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Chapter 1: Problem 26

In Exercises \(1-66,\) compute the value of each expression. $$44+(-29)$$

Short Answer

Expert verified
The value of \(44 + (-29)\) is \(15\).

Step by step solution

01

Identify the Operation

The expression given is a simple arithmetic addition involving a positive number and a negative number: \(44 + (-29)\).
02

Understand Addition with Negative Numbers

When adding a positive number to a negative number, it is the same as subtracting the absolute value of the negative number from the positive number.
03

Perform the Calculation

Subtract the absolute value of \(-29\) from \(44\): \(44 - 29 = 15\).
04

Write the Result

The result of adding \(44\) and \(-29\) is \(15\).

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Key Concepts

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

arithmetic operations
Arithmetic operations are the basic calculations we perform in mathematics. These include addition, subtraction, multiplication, and division. These operations are fundamental in nearly every area of math.
In the given exercise, we are dealing with the addition of a positive number and a negative number. Understanding how to handle these operations correctly is essential for solving problems accurately.
In the expression $$44 + (-29)$$, we see that addition is the primary operation. Combining positive and negative numbers follows specific rules, which we'll explore in the next sections.
addition of negative numbers
Adding negative numbers involves understanding simple rules. When you add a negative number to a positive one, it's the same as subtracting the absolute value of the negative number.
For example, let's understand the exercise $$44 + (-29)$$. Here, we need to consider the absolute value of -29, which is 29. The addition turns into a subtraction: $$44 - 29$$. By performing this subtraction, we get the result 15.
This rule simplifies arithmetic involving negative numbers. Whether you are dealing with large or small numbers, applying this rule ensures that you get the correct result.
absolute value
The absolute value of a number is its distance from zero on the number line, regardless of direction. Essentially, it is always a positive number or zero.
The absolute value is denoted by two vertical lines: \(|x|\). For instance, \(|-29|\ = 29\).
Understanding absolute value helps simplify operations involving negative numbers. In the exercise $$44 + (-29)$$, we used the absolute value of -29, which is 29, to transform the addition into a subtraction. This step was crucial in solving the problem correctly.
Remember, knowing how to work with absolute values makes complex expressions easier to handle.

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