiplication.

$\frac{(2 y \cdot y - 1) \cdot 4 - 2}{8 y} + \frac{- 1}{8 y}$

Step 6.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 6.1.2.1

Move $y$ .

$\frac{(2 (y \cdot y) - 1) \cdot 4 - 2}{8 y} + \frac{- 1}{8 y}$

Step 6.1.2.2

Multiply $y$ by $y$ .

$\frac{(2 y^{2} - 1) \cdot 4 - 2}{8 y} + \frac{- 1}{8 y}$

Step 6.2

Apply the distributive property.

$\frac{2 y^{2} \cdot 4 - 1 \cdot 4 - 2}{8 y} + \frac{- 1}{8 y}$

Step 6.3

Multiply $4$ by $2$ .

$\frac{8 y^{2} - 1 \cdot 4 - 2}{8 y} + \frac{- 1}{8 y}$

Step 6.4

Multiply $- 1$ by $4$ .

$\frac{8 y^{2} - 4 - 2}{8 y} + \frac{- 1}{8 y}$

Step 7

Combine into one fraction.

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Step 7.1

Subtract $2$ from $- 4$ .

$\frac{8 y^{2} - 6}{8 y} + \frac{- 1}{8 y}$

Step 7.2

Combine the numerators over the common denominator.

$\frac{8 y^{2} - 6 - 1}{8 y}$

Step 7.3

Subtract $1$ from $- 6$ .

$\frac{8 y^{2} - 7}{8 y}$