1Cademy - Simplifying $$8\left(\frac{3}{8}x + \frac{1}{4}\right)$$ Using the Distributive Property

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Distributive Property

Example

Simplifying $8\left(\frac{3}{8}x + \frac{1}{4}\right)$ Using the Distributive Property

Use the distributive property to simplify $8\left(\frac{3}{8}x + \frac{1}{4}\right)$ , an expression where the outside factor is a whole number and the terms inside the parentheses involve fractions:

Step 1 — Distribute: Multiply $8$ by each term inside the parentheses:

$8 \cdot \frac{3}{8}x + 8 \cdot \frac{1}{4}$

Step 2 — Multiply: Compute each product. For the first term, $8 \cdot \frac{3}{8} = 3$ , so $8 \cdot \frac{3}{8}x = 3x$ . For the second term, $8 \cdot \frac{1}{4} = 2$ :

$3x + 2$

The simplified result is $3x + 2$ . This example shows that the distributive property works the same way when the parenthesized expression contains fractions. The whole-number factor effectively clears the fractions by canceling with their denominators — $8$ cancels with the $8$ in $\frac{3}{8}$ and reduces the $\frac{1}{4}$ — producing a simpler expression with integer coefficients.

Updated 2026-04-21

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