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Chapter 1: Problem 14

In Exercises \(1-72\), compute the value of each expression. $$4-(-9)$$

Short Answer

Expert verified
13

Step by step solution

01

- Identify the Operation

Observe that the expression involves subtraction and a negative number inside the parentheses: 4 - (-9).
02

- Apply the Rule for Subtracting Negative Numbers

Recall that subtracting a negative number is the same as adding its positive counterpart. That is, 4 - (-9) is the same as 4 + 9.
03

- Perform the Addition

Add the two numbers together: 4 + 9 = 13.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subtracting Negative Numbers
Subtracting a negative number can initially seem confusing, but it follows a simple rule. When you see an expression like 4 - (-9), you should know that subtracting a negative number is the same as adding its positive counterpart. This means that 4 - (-9) becomes 4 + 9. This rule works because subtracting a negative number effectively cancels out the negative sign, resulting in addition.

Here's a quick way to remember this: when you have a double negative (like -(-x)), it turns into a positive. So always replace the double negative with a plus sign for easier computation.
Addition
Addition is a fundamental operation in arithmetic, and it involves finding the total sum of two or more numbers. In our exercise, after transforming the subtraction of a negative number into an addition, we simply add 4 and 9.

This step is very straightforward. You add the two numbers together: 4 + 9. When performing addition, you can visualize it by counting up from one number to the other.

So, starting at 4, you count nine steps forward: 5, 6, 7, 8, 9, 10, 11, 12, 13. Hence, 4 + 9 equals 13.
Basic Arithmetic Operations
Understanding basic arithmetic operations is crucial for solving more complex mathematical problems. The four basic operations are:
  • Addition (+)
  • Subtraction (-)
  • Multiplication (脳)
  • Division (梅)


In this problem, we specifically dealt with subtraction and addition. Subtraction can sometimes involve negative numbers, which can be tricky. Whenever it does, remember that subtracting a negative number is equivalent to addition.

The simplified problem was an addition of 4 and 9, which are positive integers and straightforward to calculate. To master these operations, practicing various problems will help you become proficient and confident in handling arithmetic challenges.

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