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Chapter 10: Problem 10

Add. Do not use the number line except as a check. $$ -13+0 $$

Short Answer

Expert verified
-13

Step by step solution

01

Identify the Numbers

In the given problem, you need to add \(-13\) and \(0\). Identify the numbers involved in the addition.
02

Understand Addition with Zero

Recall that adding \(0\) to any number does not change the value of that number. Mathematically, this is because \(0\) is the additive identity.
03

Perform the Addition

Based on the property of \(0\), \(-13 + 0 = -13\).
04

Validate Using the Number Line

Although instructed not to use the number line, if you were to use it as a check, it shows that adding zero to \(-13\) leaves it unchanged at \(-13\).

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Key Concepts

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

Additive Identity
In mathematics, the term 'additive identity' refers to a fundamental property of the number zero. The additive identity property states that adding zero to any number does not change the value of that number. This concept is crucial for understanding how addition works in arithmetic.
When we write the expression \[ -13 + 0 \], the number -13 in this scenario remains unchanged because we are adding zero to it. This property can be written as: \[ a + 0 = a \] for any real number 'a'.
So, based on this property, \[ -13 + 0 = -13 \].
Understanding this property helps simplify many arithmetic problems and also forms the basis for more complex mathematical concepts.
Properties of Zero
Zero is a unique number with several interesting and useful properties, especially in addition. One of the primary properties of zero is the additive identity property, as discussed earlier. However, zero has other properties as well:
  • Zero is the only number that, when added to itself, yields zero.
  • Multiplying any number by zero results in zero.
  • Zero is neither positive nor negative but acts as a neutral element between them.
These properties make zero a powerful and essential tool in mathematics. Its role as the additive identity simplifies operations and helps maintain consistency in various arithmetic and algebraic calculations.
Number Line
A number line is a visual representation used to illustrate the position and order of numbers along a straight horizontal line. It extends infinitely in both directions, with zero typically located at the center. Positive numbers are positioned to the right of zero, while negative numbers are to the left.
Using a number line can help visualize addition and subtraction. For example, if we start at -13 on the number line and add 0, we remain at -13:
  • Start at -13.
  • Since adding zero means no movement, we stay at -13.
Although not required for our initial problem, number lines are valuable educational tools that can clarify how operations like addition, subtraction, and even more complex functions work.

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Most popular questions from this chapter

Simplify. $$ 5^{3}-7^{2} $$

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