1Cademy - Example of Simplifying $$\frac{4(-3)+6(-2)}{-3(2)-2}$$

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Simplifying an Expression with a Fraction Bar

Example

Example of Simplifying $\frac{4(-3)+6(-2)}{-3(2)-2}$

To simplify the algebraic fraction $\frac{4(-3)+6(-2)}{-3(2)-2}$ , recognize that the fraction bar acts as a grouping symbol, which means the numerator and denominator must be simplified separately before dividing.

First, multiply within the numerator: $4(-3) = -12$ and $6(-2) = -12$ , changing the numerator to $-12 + (-12)$ . Adding these gives $-24$ . Second, multiply within the denominator: $-3(2) = -6$ , changing the denominator to $-6 - 2$ . Subtracting gives $-8$ . The fraction is now $\frac{-24}{-8}$ . Finally, divide the simplified numerator by the simplified denominator: $-24 \div (-8) = 3$ . The final result is $3$ .

Updated 2026-06-03

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OpenStax Intermediate Algebra

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A logistics coordinator is using the algebraic expression $\frac{4(-3)+6(-2)}{-3(2)-2}$ to calculate a shipping adjustment. Match each component of the simplification process with its correct numerical value or mathematical function as described in the standard order of operations.
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Role of the Fraction Bar in Simplification
A financial auditor reviewing a variance report that uses the expression $\frac{4(-3)+6(-2)}{-3(2)-2}$ must simplify the numerator and denominator separately before performing the final division.
A financial analyst is training a new hire on how to calculate corporate variance formulas, such as $\frac{4(-3)+6(-2)}{-3(2)-2}$ . The analyst emphasizes that the calculation must be structured carefully because the fraction bar acts as a ____ symbol, meaning the numerator and denominator must be simplified completely before performing the final division.
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