Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 1: Problem 28
Find the distance between the given numbers on a number line. -35 and -6
Short Answer
Expert verified
The distance between -35 and -6 is 29.
Step by step solution
01
Understanding the Problem
We need to find the distance between -35 and -6 on a number line. To do this, we'll calculate the difference between these two integers.
02
Calculate the Difference
To find the distance between two numbers on a number line, we subtract the smaller number from the larger number. In the case of -35 and -6, we subtract -35 from -6: \(-6 - (-35)\).
03
Simplify the Expression
Simplify the expression by changing the double negative to a positive: \(-6 + 35\).
04
Perform the Addition
Calculate the sum of -6 and 35: \(-6 + 35 = 29\).
05
Conclusion
The calculated distance between the two points on the number line is 29.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with 91影视!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Integers on a Number Line
Integers are whole numbers that can be positive, negative, or zero. Visualizing integers on a number line involves placing them at equally spaced intervals arranged from left to right. This allows us to see their relative positions and differences easily. A number line can help you understand how integers relate to each other:
- Positive integers are found to the right of zero, increasing in value as you move farther right.
- Negative integers are located to the left of zero, decreasing as you head further left.
- The number zero is the central point of the number line, neither positive nor negative.
Subtraction of Integers: Basic Principles
Subtraction in mathematics is the opposite operation to addition. When subtracting integers, understanding the direction on a number line is critical. Here's how it works:
- When you subtract a negative number, it鈥檚 the same as adding the opposite positive number. This is often referred to as the 'double negative' rule.
- Subtracting a positive number means moving to the left on the number line.
- Subtracting a negative number results in moving to the right on the number line.
Calculating Distance on a Number Line
Distance on a number line refers to the absolute difference between points, only concerned with how far numbers are from each other, irrespective of direction.
- To find the distance between any two integers, simply subtract the smaller one from the larger one, or vice versa.
- Always consider the absolute value of the result to ensure the distance is a positive number.
- For example, the distance between -35 and -6 is calculated as: \[-6 - (-35)\] which simplifies to \[-6 + 35 = 29.\]
Working with Negative Numbers
Negative numbers are less than zero and are typically represented to the left side of zero on a number line. Understanding their unique properties is vital for performing basic operations:
- Adding negative numbers is akin to subtracting positive numbers, moving left on the number line.
- The subtraction of negative numbers, however, is equivalent to adding their absolute values, moving right on the number line.
- Negative numbers when doubled, i.e., negative of a negative, revert to being positive.
