Evaluate each expression. -|4/7|

Verified step by step guidance

1. Understand that the expression involves the absolute value function, which always returns a non-negative value.
2. Recognize that the absolute value of a fraction, such as \( \left| \frac{4}{7} \right| \), is simply the fraction itself if it is positive, or its positive counterpart if it is negative.
3. Since \( \frac{4}{7} \) is already positive, \( \left| \frac{4}{7} \right| = \frac{4}{7} \).
4. The expression given is \(-\left| \frac{4}{7} \right|\), which means you need to take the negative of the absolute value.
5. Thus, the final step is to apply the negative sign to the absolute value result, resulting in \(-\frac{4}{7}\).

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, |4| = 4 and |-4| = 4, indicating that both 4 and -4 are 4 units away from zero.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They include integers, fractions, and finite or repeating decimals. The expression -4/7 is a rational number because it can be written as a fraction with -4 as the numerator and 7 as the denominator.

Evaluating Expressions

Evaluating an expression involves substituting values for variables and performing the necessary arithmetic operations to simplify it. In this case, evaluating -|4/7| requires first finding the absolute value of 4/7, which is 4/7, and then applying the negative sign, resulting in -4/7.