Problem 42 - Elementary and Intermediate Algebra

Question

Subtract. $$ -5-6 $$

Step-by-Step Solution

Answer

-11

Step 1: Identify the Terms

Identify the terms involved in the subtraction. Here, you need to subtract 6 from -5.

Step 2: Rewrite the Expression

Rewrite the expression for clarity: o-5 - 6 = -5 + (-6) So you are adding a negative number.

Step 3: Perform the Addition

Add the two negative numbers together. Summing -5 and -6: Target: -5 + (-6) = -11.

Key Concepts

Integer Operations

Understanding integer operations is crucial for dealing with various math problems. Integers include positive numbers, negative numbers, and zero.
When performing operations with integers, especially subtraction, it's important to remember the rules:

• Adding a positive number moves you to the right on the number line.
• Adding a negative number moves you to the left on the number line.
• Subtracting a positive number also moves you to the left on the number line.
• Subtracting a negative number moves you to the right on the number line, as it's equivalent to adding a positive.

Getting comfortable with these rules will help you easily tackle questions involving integer operations.

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (-). They are opposite to positive numbers.
When dealing with negative numbers and subtraction, it can sometimes be confusing. For example, subtracting a negative number is the same as adding its positive counterpart.
In our exercise: \[-5 - 6\], we can see that we are subtracting 6 from -5.
Remember these quick tips when working with negative numbers:

• Subtracting a positive increases the negative value.
• Subtracting a negative decreases the negative value, making it less negative or more positive.
• Visualizing a number line can help understand these concepts better.

Addition of Negatives

Adding negative numbers is simple if you remember a few key points. In the given exercise \[-5 - 6\], it is converted to an addition problem: \[-5 + (-6)\].
This method helps by keeping the operations consistent and straightforward. When adding two negative numbers:

• Add their absolute values (ignore the sign).
• Attach a negative sign to the result.

So, for \[-5 + (-6)\], you simply add 5 and 6 to get 11, and then attach the negative sign to get \[-11\]. This simplifies what initially seems like a complex operation.

Algebra Step-by-Step Solutions

Step-by-step solving ensures clarity and understanding.
Let's break down our original problem, \[-5-6\], into steps:

• Step 1: Identify the Terms - Recognize you need to subtract 6 from -5.
• Step 2: Rewrite the Expression - Turn it into an addition problem: \[-5 - 6 = -5 + (-6)\]. This keeps operations more straightforward.
• Step 3: Perform the Addition - Add the two negative numbers. Adding their absolute values (5 + 6) gives 11. Since both numbers are negative, the result is also negative, \[-11\].

This approach breaks the problem into manageable steps, helping you understand each part of the process.