# How to Solve the Absolute Value of Rational Numbers?

When working with rational numbers, the absolute value can be found by simply removing the negative sign, if present. In this article, you will learn how to find the absolute value of rational numbers.

**A step-by-step guide to** **finding the** **absolute value of rational numbers**

A rational number can be written as a fraction of two integers.

Integers would be either negative or positive.

The absolute value of rational numbers shows their distance from zero.

Since the distance can not be negative, absolute values are always positive.

A step-by-step guide to finding the absolute value of rational numbers:

- Identify the rational number for which you need to find the absolute value. Let’s use the example of \(-\frac{5}{3}\).
- Write the absolute value formula for a rational number: \(|\frac{a}{b}| = \frac{|a|}{|b|}\)
- Replace “\(a\)” with the numerator of the rational number and “\(b\)” with the denominator. In this case, \(a = -5\) and \(b = 3\). So the formula becomes: \(|-\frac{5}{3}| = \frac{|-5|}{|3|}\)
- Find the absolute value of the numerator and denominator separately. The absolute value of \(-5\) is \(5\), and the absolute value of \(3\) is \(3\). So the formula becomes: \(|-\frac{5}{3}| = \frac{5}{3}\)
- Simplify the fraction if necessary. In this case, \(\frac{5}{3}\) is already in its simplest form.
- The final answer is the absolute value of \(-\frac{5}{3}\) is \(\frac{5}{3}\).

It’s important to remember that the absolute value of a number is always positive or zero, so the absolute value of a rational number will always be a positive rational number or zero.

**Absolute Value of Rational Numbers – Example 1**

Find the absolute value of \(\frac{-6}{9}\).*Solution*:

The absolute values mean the distance from zero.

Distance is always positive.

So, the absolute value of \(|\frac{-6}{9}|\) is \(\frac{6}{9}\).

**Absolute Value of Rational Numbers – Example 2**

Find the absolute value of \(5.47\).*Solution*:

The absolute values mean the distance from zero.

Distance is always positive.

So, the absolute value of \(|5.47|\) is \(5.47\).

**Exercises for** **Absolute Value of Rational Numbers**

**Find the absolute value of each rational number.**

- \(\color{blue}{-|−\frac{17}{3}|}\)
- \(\color{blue}{|−3.67|}\)
- \(\color{blue}{|\frac{-25}{3}|}\)

- \(\color{blue}{-\frac{17}{3}}\)
- \(\color{blue}{3.67}\)
- \(\color{blue}{\frac{25}{3}}\)

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