Problem 20 Add. See Examples 1 through 12,1... [FREE SOLUTION]

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Chapter 1: Problem 20

Add. See Examples 1 through 12,18, and 19. $$ 23+(-23) $$

Short Answer

Expert verified

23 + (-23) equals 0.

Step by step solution

Identify the Numbers

We are given two numbers: 23 and -23.

Apply the Rule for Adding Opposite Numbers

When you add a number and its opposite (also known as its additive inverse), the result is always zero because the two numbers cancel each other out.

Perform the Addition

Add 23 and -23 together: \[ 23 + (-23) = 0 \]

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Key Concepts

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

Additive Inverse

The concept of an additive inverse is essential in understanding how numbers can cancel each other out during addition. In simple terms, the additive inverse of a number is another number that, when added to the original number, results in a sum of zero.
This means they completely "erase" each other鈥檚 values. For any given number $ x $, its additive inverse is $ -x $.
For example, the additive inverse of $ 23 $ is $ -23 $.

The positive and negative numbers act like two opposite forces.
When combined, they create a neutral sum, which is zero.

Recognizing additive inverses can simplify calculations by quickly identifying pairs of numbers that will sum to zero.

Addition

Addition is one of the most basic arithmetic operations, and it involves combining numbers to get a total sum. When adding numbers that are opposites, such as 23 and -23, the process involves the concept of cancellation.
Since one is positive and the other negative, their combination yields zero. This specific situation is a unique example of addition where:

It requires understanding how to handle different signs.
Positive and negative cancel each other out.

Through addition, we see how even complex problems can be simplified using rules like cancellation of opposites.

Integer Operations

Integer operations encompass various arithmetic actions involving whole numbers, including addition, subtraction, multiplication, and division. Here, we're focusing on addition, especially involving integers with different signs.
When adding integers:

Note that the addition of opposite integers, such as $ a + (-a) $, results in zero.
This aligns with the rule of additive inverses.
Understanding these operations ensures clarity when solving equations.

By mastering how integer operations work, students can approach and solve real-world problems with higher efficiency and accuracy.
This foundation is critical in progressing through more advanced mathematical topics.

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91影视

Add. See Examples 1 through 12,18, and 19. $$ 23+(-23) $$

Short Answer

Step by step solution

Identify the Numbers

Apply the Rule for Adding Opposite Numbers

Perform the Addition

Key Concepts

Additive Inverse

Addition

Integer Operations

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