Problem 61 - Elementary and Intermediate Algebra

Question

Subtract. $$ -6-(-5) $$

Step-by-Step Solution

Answer

- 6 - (- 5) = - 1

Step 1: Understand the Problem

The expression to solve is ewline ewline Step 1 Titleewline -6 - (-5)ewline This is a subtraction operation involving negative numbers.

Step 2: Rewrite the Expression

To better understand the problem, rewrite the subtraction of a negative number as an addition. This transforms the expression into ewline - 6 + 5 .

Step 3: Perform the Addition

Now, add the numbers: ewline - 6 + 5 = -1.

Step 4: Verify the Result

Check the result by redoing the steps or using a calculator for confirmation: ewline - 6 - (-5) indeed simplifies to -1.

Key Concepts

Negative Numbers

Negative numbers are values less than zero. They are often used to represent losses or decreases. For example, -6 signifies a point 6 units below zero on the number line.

In arithmetic, negative numbers have different rules compared to positive numbers. When two negative numbers are added, the result is a more negative number. However, when a negative number is subtracted, the operation changes into an addition problem.

Understanding how to manipulate negative numbers is crucial for solving subtraction and addition problems involving them.

Subtraction Operation

A subtraction operation involves finding the difference between two numbers. Normally, you might see a problem like 8 - 5, which means 'take 5 away from 8'.

When dealing with negative numbers like -6 - (-5), the operation becomes a bit trickier. Here, instead of simply subtracting, we need to remember that subtracting a negative number is like adding its positive equivalent.

This is why the expression -6 - (-5) transforms into -6 + 5 in the next step.

Addition Transformation

Transforming a subtraction problem into an addition problem can make it easier to solve. This concept is especially helpful when dealing with negative numbers.

In our problem, -6 - (-5), we rewrite it as -6 + 5. This step simplifies the operation since most people find addition easier to manage than subtraction, especially when negatives are involved.

Remember this key rule: Subtracting a negative number is the same as adding the positive version of that number.

Basic Arithmetic

Basic arithmetic involves four main operations: addition, subtraction, multiplication, and division. In this exercise, we are primarily concerned with addition and subtraction, specifically involving negative numbers.

After transforming -6 - (-5) into -6 + 5, the problem becomes a simple arithmetic addition. Adding 5 to -6 results in -1.

Understanding basic arithmetic rules helps in breaking down more complex problems into simpler steps, making them easier to solve accurately.