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

Verified step by step guidance

1. Step 1: Understand the properties of absolute values. The absolute value of a number is always non-negative.
2. Step 2: Calculate the absolute value of each number separately. |-14| = 14 and |2| = 2.
3. Step 3: Divide the absolute values calculated in Step 2. 14 / 2.
4. Step 4: Calculate the absolute value of the division inside the absolute value on the right side of the equation. |-14/2| = |-7|.
5. Step 5: Compare the results from Step 3 and Step 4 to determine if the statement is true or 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|. For example, |-14| equals 14, as it represents the distance of -14 from 0.

Properties of Absolute Values

One important property of absolute values is that |a/b| = |a| / |b| for any non-zero b. This means that the absolute value of a quotient is equal to the quotient of the absolute values. This property is essential for simplifying expressions involving absolute values.

Equivalence of Expressions

To determine if two expressions are equivalent, we can simplify both sides and compare their values. In this case, we need to evaluate |-14| / |2| and |-14/2| to see if they yield the same result. Understanding how to manipulate and simplify expressions is crucial for solving such problems.