Chapter 2: Problem 2
Use the number line to complete: \(-2-5=?\)
Short Answer
Expert verified
\(-2 - 5 = -7\)
Step by step solution
01
Start at -2 on the number line
Begin at the position -2 on the number line. Since we're subtracting 5, we'll move 5 units to the left as is the standard operation to perform during subtraction.
02
Move to the left
As we move 5 units left from -2, our position on the number line after moving 1 unit is -3, after moving 2 units is -4, after moving 3 units is -5, after moving 4 units is -6 and after moving 5 units is -7.
03
Identify the final position
We have successfully moved 5 units to the left from -2, we landed on -7. This would give us the result of the subtraction, -7.
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 91Ó°ÊÓ!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding the Number Line
The number line is a visual representation of numbers placed in a linear sequence. It helps us easily understand mathematical operations like addition and subtraction, especially involving integers.
- **Positive numbers** are located to the right of zero. - **Negative numbers** are to the left of zero. Every number is equally spaced from its neighbors, making it a very intuitive tool. For the exercise, we start at the position ",-2" on the number line, which is to the left of zero.
Using the number line, subtraction involves moving towards the left. This direction has a clear association—moving left means reducing the value. Remembering the leftward movement can help visualize how subtraction works, particularly with negative numbers.
- **Positive numbers** are located to the right of zero. - **Negative numbers** are to the left of zero. Every number is equally spaced from its neighbors, making it a very intuitive tool. For the exercise, we start at the position ",-2" on the number line, which is to the left of zero.
Using the number line, subtraction involves moving towards the left. This direction has a clear association—moving left means reducing the value. Remembering the leftward movement can help visualize how subtraction works, particularly with negative numbers.
Basics of Subtraction
Subtraction is a fundamental mathematical operation that involves taking away a number from another. In our given exercise,
"-2-5",
the subtraction of five from ",-2"
uses a number line to move you in the leftward direction. When you subtract a positive number on a number line, it reflects moving left by that many units.
For instance, subtracting 5 from ",-2" requires moving left five units: - Start at ",-2" - Move past "-3, -4, -5, -6" and finally reach "-7." This "moving 5 units left" helps simplify this operation visually. The complete movement helps to understand that the answer to ",-2-5" is "-7." Practice with the number line can make subtraction with integers more intuitive and less intimidating.
For instance, subtracting 5 from ",-2" requires moving left five units: - Start at ",-2" - Move past "-3, -4, -5, -6" and finally reach "-7." This "moving 5 units left" helps simplify this operation visually. The complete movement helps to understand that the answer to ",-2-5" is "-7." Practice with the number line can make subtraction with integers more intuitive and less intimidating.
Working with Negative Numbers
Negative numbers can be confusing at first, but they play a crucial role in mathematical operations. Negative numbers are those less than zero, and they have distinct characteristics:
- Represent losses or decreases
- Situated to the left of zero on the number line
Understanding negative numbers becomes necessary, especially when learning subtraction.
In integer operations, "-5" is seen as moving 5 units left. For example, when starting from ",-2," subtracting "5" involves relocation 5 units leftwards on the number line. Each negative step takes you further left, deepening the negative value.
By treating negative numbers with familiarity and using them confidently on a number line, mathematical operations become clearer, empowering you to handle more complex equations in the future.
In integer operations, "-5" is seen as moving 5 units left. For example, when starting from ",-2," subtracting "5" involves relocation 5 units leftwards on the number line. Each negative step takes you further left, deepening the negative value.
By treating negative numbers with familiarity and using them confidently on a number line, mathematical operations become clearer, empowering you to handle more complex equations in the future.