Algebra Examples

$\frac{5}{8} y - \frac{3}{8} y + 2 y$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{5}{8}$ and $y$ .

$\frac{5 y}{8} - \frac{3}{8} y + 2 y$

Step 1.2

Combine $y$ and $\frac{3}{8}$ .

$\frac{5 y}{8} - \frac{y \cdot 3}{8} + 2 y$

Step 1.3

Move $3$ to the left of $y$ .

$\frac{5 y}{8} - \frac{3 y}{8} + 2 y$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$2 y + \frac{5 y - 3 y}{8}$

Step 2.2

Subtract $3 y$ from $5 y$ .

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

Step 2.3

Cancel the common factor of $2$ and $8$ .

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Step 2.3.1

Factor $2$ out of $2 y$ .

$2 y + \frac{2 (y)}{8}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $8$ .

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

Step 2.3.2.2

Cancel the common factor.

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

Step 2.3.2.3

Rewrite the expression.

$2 y + \frac{y}{4}$

Step 3

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

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

Step 4

Simplify terms.

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Step 4.1

Combine $2 y$ and $\frac{4}{4}$ .

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

Step 4.2

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Factor $y$ out of $2 y \cdot 4 + y$ .

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Step 5.1.1

Factor $y$ out of $2 y \cdot 4$ .

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

Step 5.1.2

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

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

Step 5.1.3

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

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

Step 5.1.4

Factor $y$ out of $y (2 \cdot 4) + y \cdot 1$ .

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

Step 5.2

Multiply $2$ by $4$ .

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

Step 5.3

Add $8$ and $1$ .

$\frac{y \cdot 9}{4}$

Step 6

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

$\frac{9 y}{4}$