# 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 find 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.

1. 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 forAbsolute Values and Opposites of Rational Numbers

### Write the opposite ofrational 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. $$\color{blue}{5.4}$$

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