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.

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

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