Problem 11 - Elementary Algebra

Question

Simplify the following problems. $$ 4+(-6) $$

Step-by-Step Solution

Answer

Question: Simplify the expression 4 + (-6). Answer: -2

Step 1: Rewrite the expression as a subtraction problem

We can rewrite the given expression as a subtraction problem by changing the addition of a negative number to subtraction. $$ 4 + (-6) = 4 - 6 $$

Step 2: Subtract to simplify the expression

Now we will find the difference between the two numbers. $$ 4 - 6 = -2 $$ So the simplified result of the given expression is: $$ 4 + (-6) = -2 $$

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero, and they are represented with a minus sign (-). They are important in math because they help us express values below zero, such as temperatures or financial debts. Negative numbers can sometimes seem tricky, but they become easier to understand with practice.

When working with negative numbers, it's important to remember:

• A negative number + a positive number = subtraction, depending on magnitude.
• A negative number - a positive number means you're subtracting more from a debt or loss.
• Adding two negative numbers results in a more negative number.

In problems like the one given, where the operation involves both positive and negative numbers, it helps to rewrite it for clarity. This brings us to subtraction, which closely connects to negative numbers.

Subtraction

Subtraction is one of the basic arithmetic operations where you take a number away from another. In general, subtraction is the process of finding the difference between two numbers. Understanding subtraction becomes essential when you're working with both positive and negative numbers.

When you have a problem like "4 + (-6)", you can convert it into a simpler form:

• In our problem, "4 + (-6)" can be rewritten as "4 - 6".
• This conversion helps us see that it’s basically a subtraction that results in a difference.

Handling subtraction in practical terms can be like adjusting balances, where losing more (negative) than you have (positive) will result in a deficit or negative number. Here, the outcome is (-2) because six is more than four, and you end up with a negative difference.

Simplification

Simplification is the process of making a math expression easier to understand or solve by condensing it into a single value or a simpler form. It's like cleaning up a messy problem to find the core answer. In the original exercise, this involved two steps: rewriting and then computing the answer.

To simplify, you typically:

• Identify complicated parts of the expression (like mixed signs).
• Rewrite the expression in a simpler equivalent form.
• Perform standard arithmetic operations, like subtraction, to reach a concise answer.

By simplifying "4 + (-6)" to "4 - 6", you allow for an easier calculation. This process not only clears any confusion around negative numbers but also makes the solving process more straightforward. The ultimate aim of simplification is to present the solution in a neat and understandable manner, delivering clear results.