Problem 74 - Algebra A Combined Function

Question

Perform the indicated operation. \(-8-11\)

Step-by-Step Solution

Answer

The result is -19.

Step 1: Recognize the Operation

In this problem, we are asked to perform a subtraction operation. The expression given is \(-8 - 11\). This involves subtracting 11 from -8.

Step 2: Convert Subtraction to Addition

Subtracting a number is the same as adding its opposite. Thus, we can rewrite \(-8 - 11\) as \(-8 + (-11)\).

Step 3: Add the Integers

When adding two negative numbers, you add their absolute values and keep the negative sign. The absolute values of -8 and -11 are 8 and 11, respectively. So, we calculate \(8 + 11 = 19\), and the result is \(-19\).

Step 4: Verify the Result

Check the steps to ensure accuracy: We have correctly converted \(-8 - 11\) to \(-8 + (-11)\), summed the absolute values, and added the negative sign. Thus, the final answer is correct.

Key Concepts

Subtraction of Integers

Subtraction of integers might seem tricky at first but it's essentially about finding the difference. In simple terms, when subtracting a positive number from another number, it can be helpful to view subtraction as adding the opposite. For example, when you see \(-8 - 11\), the subtraction can be converted into an addition operation by changing the subtraction sign to addition and the following number to its opposite.

• Instead of subtracting, you add a negative: \(-8 - 11\) turns into \(-8 + (-11)\).
• This conversion helps simplify calculations involving negative numbers.

Understanding this concept can help you handle any subtraction problem involving integers. It simplifies the process and aligns with basic addition practices.

Addition of Integers

The addition of integers is an important concept when it comes to combining both positive and negative numbers. When adding two integers:- If both numbers have the same sign, you simply add their absolute values and maintain the common sign.- If the integers have different signs, subtract the smaller absolute value from the larger one and adopt the sign of the number with the larger absolute value.For example, in \(-8 + (-11)\):

• Both numbers are negative.
• Add their absolute values: \(8 + 11 = 19\).
• Apply the negative sign to the result, giving \(-19\).

Mastering these rules aids in understanding more complex equations and integer operations.

Absolute Value

The absolute value of a number is its distance from zero on the number line, without considering the direction. It is always a non-negative number. Absolute values are essential in integer operations like addition and subtraction since they help determine the size of a number without regard to sign.

• The absolute value of -8 is 8, represented as \(|-8| = 8\).
• Similarly, the absolute value of -11 is 11, represented as \(|-11| = 11\).

Using absolute values in operations allows for straightforward addition or subtraction, as you operate with these positive figures and apply the original signs as needed. Understanding absolute values not only simplifies calculations but gives you a groundwork for exploring more advanced mathematical concepts.