How to Find 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.

Pre-Algebra for Beginners 2027 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

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.

Quick reference: opposites and absolute values

Two facts to remember: the opposite of the opposite is the number itself, -(-5) = 5; and 0 is the only number that is its own opposite. Rational numbers include integers, fractions, terminating decimals and repeating decimals, so these rules apply to all of them.

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. \(\color{blue}{5.4}\)