Evaluate each expression. -|4/7|

Verified step by step guidance

1. Identify the expression to evaluate: \(-\left| \frac{4}{7} \right|\).
2. Recall that the absolute value \(|x|\) of a number \(x\) is the distance of \(x\) from zero on the number line, which is always non-negative. So, \(\left| \frac{4}{7} \right| = \frac{4}{7}\) because \(\frac{4}{7}\) is already positive.
3. Substitute the absolute value back into the expression: \(-\left| \frac{4}{7} \right| = -\frac{4}{7}\).
4. Understand that the negative sign outside the absolute value means you take the opposite (negative) of the absolute value result.
5. Therefore, the expression simplifies to \(-\frac{4}{7}\), which is the final simplified form.

Key Concepts

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, |4/7| equals 4/7 because it is already positive, while |-4/7| also equals 4/7.

Negative Sign Outside Absolute Value

When a negative sign is placed outside the absolute value, it negates the result of the absolute value operation. For instance, -|4/7| means first find |4/7| = 4/7, then apply the negative sign to get -4/7.

Evaluating Rational Expressions

A rational expression is a fraction where the numerator and denominator are integers or algebraic expressions. Evaluating such expressions involves simplifying the fraction and applying operations like absolute value or negation correctly.