Question
Find the negatives (the additive inverses) of the given rational numbers. Show each number and its negative on the number line. \( \begin{array}{llll}\text { (a) } \frac{2}{5} & \text { (b) } \frac{-3}{2} & \text { (c) } \frac{8}{-3} & \text { (d) } \frac{8}{2}\end{array} \) (a) The additive inverse of \( \frac{2}{5} \) is
Ask by Pena Weaver. in the United States
Feb 27,2025
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Answer
The additive inverse of \( \frac{2}{5} \) is \( -\frac{2}{5} \).
On the number line:
————(–2/5)————0————(2/5)————
Solution
For any number, its additive inverse (or negative) is the number that, when added to the original, gives 0. For example, if you have a number a, then its additive inverse is –a because a + (–a) = 0.
(a) The additive inverse of 2/5 is –2/5.
To illustrate on the number line:
————(–2/5)————0————(2/5)————
Here, starting at 0, moving 2/5 units to the right gets you to 2/5, and moving 2/5 units to the left gets you to –2/5.
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(a) The additive inverse of \( \frac{2}{5} \) is \( -\frac{2}{5} \). On the number line, \( \frac{2}{5} \) is located to the right of zero, while \( -\frac{2}{5} \) is positioned to the left, demonstrating how they balance each other out at the origin. (b) The additive inverse of \( \frac{-3}{2} \) is \( \frac{3}{2} \). On the number line, you’ll find \( \frac{-3}{2} \) on the left side, while \( \frac{3}{2} \) sits on the right side, perfectly representing the idea that one number negates the other, bringing them back to zero when combined!
