Determine whether each statement is true or false. |-5| ∙ |6| = |-5∙6|

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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.

Calculate the left side of the equation: \(|-5| * |6|\). Since \(|-5| = 5\) and \(|6| = 6\), multiply these two values to get \(5 * 6\).

Calculate the right side of the equation: \(|-5 * 6|\). First, multiply \(-5\) and \(6\) to get \(-30\), then find the absolute value \(|-30|\).

Compare the results from the left side and the right side to see if they are equal.

Conclude whether the statement \(|-5| * |6| = |-5*6|\) is true or false based on the comparison.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |-5| equals 5, and |6| equals 6, regardless of the original sign of the number.

Properties of Absolute Value

One key property is that the absolute value of a product equals the product of the absolute values: |a * b| = |a| * |b|. This means multiplying inside the absolute value or multiplying the absolute values separately yields the same result.

Evaluating Expressions with Absolute Values

To evaluate expressions like |-5| * |6| and |-5*6|, compute each absolute value first, then perform multiplication. This step-by-step approach helps verify if the equality holds true by comparing both sides.