In Exercises 51–60, rewrite each expression without absolute value bars. -3/|-3|

Verified step by step guidance

1. Identify the expression inside the absolute value bars: $-3$.
2. Recall that the absolute value of a number is its distance from zero on the number line, which is always non-negative. Therefore, $|-3|=3$.
3. Substitute the absolute value into the original expression: $-\frac{3}{|-3|}=-\frac{3}{3}$.
4. Simplify the fraction by dividing the numerator by the denominator: $-\frac{3}{3}=-1$.
5. The expression without absolute value bars is $-1$.

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, |3| equals 3, and |-3| also equals 3. Understanding absolute value is crucial for simplifying expressions that involve negative numbers.

Properties of Absolute Value

The properties of absolute value include that |a| = a if a is non-negative, and |a| = -a if a is negative. This means that when rewriting expressions involving absolute values, one must consider the sign of the number inside the absolute value bars. This property is essential for correctly simplifying expressions like -3/|-3|.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form, often by performing arithmetic operations and applying mathematical properties. In the context of the given expression, it requires substituting the absolute value with its equivalent based on the sign of the number. This skill is fundamental in algebra for solving equations and inequalities.