Problem 57 - Elementary Algebra

Question

Rewrite the problem in a simpler form. $$ 24-(-8)-(-13) $$

Step-by-Step Solution

Answer

Question: Simplify the given expression: 24 - (-8) - (-13). Answer: 45

Step 1: Identify negative numbers

Observe the given expression: $$ 24-(-8)-(-13) $$ Here, we have two negative numbers, -8 and -13.

Step 2: Apply the rule for subtraction of negative numbers

Recall the rule for subtracting negative numbers: $$a - (-b) = a + b$$ So, we can rewrite the expression as follows: $$ 24 - (-8) - (-13) = 24 + 8 + 13 $$

Step 3: Simplify the expression

Now, we just need to add the numbers: $$ 24 + 8 + 13 = 45 $$ So, the simplified form of the given expression is 45.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are usually represented with a minus sign (-) in front of them. In the context of our exercise, we have two negative numbers: -8 and -13.

• The "negative" sign signifies a value below zero, often implying a removal or loss.
• Negative numbers play a crucial role in mathematics as they help us perform subtraction.

Handling negative numbers requires understanding their impact on operations. For instance, subtracting a negative number is the same as adding its positive counterpart. This is crucial for algebraic manipulation and solving equations correctly.

Subtraction Rules

Subtraction in mathematics is often about finding the difference between numbers. However, when dealing with negative numbers, subtraction rules require special attention. One key rule to remember is:

• Subtracting a negative number is equivalent to addition.
• This means if you see an expression like \(24 - (-8)\), it transforms to \(24 + 8\).

This rule may seem counterintuitive at first, but it stems from the fact that subtracting negative is akin to removing a debt, thus increasing the total. Always convert subtracting a negative to addition to simplify calculations in solving problems.

Simplification of Expressions

Simplifying expressions is the process of making an algebraic expression cleaner and more concise. In our example, after applying the subtraction rules, the expression \(24 - (-8) - (-13)\) becomes \(24 + 8 + 13\).

• Add the numbers sequentially: \(24 + 8 = 32\), then \(32 + 13 = 45\).
• Ensure all operations follow the correct mathematical principles to avoid mistakes.

The goal of simplification is to reduce complexity and make expressions easier to understand and work with. Always check your steps to confirm that each transformation is accurate, leading to the correct simplified form.