Problem 57 - Algebra A Combined Function

Question

Find the sum of -38 and 12 .

Step-by-Step Solution

Answer

The sum of -38 and 12 is -26.

Step 1: Identify the Numbers

The numbers given in the problem are -38 and 12. We need to add them to find the sum.

Step 2: Add the Numbers

When adding a negative and a positive number, you subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value. Here, we subtract 12 from 38, which gives us 26. Since -38 has a greater absolute value, the sum is negative.

Step 3: Determine the Result

After performing the subtraction, the result is -26. Thus, the sum of -38 and 12 is -26.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are usually accompanied by a minus sign. These numbers play an important role in mathematics, particularly in operations like addition and subtraction.

When working with negative numbers, it's essential to remember:

• Negative numbers are typically used to represent losses, debts, or decreases.
• On a number line, negative numbers are located to the left of zero.

In the context of the given exercise, -38 is a negative number, indicating a shift 38 units to the left of zero on a number line.

Absolute Value

The absolute value of a number is the non-negative value of that number, regardless of its sign. It measures the distance between a number and zero on a number line.

Absolute value is denoted by vertical bars around the number, like this: \(|x|\). For example, the absolute value of -38 is 38, and the absolute value of 12 is 12. This is because absolute value disregards whether a number is positive or negative, focusing solely on its magnitude.

Understanding absolute value is crucial when determining which number has a greater influence in an operation involving both positive and negative numbers, such as in our exercise.

Addition Rules

Adding integers involving both positive and negative numbers might seem challenging at first, but there are straightforward rules to simplify the process. When adding:

• Two positive numbers, simply add their absolute values, and the result is positive.
• Two negative numbers, add their absolute values, and the result is negative.
• A positive and a negative number, subtract the smaller absolute value from the larger absolute value. The sign of the result will be that of the integer with the larger absolute value.

In our exercise, we added -38 and 12. Following the rules, since the absolute value of -38 is greater than that of 12, the final sum will keep the sign of -38.

Sum of Integers

Finding the sum of integers involves determining how different numbers come together to form a total. Whether dealing with whole numbers, positive numbers, or negative numbers, the sum process remains consistent.

In our exercise, we calculated the sum of -38 and 12 by following these key steps:

• Identify and compare the absolute values.
• Subtract the smaller absolute value from the larger one, as we're dealing with opposite signs.
• Attach the sign of the integer with the larger absolute value to the result.

Thus, the sum of -38 and 12 is -26, reflecting the overall impact of combining these two integers on the number line.