Basic Math Examples

$\frac{5}{4} y + \frac{1}{8} y = \frac{9}{8} + y$

Step 1

Simplify $\frac{5}{4} y + \frac{1}{8} y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{5}{4}$ and $y$ .

$\frac{5 y}{4} + \frac{1}{8} y = \frac{9}{8} + y$

Step 1.1.2

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

$\frac{5 y}{4} + \frac{y}{8} = \frac{9}{8} + y$

Step 1.2

To write $\frac{5 y}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 y}{4} \cdot \frac{2}{2} + \frac{y}{8} = \frac{9}{8} + y$

Step 1.3

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

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Step 1.3.1

Multiply $\frac{5 y}{4}$ by $\frac{2}{2}$ .

$\frac{5 y \cdot 2}{4 \cdot 2} + \frac{y}{8} = \frac{9}{8} + y$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{5 y \cdot 2}{8} + \frac{y}{8} = \frac{9}{8} + y$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5 y \cdot 2 + y}{8} = \frac{9}{8} + y$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $y$ out of $5 y \cdot 2 + y$ .

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Step 1.5.1.1

Factor $y$ out of $5 y \cdot 2$ .

$\frac{y (5 \cdot 2) + y}{8} = \frac{9}{8} + y$

Step 1.5.1.2

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

$\frac{y (5 \cdot 2) + y^{1}}{8} = \frac{9}{8} + y$

Step 1.5.1.3

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

$\frac{y (5 \cdot 2) + y \cdot 1}{8} = \frac{9}{8} + y$

Step 1.5.1.4

Factor $y$ out of $y (5 \cdot 2) + y \cdot 1$ .

$\frac{y (5 \cdot 2 + 1)}{8} = \frac{9}{8} + y$

Step 1.5.2

Multiply $5$ by $2$ .

$\frac{y (10 + 1)}{8} = \frac{9}{8} + y$

Step 1.5.3

Add $10$ and $1$ .

$\frac{y \cdot 11}{8} = \frac{9}{8} + y$

Step 1.6

Move $11$ to the left of $y$ .

$\frac{11 y}{8} = \frac{9}{8} + y$

Step 2

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

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Step 2.1

Subtract $y$ from both sides of the equation.

$\frac{11 y}{8} - y = \frac{9}{8}$

Step 2.2

To write $- y$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{11 y}{8} - y \cdot \frac{8}{8} = \frac{9}{8}$

Step 2.3

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

$\frac{11 y}{8} + \frac{- y \cdot 8}{8} = \frac{9}{8}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{11 y - y \cdot 8}{8} = \frac{9}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $y$ out of $11 y - y \cdot 8$ .

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Step 2.5.1.1

Factor $y$ out of $11 y$ .

$\frac{y \cdot 11 - y \cdot 8}{8} = \frac{9}{8}$

Step 2.5.1.2

Factor $y$ out of $- y \cdot 8$ .

$\frac{y \cdot 11 + y (- 1 \cdot 8)}{8} = \frac{9}{8}$

Step 2.5.1.3

Factor $y$ out of $y \cdot 11 + y (- 1 \cdot 8)$ .

$\frac{y (11 - 1 \cdot 8)}{8} = \frac{9}{8}$

Step 2.5.2

Multiply $- 1$ by $8$ .

$\frac{y (11 - 8)}{8} = \frac{9}{8}$

Step 2.5.3

Subtract $8$ from $11$ .

$\frac{y \cdot 3}{8} = \frac{9}{8}$

Step 2.6

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

$\frac{3 y}{8} = \frac{9}{8}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 y = 9$

Step 4

Divide each term in $3 y = 9$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 y = 9$ by $3$ .

$\frac{3 y}{3} = \frac{9}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{9}{3}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{9}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $9$ by $3$ .

$y = 3$