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

Verified step by step guidance

1. Step 1: Understand the absolute value concept. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, the absolute value of any number is always non-negative.
2. Step 2: Calculate the absolute value of each number separately. For example, \(|-5|\) is 5 and \(|6|\) is 6.
3. Step 3: Multiply the absolute values obtained in Step 2. So, calculate \(5 \times 6\).
4. Step 4: Calculate the absolute value of the product of the numbers. First, find the product \(-5 \times 6\), which is -30, and then find its absolute value, \(|-30|\).
5. Step 5: Compare the results from Step 3 and Step 4. If they are equal, the statement is true; otherwise, it is false.

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|, and is always non-negative. For example, |-5| equals 5, as it measures the distance of -5 from 0.

Properties of Absolute Values

One important property of absolute values is that the absolute value of a product is equal to the product of the absolute values. This means |a * b| = |a| * |b| for any real numbers a and b. This property is crucial for simplifying expressions involving absolute values.

Multiplication of Real Numbers

Multiplication of real numbers follows specific rules, including the commutative property (a * b = b * a) and the associative property ((a * b) * c = a * (b * c)). Understanding these properties helps in manipulating and simplifying expressions involving multiplication, especially when combined with absolute values.