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Chapter 1: Problem 112

How is \(4-(-2)\) read?

Short Answer

Expert verified
The expression '4 minus negative 2' simplifies to 6.

Step by step solution

01

Understand the Problem

First, note that there are two different operations: subtraction and a negative. Note that subtraction of a negative is the same as addition.
02

Apply rules for subtracting negatives

The problem is \(4 - (-2)\). According to the rule for subtracting negatives, this can be rewritten as \(4 + 2\)
03

Simplify

Now simplified it becomes \(6\)

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Key Concepts

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

Understanding Mathematical Operations
Understanding different mathematical operations is crucial when dealing with problems like the subtraction of negative numbers. In mathematics, the key operations include addition, subtraction, multiplication, and division. Each has its own set of rules and operations, making it important to distinguish between them. For instance, subtraction is represented by the minus sign (-), whereas addition is represented by the plus sign (+). However, when negative signs come into play within subtraction, the meaning shifts slightly. Recognizing these signs and understanding their implications is vital for simplifying any mathematical expression accurately.
Rules for Subtracting Negatives
The operation of subtracting a negative number might initially seem puzzling, but there's a straightforward rule to follow: subtracting a negative is the same as addition. Here's why:

  • When you see two minus signs next to each other, one representing subtraction and the other a negative number, it turns into a plus sign.
  • For example, in the problem \(4 - (-2)\), the double negative \((- -)\) changes to a plus, rewriting the expression as \(4 + 2\).
  • This transformation simplifies the operation, making it equivalent to adding two numbers together.
These rules help simplify your calculations and let you transform a seemingly complex expression into a simple arithmetic operation.
Simplifying Mathematical Expressions
After applying the rules and understanding the signs, the next step is to simplify the mathematical expression. Simplification is the process of reducing an expression to its simplest form, where no further operations can be performed. In our example, after applying the rule of subtracting negatives, we got the expression \(4 + 2\).

  • First, identify the operations needed to solve the problem after transformation; in this case, it's simply addition.
  • Perform the arithmetic: \(4 + 2 = 6\).
  • Thus, the simplified form of \(4 - (-2)\) is 6, as \(4 + 2\) equals 6.
Simplifying makes calculations manageable and helps ensure precision, especially in larger, more complex problems.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(x\) is \(-3,\) then the value of \(-3 x-9\) is \(-18\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The value of \(\frac{|3-7|-2^{3}}{(-2)(-3)}\) is the fraction that results when \(\frac{1}{3}\) is subtracted from \(-\frac{1}{3}\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The algebraic expression \(\frac{6 x+6}{x+1}\) cannot have the same value when two different replacements are made for \(x\) such as \(x=-3\) and \(x=2\)

Simplify: \(-8-2-(-5)+11 .\) (Section \(1.6,\) Example 3 )

Why is the order of operations agreement needed?
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