Give (a) the additive inverse and (b) the absolute value of each number. -6⁄5

Verified step by step guidance

1. Step 1: Identify the given number, which is $-\frac{6}{5}$.
2. Step 2: To find the additive inverse, change the sign of the number. The additive inverse of $-\frac{6}{5}$ is $\frac{6}{5}$.
3. Step 3: To find the absolute value, consider the distance of the number from zero on the number line, which is always positive.
4. Step 4: The absolute value of $-\frac{6}{5}$ is $\frac{6}{5}$.
5. Step 5: Summarize: The additive inverse is $\frac{6}{5}$ and the absolute value is $\frac{6}{5}$.

Key Concepts

Additive Inverse

The additive inverse of a number is the value that, when added to the original number, results in zero. For any real number 'x', the additive inverse is '-x'. In the case of -6/5, its additive inverse is 6/5, since -6/5 + 6/5 = 0.

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, e.g., |x|. For negative numbers, the absolute value is the positive counterpart; thus, the absolute value of -6/5 is 6/5, as it represents the same distance from zero.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. The number -6/5 is a rational number because it can be written as -6 divided by 5. Understanding rational numbers is essential for working with operations like finding additive inverses and absolute values.