Pre-Algebra Examples

$\frac{1}{4} \cdot (5 y - 3) + \frac{1}{8} \cdot (6 y + 9)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{4} (5 y) + \frac{1}{4} \cdot - 3 + \frac{1}{8} \cdot (6 y + 9)$

Step 1.2

Multiply $\frac{1}{4} (5 y)$ .

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Step 1.2.1

Combine $5$ and $\frac{1}{4}$ .

$\frac{5}{4} y + \frac{1}{4} \cdot - 3 + \frac{1}{8} \cdot (6 y + 9)$

Step 1.2.2

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

$\frac{5 y}{4} + \frac{1}{4} \cdot - 3 + \frac{1}{8} \cdot (6 y + 9)$

Step 1.3

Combine $\frac{1}{4}$ and $- 3$ .

$\frac{5 y}{4} + \frac{- 3}{4} + \frac{1}{8} \cdot (6 y + 9)$

Step 1.4

Move the negative in front of the fraction.

$\frac{5 y}{4} - \frac{3}{4} + \frac{1}{8} \cdot (6 y + 9)$

Step 1.5

Apply the distributive property.

$\frac{5 y}{4} - \frac{3}{4} + \frac{1}{8} (6 y) + \frac{1}{8} \cdot 9$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $8$ .

$\frac{5 y}{4} - \frac{3}{4} + \frac{1}{2 (4)} (6 y) + \frac{1}{8} \cdot 9$

Step 1.6.2

Factor $2$ out of $6 y$ .

$\frac{5 y}{4} - \frac{3}{4} + \frac{1}{2 (4)} (2 (3 y)) + \frac{1}{8} \cdot 9$

Step 1.6.3

Cancel the common factor.

$\frac{5 y}{4} - \frac{3}{4} + \frac{1}{2 \cdot 4} (2 (3 y)) + \frac{1}{8} \cdot 9$

Step 1.6.4

Rewrite the expression.

$\frac{5 y}{4} - \frac{3}{4} + \frac{1}{4} (3 y) + \frac{1}{8} \cdot 9$

Step 1.7

Combine $3$ and $\frac{1}{4}$ .

$\frac{5 y}{4} - \frac{3}{4} + \frac{3}{4} y + \frac{1}{8} \cdot 9$

Step 1.8

Combine $\frac{3}{4}$ and $y$ .

$\frac{5 y}{4} - \frac{3}{4} + \frac{3 y}{4} + \frac{1}{8} \cdot 9$

Step 1.9

Combine $\frac{1}{8}$ and $9$ .

$\frac{5 y}{4} - \frac{3}{4} + \frac{3 y}{4} + \frac{9}{8}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 y - 3 + 3 y}{4} + \frac{9}{8}$

Step 2.2

Add $5 y$ and $3 y$ .

$\frac{8 y - 3}{4} + \frac{9}{8}$

Step 3

To write $\frac{8 y - 3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{8 y - 3}{4} \cdot \frac{2}{2} + \frac{9}{8}$

Step 4

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

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Step 4.1

Multiply $\frac{8 y - 3}{4}$ by $\frac{2}{2}$ .

$\frac{(8 y - 3) \cdot 2}{4 \cdot 2} + \frac{9}{8}$

Step 4.2

Multiply $4$ by $2$ .

$\frac{(8 y - 3) \cdot 2}{8} + \frac{9}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{(8 y - 3) \cdot 2 + 9}{8}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{8 y \cdot 2 - 3 \cdot 2 + 9}{8}$

Step 6.2

Multiply $2$ by $8$ .

$\frac{16 y - 3 \cdot 2 + 9}{8}$

Step 6.3

Multiply $- 3$ by $2$ .

$\frac{16 y - 6 + 9}{8}$

Step 6.4

Add $- 6$ and $9$ .

$\frac{16 y + 3}{8}$