Problem 35 - Fundamentals of Mathematics

Question

For the following 6 problems, rewrite each number in simpler form. $$ 6-(-4) $$

Step-by-Step Solution

Answer

10

Step 1: Understand the Expression

The problem asks us to simplify the expression \(6 - (-4)\). It involves a subtraction of a negative number.

Step 2: Recognize the Mathematical Rule

Remember that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, \(a - (-b) = a + b\).

Step 3: Apply the Rule

Using the rule, we can convert \(6 - (-4)\) into \(6 + 4\). This is because subtracting \(-4\) is the same as adding \(+4\).

Step 4: Perform the Addition

Now, add the numbers: \(6 + 4 = 10\).

Step 5: Write the Simplified Answer

The simplified form of the expression \(6 - (-4)\) is 10.

Key Concepts

Understanding Negative Numbers

Negative numbers can be a bit tricky, but once you get the hang of them, they aren't hard to understand. In mathematics, negative numbers represent values that are less than zero. They have the ability to reverse direction or, in a more practical sense, indicate something like a debt or temperature below freezing. Here’s something important to remember: - **Negative numbers are always shown with a minus sign in front**. For example, (-4) is four units below zero on a number line. - Additionally, when adding and subtracting negative numbers, things can get interesting. The interplay between positive and negative values is crucial, especially in expressions. With negative numbers, flipping the sign as needed—such as subtracting a negative which becomes adding a positive—is often key to simplifying expressions.

Simplifying Expressions

Simplification of expressions simply means making them easier to understand or work with. This often involves performing operations or rewriting expressions in more familiar terms. Let’s simplify the expression in our exercise:1. Start with the given expression: - Example: Simplify \(6 - (-4)\).2. Recognize the involved operations: - Here, we are dealing with subtraction of a negative number.3. Apply mathematical rules to simplify: - Use the rule that states: subtracting a negative is equivalent to addition.4. Write it in a simpler form: - Rewrite \(6 - (-4)\) as \(6 + 4\).This simplification helps everyone quickly see the straightforward arithmetic behind the expressions, making math easier to manage!

Mathematical Rules in Subtraction

When dealing with subtraction in expressions, understanding the math rules is vital. The rule that is often highlighted is with negative numbers. Let's take a closer look:- **Subtracting a Negative Number**: - The rule states that subtracting a negative number is the same as adding the positive version of that number. - This can be visualized on a number line: moving to the right when subtracting negative numbers. - For instance, converting \(6 - (-4)\) into \(6 + 4\) simplifies the calculation.The essence of these rules is to ease the process of working with expressions, especially when negative numbers are present. By applying these rules consistently, you can confidently simplify even the most complex expressions. It's all about removing that negative to reveal a positive result!