Problem 87 - Elementary and Intermediate Algebra

Question

Perform the operations. $$ 0-(-1) $$

Step-by-Step Solution

Answer

The result of \(0 - (-1)\) is 1.

Step 1: Identify the Expression

The expression provided is \(0 - (-1)\). Your task is to perform the subtraction of negative numbers.

Step 2: Understand Subtraction of Negative Numbers

Subtracting a negative number is equivalent to adding its corresponding positive number. Thus, \(0 - (-1)\) is equivalent to \(0 + 1\).

Step 3: Perform the Addition

Calculate \(0 + 1\). When you add 1 to 0, the result is 1.

Key Concepts

Adding Positive Numbers

When we talk about adding positive numbers, we mean combining quantities in a way that we increase the value. This is the simplest form of arithmetic.
For instance, if you have 2 apples and you get 1 more, you now have 3 apples. This is what adding positive numbers is all about: finding the total or sum by putting together individual values.
In an expression, addition is often represented by the plus sign "+". For example:

• 3 + 4 = 7
• 5 + 7 = 12
• 0 + 1 = 1

Even when starting from zero, when you add a positive number, you simply move on the number line to the right. This is exactly what happens in the exercise: taking 0 and adding 1 gives you a result of 1, as shown in the solution steps.

Understanding Expressions

Expressions in mathematics are combinations of numbers, operations, and sometimes variables. They are used to represent mathematical situations and relationships.
In the provided exercise, the expression is "0 - (-1)". When you first see an expression, your goal is to understand what is being asked. Here, it shows subtraction involving a negative number.
Breaking it down helps:

• The number 0 is your starting point.
• "-(-1)" indicates subtracting a negative, which can be a bit confusing at first.

It's crucial to remember that subtracting a negative is the same as adding a positive. Understanding this transform converts complex scenarios into manageable tasks with simpler operations, like adding.

Basic Algebra

Algebra is a branch of mathematics dealing with symbols and rules for manipulating those symbols. It's the language through which we can express general mathematical ideas and solve equations.
One of the foundational concepts in algebra is understanding how to handle negative numbers. Knowing that subtracting a negative number is the same as adding a positive number is crucial.
Consider the expression we worked with earlier:
The transformation from "0 - (-1)" to "0 + 1" demonstrates a fundamental algebraic principle:

• Changing the operation (from subtraction to addition)
• Recognizing that two negatives in sequence result in a positive

This mental shift is essential and is important in many algebraic processes. It allows you to simplify problems and progress through more complex algebraic operations with confidence.