Determine whether each statement is true or false. |11| * |-6| = |-66|

Verified step by step guidance

1. Understand the concept of absolute value: The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, the absolute value of a number is always non-negative.
2. Calculate the absolute value of each number: \(|11| = 11\) and \(|-6| = 6\).
3. Multiply the absolute values: \(11 \times 6\).
4. Calculate the absolute value of the product: The absolute value of \(-66\) is \(|-66| = 66\).
5. Compare the results: Check if the product of the absolute values \(11 \times 6\) is equal to \(|-66|\).

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |11| equals 11 and |-6| equals 6, as both represent their distances from zero.

Multiplication of Absolute Values

When multiplying two numbers, the absolute value of the product is equal to the product of their absolute values. This means |a * b| = |a| * |b|. In the given statement, |11| * |-6| translates to 11 * 6, which equals 66.

Properties of Equality

In mathematics, properties of equality allow us to manipulate equations and inequalities. If two expressions are equal, any operation performed on one side must also be performed on the other. In this case, we need to verify if 66 equals |-66|, which is true since the absolute value of -66 is also 66.