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Chapter 1: Problem 12

Add using the number line. \(-6+0\)

Short Answer

Expert verified
The sum is -6.

Step by step solution

01

- Identify the starting point

Locate the number -6 on the number line. This is where the addition process will begin.
02

- Determine the movement

Since we are adding 0, determine that there will be no movement on the number line. The starting point will be the same as the ending point.
03

- Identify the result

Since there is no movement, the final position on the number line remains at -6.
04

- Conclude the addition

The sum of -6 and 0 is -6.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Line
A number line is a visual representation of numbers along a straight line. It can include both positive and negative numbers, as well as zero. Using a number line can simplify the process of adding and subtracting integers.

To understand how to use a number line for addition, consider this example: \(-6 + 0\). On the number line:
  • Locate the starting point at -6.
  • Since you add 0, there is no movement on the number line.
  • The final position is -6, which is also the result of the addition.
Using a number line helps you visually understand why adding zero to any number leaves it unchanged.
Negative Numbers
Negative numbers represent values less than zero. They are located to the left of zero on a number line. Adding negative numbers can be different from adding positive numbers, but using a number line can help.

For our example \(-6 + 0\):
  • Start at -6, which is a negative number.
  • Adding 0 means there is no change in position.
  • The sum remains -6, indicating that adding zero does not affect the value of the negative number.
Negative numbers are crucial in various real-life applications, like temperatures below freezing or financial debts.
Zero
Zero is a unique number on the number line. It acts as the neutral element in addition. When you add zero to any number, the original number remains the same. This property is useful in understanding integer operations.

Let's review the example \(-6 + 0\):
  • Start at -6 on the number line.
  • Adding 0 means you stay at -6 with no movement.
  • The result remains -6, showing that zero doesn't change the value of the number it is added to.
Understanding zero's role is essential in mathematics, making complex problems easier to solve by breaking them into simpler parts.

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