Basic Math Examples

$0.25 y + \frac{1}{4 y} + 0.5$

Step 1

To write $0.25 y$ as a fraction with a common denominator, multiply by $\frac{4 y}{4 y}$ .

$0.25 y \cdot \frac{4 y}{4 y} + \frac{1}{4 y} + 0.5$

Step 2

Simplify terms.

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Step 2.1

Combine $0.25 y$ and $\frac{4 y}{4 y}$ .

$\frac{0.25 y (4 y)}{4 y} + \frac{1}{4 y} + 0.5$

Step 2.2

Combine the numerators over the common denominator.

$\frac{0.25 y (4 y) + 1}{4 y} + 0.5$

Step 3

Simplify the numerator.

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Step 3.1

Factor $0.25$ out of $0.25 y (4 y) + 1$ .

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Step 3.1.1

Move $y$ .

$\frac{0.25 \cdot 4 y \cdot y + 1}{4 y} + 0.5$

Step 3.1.2

Factor $0.25$ out of $0.25 \cdot 4 y \cdot y$ .

$\frac{0.25 (4 y \cdot y) + 1}{4 y} + 0.5$

Step 3.1.3

Factor $0.25$ out of $1$ .

$\frac{0.25 (4 y \cdot y) + 0.25 (4)}{4 y} + 0.5$

Step 3.1.4

Factor $0.25$ out of $0.25 (4 y \cdot y) + 0.25 (4)$ .

$\frac{0.25 (4 y \cdot y + 4)}{4 y} + 0.5$

Step 3.2

Factor $4$ out of $4 y \cdot y + 4$ .

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Step 3.2.1

Factor $4$ out of $4 y \cdot y$ .

$\frac{0.25 (4 (y \cdot y) + 4)}{4 y} + 0.5$

Step 3.2.2

Factor $4$ out of $4$ .

$\frac{0.25 (4 (y \cdot y) + 4 (1))}{4 y} + 0.5$

Step 3.2.3

Factor $4$ out of $4 (y \cdot y) + 4 (1)$ .

$\frac{0.25 (4 (y \cdot y + 1))}{4 y} + 0.5$

Step 3.3

Multiply $y$ by $y$ .

$\frac{0.25 \cdot 4 (y^{2} + 1)}{4 y} + 0.5$

Step 3.4

Combine exponents.

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Step 3.4.1

Multiply $0.25$ by $4$ .

$\frac{1 (y^{2} + 1)}{4 y} + 0.5$

Step 3.4.2

Multiply $y^{2} + 1$ by $1$ .

$\frac{y^{2} + 1}{4 y} + 0.5$

Step 4

To write $0.5$ as a fraction with a common denominator, multiply by $\frac{4 y}{4 y}$ .

$\frac{y^{2} + 1}{4 y} + 0.5 \cdot \frac{4 y}{4 y}$

Step 5

Simplify terms.

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Step 5.1

Combine $0.5$ and $\frac{4 y}{4 y}$ .

$\frac{y^{2} + 1}{4 y} + \frac{0.5 (4 y)}{4 y}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{y^{2} + 1 + 0.5 (4 y)}{4 y}$

Step 6

Factor using the perfect square rule.

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Step 6.1

Rearrange terms.

$\frac{y^{2} + 0.5 \cdot 4 y + 1}{4 y}$

Step 6.2

Rewrite $1$ as $1^{2}$ .

$\frac{y^{2} + 0.5 \cdot 4 y + 1^{2}}{4 y}$

Step 6.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$0.5 \cdot 4 y = 2 \cdot y \cdot 1$

Step 6.4

Rewrite the polynomial.

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

Step 6.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 1$ .

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