Determine whether each statement is true or false. |-14| / |2| = |-14/2|

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Recall the definition of absolute value: for any real number $x$, $|x|$ represents the distance of $x$ from zero on the number line, and it is always non-negative.

Evaluate the left side of the equation: calculate $|-14|$ and $|2|$ separately. Since absolute value makes numbers positive, $|-14| = 14$ and $|2| = 2$.

Divide the absolute values on the left side: compute $\frac{|-14|}{|2|} = \frac{14}{2}$.

Evaluate the right side of the equation: calculate the absolute value of the quotient $\left| \frac{-14}{2} \right|$. First, divide $-14$ by $2$ to get $-7$, then find $|-7|$.

Compare the results from the left and right sides to determine if the equation $\frac{|-14|}{|2|} = \left| \frac{-14}{2} \right|$ holds true.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value Definition

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |−14| equals 14 because distance is positive regardless of direction.

Properties of Absolute Value with Division

The absolute value of a quotient equals the quotient of the absolute values: |a/b| = |a| / |b|, provided b ≠ 0. This property allows simplification of expressions involving division inside absolute values.

Evaluating Expressions Step-by-Step

To determine the truth of an equation involving absolute values, evaluate each side separately using the definitions and properties, then compare results. This method ensures accurate verification of statements.

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