Problem 36 - Fundamentals of Mathematics

Question

Rewrite each expression in simpler form. $$ 0-(-1) $$

Step-by-Step Solution

Answer

The simplified expression is 1.

Step 1: Identify the Expression

The given expression is \(0 - (-1)\). Our goal is to simplify this expression.

Step 2: Rewrite the Expression

We have a subtraction involving a negative number. According to the rule of subtracting negative numbers, \(a - (-b)\), it can be rewritten as \(a + b\). Therefore, \(0 - (-1)\) becomes \(0 + 1\).

Step 3: Perform the Addition

Now, add the numbers together. Since the expression becomes \(0 + 1\), adding gives us the result: \(1\).

Key Concepts

Understanding Subtracting Negative Numbers

When you subtract a negative number, it can initially feel confusing, but with the right approach, it becomes simple. Think of subtraction as the opposite of addition. Thus, when you subtract a negative number, you are actually adding. This is because two negatives make a positive. For example, in the expression

• \( 0 - (-1) \)

replaces the minus-minus with a plus sign:

• \( 0 + 1 \)

Consider that subtracting negatives essentially shifts you forward on the number line. If you have a number and you subtract a negative, you go in the positive direction. Remember this simple rule: turn subtraction of a negative into addition. This fundamental concept helps simplify many similar mathematical challenges.

Simplifying Expressions Efficiently

Simplifying expressions is an essential skill in mathematics. It helps in reducing complex problems into more manageable ones. The key is to apply mathematical rules to make the expression easier.

• For instance, in simplifying \(0 - (-1)\), we first recognized the subtraction of a negative number process.
• Then, by converting it to addition, we streamlined the expression to \(0 + 1\).

This simplification step is not just about numbers; it's about reorganizing parts of an expression according to mathematical principles to get clearer results. Always look for ways to apply known rules, like combining like terms or changing subtraction to addition when involving negatives, to make expressions simpler. Approach each expression with the goal of making it as straightforward as possible.

Addition of Integers in Practice

Adding integers involves considering both positive and negative numbers. When integers have different signs, the addition process determines the final sign based on the larger absolute value. However, when both integers are positive or both are negative, their addition is straightforward. In the original expression

• \( 0 + 1 \)

adding these integers involves straightforward addition since both are either positive or effectively neutral. To add 0 and 1, simply take the larger integer value, which in addition simplifies quickly to 1. Always ensure your basic operations like addition are performed accurately, as they form the basis for solving more complicated mathematical problems. Practice regularly to become proficient in identifying when to use addition rules effectively, especially with varying integer signs.