What Is Absolute Value and How Does It Represent Distance?

TL;DR

Absolute value represents the distance between two numbers on a number line, specifically calculated as the absolute value of A minus B. This means that absolute value of the difference yields a positive distance, while adding absolute values does not indicate the true distance. Thus, the absolute value of A minus B directly gives the correct distance between A and B.

Transcript

• [Voiceover] What I hope to do in this video is get a little bit more practice thinking about absolute value of the difference of numbers as the distance between those two numbers. So in this first question, we are asked which of the following expressions are equivalent to the absolute value of A minus B. And just as a reminder, the absolute value... Read More

Key Insights

• #️⃣ The absolute value of the difference between two numbers represents the distance between them on a number line.
• 🪜 Adding the absolute values of two numbers does not give the distance between them.
• #️⃣ Subtracting a larger number from a smaller number results in a negative value.
• 🤘 The order of subtraction affects the sign of the result.
• 🍹 The absolute value of the sum of two numbers will always be larger than or equal to the absolute value of their difference.
• 🙃 The area of a rectangle can be found by multiplying the lengths of its sides.

Questions & Answers

Q: What does the absolute value of A minus B represent?

The absolute value of A minus B represents the distance between A and B on a number line.

Q: Are the expressions A minus B and B minus A equivalent?

No, they are not. A minus B represents the distance from A to B, while B minus A represents the distance from B to A.

Q: Can the absolute value of A plus the absolute value of B represent the distance between A and B?

No, adding the absolute values of A and B would give a larger distance than the distance between A and B.

Q: Can you provide an example of numbers where the absolute value of A minus B is equal to the absolute value of A plus the absolute value of B?

No, such numbers do not exist. For any given numbers A and B, the two expressions will not be equal.

Summary & Key Takeaways

• The absolute value of A minus B is equivalent to the distance between A and B.

• The absolute value of A plus the absolute value of B is not equivalent to the distance between A and B.

• The expressions A minus B and the negative of B minus A are not equivalent to the distance between A and B.