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Chapter 2: Problem 51

Add. $$ 3+(-23)+6 $$

Short Answer

Expert verified
The result of the expression is -14.

Step by step solution

01

Identify the numbers

The expression to solve is \(3 + (-23) + 6\). We have three numbers: 3, -23, and 6.
02

Add the first two numbers

Start by adding the first two numbers: \(3 + (-23)\). This is the same as \(3 - 23\), which equals \(-20\).
03

Add the result to the third number

Now add the result from Step 2, which is \(-20\), to the third number: \(-20 + 6\). This calculation gives us \(-14\).

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are a crucial concept in mathematics. They are numbers that appear on the left side of zero on the number line.
While positive numbers represent quantities, negative numbers can represent deficits or losses. For example, a temperature of -5掳C means it鈥檚 5 degrees below zero.
When working with negative numbers, it鈥檚 helpful to remember these key points:
  • Adding a negative number is the same as subtracting its absolute value.
  • The further left a number is from zero, the smaller its value.
  • Subtracting a negative number is like adding a positive one.
These principles simplify operations involving negative numbers and assist in understanding more complex concepts.
Step-by-Step Solutions for Integer Addition
A step-by-step approach is the key to tackling integer addition problems effectively. It allows learners to follow a clear path and understand each part of the process.
Let's take a closer look at how this approach was applied in the original exercise:
  • Identify the numbers: Begin by listing the numbers you need to add, which are 3, -23, and 6 in this scenario.
  • Add the first pair: Start with the first two numbers. Notice that adding negative 23 is the same as subtracting 23. It simplifies the calculation, leading to -20.
  • Add the subsequent result: Finally, take the result from the previous step (-20) and add it to the remaining number, which is 6. This will give you -14.
By breaking down problems into manageable steps, a step-by-step solution helps solidify understanding and fosters confidence in dealing with integers.
Exploring Prealgebra Concepts
Prealgebra lays the foundation for more advanced mathematical ideas. It often involves mastering basic arithmetic operations, such as addition and subtraction, especially with integers.
In prealgebra, students learn to:
  • Recognize and properly handle negative numbers in arithmetic.
  • Understand the effects of adding and subtracting negative numbers on calculations.
  • Grasp the importance of the order of operations to solve more complex expressions.
These concepts serve as stepping stones to more intricate algebraic topics. By ensuring a solid grasp of these prealgebra fundamentals, students are well-equipped for future mathematical challenges. Each concept builds upon the previous one, creating a comprehensive understanding of math basics.

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Most popular questions from this chapter

Write the given numbers in order from least to greatest. $$ -(-2), 5^{2},-10,-|-9|,|-12| $$

Graph each integer in the list on the same number line. $$ 0,-2,-7,-5 $$

Evaluate. $$ -|-x| \text { if } x=2 $$

Represent each quantity by an integer. A scuba diver is swimming 25 feet below the surface of the water in the Gulf of Mexico.

Answer true or false. The number \(-a\) is always a negative number. (Hint: Read "-" as "the opposite of.")
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