Problem 9 - Algebra A Combined Function

Question

Subtract. \(-26-(-18)\)

Step-by-Step Solution

Answer

The result of \(-26 - (-18)\) is \(-8\).

Step 1: Identify the expression

The expression to solve is \(-26 - (-18)\). We need to perform this subtraction.

Step 2: Understand negative subtraction

When subtracting a negative number, it is equivalent to adding the positive of that number. For example, \(-a - (-b) = -a + b\). In this case, \(-26 - (-18)\) becomes \(-26 + 18\).

Step 3: Perform the addition

Now we solve \(-26 + 18\). To do this, consider it as a comparison between negative and positive values: - Start at -26 and move 18 steps towards the positive on the number line.Ultimately, the calculation will be:- Find the difference between absolute values: \(26 - 18 = 8\).- The result takes the sign of the originally larger absolute value (26), which is negative.

Step 4: Write the result

The result of the calculation \(-26 + 18\) is \(-8\), since the result of subtracting 18 from 26 (when seen as movement on the number line) keeps us in the negative zone.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (e.g., -5, -26). They are the opposite of positive numbers and can be visualized on a number line to the left of zero. Negative numbers become essential when dealing with real-world contexts, such as temperatures below freezing or depths below sea level.

• In arithmetic operations, handling negative numbers requires careful attention, especially in subtraction.
• Subtracting a negative number can initially seem confusing but is straightforward once you understand it changes to addition.

For example, subtracting -18 from -26 can be translated to adding the opposite of -18, which is 18, i.e., \[-26 - (-18) = -26 + 18\]. This transformation is pivotal in easing the complexity from subtraction into a more familiar addition operation.

Absolute Value

The absolute value of a number refers to its distance from zero on a number line, regardless of direction. This concept is crucial when comparing magnitudes of numbers without considering their signs.

• For instance, the absolute value of -26 is 26, and the absolute value of 18 is 18.
• It transforms a negative number into its positive counterpart.

This property is particularly useful in our original exercise where we observe the difference between the absolute values. To calculate \(-26 + 18\), find:

• The absolute value of -26: 26
• The absolute value of 18: 18
• Subtract these values: \(26 - 18 = 8\)

The actual result takes the sign of the number with the larger absolute value, resulting in \(-8\). Understanding absolute value helps simplify operations with negative numbers by temporarily ignoring their sign.

Number Line

A number line is a straight line with numbers placed at intervals along its length, which visually represents real numbers, including negative numbers and zero. It's a useful tool for visualizing operations like addition and subtraction.

• Negative numbers are plotted on the left side of zero, while positive numbers are on the right.
• Each position on the number line corresponds to a real number.

When subtracting as in \(-26 - (-18)\), thinking about moving along a number line can clarify the operation. Starting at -26, you move 18 steps to the right (since subtracting a negative is the same as adding).- This movement results in a position of -8 on the number line.Using a number line can be particularly helpful for students to visually comprehend how integers interact in addition and subtraction operations.