Problem 64 - Prealgebra

Question

Find each sum. $$4+(-9)+(-9)+5$$

Step-by-Step Solution

Answer

The sum is -9.

Step 1: Combine the Positive Numbers

Start by identifying and adding together the positive numbers in the expression. Here, we have the numbers 4 and 5.Adding these together gives: \[4 + 5 = 9\]

Step 2: Combine the Negative Numbers

Identify and add together the negative numbers in the expression. The negative numbers are -9 and -9.Adding these together gives: \[-9 + (-9) = -18\]

Step 3: Sum the Results from Step 1 and Step 2

Now, take the result from Step 1, which is 9, and the result from Step 2, which is -18, and add them together.\[9 + (-18) = 9 - 18 = -9\]

Step 4: Verify the Sum

To ensure the accuracy, recheck the calculations. First combine the individual sums: - The positive sum: 4 + 5 = 9. - The negative sum: -9 + (-9) = -18. Combining them gives: 9 + (-18) = -9, which is consistent with our earlier result.

Key Concepts

Addition of Integers

When working with the addition of integers, we deal with both positive and negative whole numbers. The standard approach is to identify and group numbers by their signs—positive or negative—before performing the addition. This process helps simplify calculations and avoids potential errors.

To add integers:

• Group same-sign numbers: First, sum all the positive integers together. Then, add all the negative integers together.
• Combine results: Finally, combine the results of the two groups to find the overall sum.

This method simplifies the process and is particularly useful for larger calculations. The same principle applies no matter how many integers you're adding.
By breaking down the integers into their positive and negative components, you ensure accuracy and clarity in your math work.

Negative Numbers

Negative numbers are numbers that are less than zero. They are often used to represent a loss, temperature below zero, or debts. An important understanding is that negative numbers, when added together, become more negative.

When dealing with calculations, remember that:

• Negative plus negative: Adding two negative numbers increases their absolute value in the negative direction. For example, \(-9 + (-9) = -18\).
• Negative and positive: When adding a negative number to a positive one, it's similar to subtraction, where you take away from the positive value. A useful way to think about it is: \(a + (-b) = a - b\).

Understanding how negative numbers behave with other numbers is crucial for accurate integer operations. Keep these basic rules in mind when performing additions that involve negatives.

Positive Numbers

Positive numbers are numbers greater than zero. They are used to represent various real-world quantities like profit, height above sea level, or temperature above freezing. Their behavior in calculations is straightforward, especially when adding.

Here's how positive numbers work:

• Positive plus positive: When adding two or more positive numbers, you simply add their values normally, resulting in a larger positive number. For instance, \(4 + 5 = 9\).
• Influence of positivity in mixed sums: When positive numbers are combined with negative numbers, their role is to offset the negatives up to their total value. If the positive sum is larger than the negative sum, the overall result remains positive.

Knowing how positive numbers interact in the context of integer operations allows for effective and simplified calculation processes.