How to Solve Absolute Values and Opposites of Rational Numbers?

A step-by-step guide to finding absolute values and opposites of rational numbers

The opposite of a rational number can be either positive or negative.
A rational number is considered a fraction of two integers.
If a rational number is positive, its opposite is negative.
If a rational number is negative, its opposite is positive.
The absolute values show a number’s distance from zero and it is always positive.

Here’s a step-by-step guide to finding absolute values and opposites of rational numbers:

1. Absolute value: The absolute value of a rational number is its distance from 0 on a number line. To find the absolute value of a rational number, simply remove the negative sign, if present. The absolute value of a number is always positive or 0.

For example, the absolute value of -5/3 is 5/3, and the absolute value of 4/2 is 4/2.

2. Opposite: The opposite of a rational number is the number that is the same distance from 0 but on the opposite side of the number line. To find the opposite of a rational number, simply change the sign.

For example, the opposite of -5/3 is 5/3, and the opposite of 4/2 is -4/2.

Absolute Values and Opposites of Rational Numbers – Example 1

Write the opposite of \(\frac{-2}{7}\).
Solution:
\(\frac{-2}{7}\) has \(\frac{-2}{7}\) distance from zero. It is on the left-hand side of the number line.
So, its opposite is \(\frac{2}{7}\). It has the same distance from zero but it is on the right-hand side of the number line.

Absolute Values and Opposites of Rational Numbers – Example 2

Write the opposite of \(-2 \frac{5}{19}\).
Solution:
\(-2 \frac{5}{19}\) has \(-2 \frac{5}{19}\) distance from zero. It is on the left-hand side of the number line.
So, its opposite is \(2 \frac{5}{19}\). It has the same distance from zero but it is on the right-hand side of the number line.

Exercises for Absolute Values and Opposites of Rational Numbers

Write the opposite of rational numbers.

1. \(\color{blue}{2\frac{3}{4}}\)
2. \(\color{blue}{-4\frac{1}{4}}\)
3. \(\color{blue}{\left|5.4\right|}\)

1. \(\color{blue}{-2\frac{3}{4}}\)
2. \(\color{blue}{4\frac{1}{4}}\)
3. \(\color{blue}{5.4}\)