1Cademy - Solving $$\frac{1}{2}(y - 5) = \frac{1}{4}(y

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Strategy for Solving Equations with Fraction or Decimal Coefficients

Example

Solving $\frac{1}{2}(y - 5) = \frac{1}{4}(y - 1)$ by Clearing Fractions

To solve the linear equation $\frac{1}{2}(y - 5) = \frac{1}{4}(y - 1)$ , one efficient approach is to clear the fractions before distributing. First, identify the least common denominator (LCD) of the fractions $\frac{1}{2}$ and $\frac{1}{4}$ , which is $4$ . Multiply both sides of the equation by $4$ : $4 \cdot \frac{1}{2}(y - 5) = 4 \cdot \frac{1}{4}(y - 1)$ . Simplifying the fractional parts yields $2(y - 5) = 1(y - 1)$ . Next, distribute the constants into the parentheses to get $2y - 10 = y - 1$ . Collect the variable terms on the left side by subtracting $y$ from both sides, resulting in $y - 10 = -1$ . Finally, collect the constant terms on the right side by adding $10$ to both sides, which gives the solution $y = 9$ . Alternatively, one could distribute the fractions first and then multiply every term by the LCD, but clearing fractions without distributing first is often simpler and less error-prone.

Updated 2026-05-02

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OpenStax Intermediate Algebra

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