# How to Solve Absolute Values and Opposites of Rational Numbers?

In this article, you will learn how to solve absolute value problems and how to find 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:

- 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.

- 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**.

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

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

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