Problem 11 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$-7-(-18)$$

Step-by-Step Solution

Answer

The result of -7-(-18) is 11.

Step 1: Understand the Problem

The problem is asking to subtract a negative from a negative number: -7-(-18). This might seem confusing because of the two negative signs close together.

Step 2: Rewrite the Problem

The problem can be rewritten as follows: -7 + 18. This is because subtracting a negative is the same as adding a positive.

Step 3: Perform the addition

Now to perform the addition. You are adding 18 and -7. The answer is 11.

Key Concepts

Negative Numbers

Negative numbers are essential in mathematics, especially when dealing with operations like subtraction and addition. Understanding how they work is crucial for mastering any related math problem.

Negative numbers are numbers less than zero. They are represented with a minus sign. For example,

• -7 is seven units below zero on the number line.
• -18 is eighteen units below zero.

Frequently, students might find them confusing, especially when performing operations like subtraction, which might involve two negative signs close together. Always remember that:

• Subtracting a negative number is equivalent to adding a positive number.
• Addition and subtraction operations involving negative numbers often change their initial values depending on the signs and magnitude.

Be patient with yourself when learning about negative numbers. With practice, they become much easier to manage.

Performing Operations

Performing operations with integers can include tasks like addition, subtraction, multiplication, and division, but let's focus on subtraction involving negative numbers.

When you subtract a negative number, you are essentially adding its positive equivalent. This operation can be rephrased as swapping two negative signs with a plus sign. As an example:

• For the expression \[-7 - (-18)\], this can be reframed as \[-7 + 18\].

Here's how you can simplify the process:

• Identify the negative signs.
• Recognize that subtracting a negative becomes adding a positive.
• Transform the equation by removing the negative signs and adding what's left.

By understanding this principle, you simplify the operation and avoid common mistakes.

Addition of Integers

Addition of integers, including both positive and negative values, is fundamental to handling more complex operations.

When adding integers, consider these important points:

• If two numbers have the same sign (both positive or both negative), you add their absolute values. The sum carries their common sign.
• If two numbers have different signs, like 18 and -7 in the exercise, subtract the smaller absolute value from the larger absolute value. The result takes the sign of the number with the larger absolute value.

For example, in \[-7 + 18\]:

• The integers have different signs.
• The absolute value of 18 is larger than that of 7.
• The result is \[18 - 7 = 11\], keeping the positive sign of 18.

With these rules, adding integers of any kind becomes straightforward. Always carefully consider the signs and magnitudes involved.