Lesson 2: Adding and Subtracting Rational Numbers

Property

To add or subtract rational numbers in different forms (like fractions and decimals), first convert them to the same form. You can either convert the fraction to a decimal or the decimal to a fraction.

Examples

Property

The distance between two rational numbers $a$ and $b$ on a number line is the absolute value of their difference.

Examples

• The distance between $-2.5$ and $5.1$ is:

$|5.1 - (-2.5)| = |-2.5 - 5.1| = 7.6$

• The distance between $-\frac{1}{4}$ and $-\frac{7}{8}$ is:

$|-\frac{1}{4} - (-\frac{7}{8})| = |-\frac{7}{8} - (-\frac{1}{4})| = \frac{5}{8}$

Explanation

To find the distance between any two rational numbers, you subtract one number from the other and then find the absolute value of the result. Since distance cannot be negative, taking the absolute value ensures the answer is always positive. The order of subtraction does not matter because the absolute value of a number and its opposite are the same. This calculation represents the length of the segment connecting the two points on the number line.