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Chapter 1: Problem 62

Find each difference. $$ 9-(-2) $$

Short Answer

Expert verified
The difference is 11.

Step by step solution

01

Understand the Problem

The exercise requires finding the difference between the numbers 9 and -2. This involves the operation of subtracting a negative number.
02

Rewrite the Expression

Subtracting a negative number is the same as adding its positive counterpart. Therefore, we rewrite the expression as: \( 9 - (-2) = 9 + 2 \)
03

Perform the Addition

Now, simply add the two numbers: \( 9 + 2 = 11 \)
04

State the Result

The result of the expression \( 9 - (-2) \) is 11.

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Key Concepts

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

algebra subtraction
In algebra, subtraction operates under specific rules, especially when involving negative numbers. We often see problems like 9 - (-2), which may look tricky at first. To solve these, the key is to understand that subtracting a negative number is equivalent to adding its positive counterpart. When we change the subtraction of a negative number to addition, it simplifies the process.

For example, consider the expression 9 - (-2). Subtracting -2 is the same as adding 2. This changes it to 9 + 2. The fundamentals of algebra subtraction hold this transformation as a core principle, making it easier to work with equations involving negative numbers.
basic arithmetic
Basic arithmetic, the foundation of mathematics, includes operations like addition, subtraction, multiplication, and division. A common confusion arises when these operations involve negative numbers. Subtracting a negative number is an important concept.

In the expression given, 9 - (-2), we use basic arithmetic rules: changing the subtraction of a negative to addition. This is crucial for correctly solving arithmetic problems.

Let's look at it step-by-step:
  • Rewrite the subtraction: 9 - (-2) becomes 9 + 2.
  • Then, perform the simple addition: 9 + 2 = 11.
Understanding these steps is essential for mastering arithmetic operations.
negative numbers
Negative numbers are numbers less than zero, commonly represented with a minus sign (-). Adding and subtracting them follow particular rules which can initially feel non-intuitive.

For instance, when subtracting a negative number, you are essentially adding its positive counterpart. With 9 - (-2), the two negative signs (one from subtraction and one from the negative number) combine to form a positive, making it 9 + 2. This rule arises because the operation 'subtracting a negative' negates the minus, similar to how removing a debt increases your total.

For clarity:
  • Start with identifying the operation: subtraction of a negative.
  • Convert it: subtracting -2 is adding 2.
  • Finally, add: 9 + 2 = 11.
Grasping these rules helps handle negative numbers confidently in complex equations.

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Most popular questions from this chapter

Use the distributive property to rewrite each expression. $$ -8(r+3) $$

Write a numerical expression for each phrase, and simplify the expression. The sum of 12 and \(-7,\) decreased by 14

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. (a) Is 2,287,321 divisible by \(9 ?\) (b) Is 4,114,107 divisible by \(9 ?\)

Twice the product of -1 and \(6,\) subtracted from -4

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \((6-x)(5+y)(3+a)\)
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