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Chapter 1: Problem 63

Subtract. $$ 5-(-12) $$

Short Answer

Expert verified
The result is 17.

Step by step solution

01

Identify the Operation

The problem given is to subtract: 5 - (-12). Notice that you are subtracting a negative number.
02

Apply the Rule of Subtracting Negatives

When subtracting a negative number, you add the absolute value of that number. Hence, 5 - (-12) becomes 5 + 12.
03

Perform the Addition

Now, simply add the two numbers together: 5 + 12 = 17.

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Key Concepts

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

Absolute Value
Absolute value refers to the distance of a number from zero on the number line, regardless of the direction. It is always a non-negative number. For instance, the absolute value of both -12 and 12 is 12. You can denote absolute value using vertical bars, like this: \(|-12|\) and \(|12|\). Absolute value is crucial because it helps in converting negative numbers into positive numbers, making operations like subtraction simpler. When solving the problem, understanding that the absolute value of -12 is 12 helps clarify why subtracting -12 is the same as adding 12.
Addition
Addition is one of the basic arithmetic operations. It involves combining two or more numbers to get a total sum. In the exercise, you convert the subtraction of a negative number into an addition. The subtraction of a negative number works by turning it into the addition of its absolute value. So, 5 - (-12) becomes 5 + 12. Here鈥檚 why: subtracting a negative is like removing a debt, which means you actually have more. Thus, you add the absolute value of the negative number. Adding 5 and 12 is straightforward: \(5 + 12 = 17\). This simple transformation makes even tricky-looking problems solvable.
Mathematical Operations
Mathematical operations, such as addition, subtraction, multiplication, and division, are the foundation of most math problems. To subtract negative numbers, you must switch the operation because subtracting a negative is equivalent to adding. Always remember to change the subtraction of a negative number to the addition of its absolute value.
Here is how it works:
  • Identify the original operation: 5 - (-12)
  • Change the subtraction of a negative number to addition: 5 + 12
  • Perform the addition: 5 + 12 = 17
Understanding these basics lets you consistently solve problems correctly.

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