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Chapter 1: Problem 14

Perform the indicated subtraction. \(-21-(-3)\)

Short Answer

Expert verified
The result of the operation \(-21-(-3)\) is -18.

Step by step solution

01

Identify the Numbers

The two numbers that are involved in this operation are -21 and -3.
02

Understand the Double Negative

A double negative, --, can be replaced with a + symbol. Therefore, the expression \(-21 - (-3)\) becomes \(-21 + 3\).
03

Perform the Operation

Perform the operation with these two numbers: \(-21 + 3 = -18\).

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Key Concepts

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

Negative Numbers
Negative numbers are a fundamental concept in mathematics, representing values less than zero. They are the opposite of positive numbers and are typically written with a minus sign (鈭�) in front. Negative numbers are essential for showing loss, debt, decline, or any context where a decrease from a reference point is necessary.

When working with negative numbers, it is important to recognize that they follow specific arithmetic rules. For example:
  • Adding a negative number is like subtracting the corresponding positive number. For instance, adding \(-3\) to a number is the same as subtracting 3.
  • Subtracting a negative number can be compared to adding its positive counterpart.
  • Multiplying or dividing two negative numbers results in a positive number, while doing so with one negative and one positive number results in a negative number.
Understanding these rules helps with performing arithmetic operations involving negative numbers, such as subtraction, as demonstrated in exercises like \(-21 - (-3)\).
Double Negative
The double negative is a concept that can initially seem confusing but is straightforward with practice. In mathematics, when you encounter two negative signs in a row, such as in subtraction operations, they can be transformed into a positive operation. This is because subtracting a negative number is equivalent to adding the opposite.
  • If you see \(-(-x)\), it changes to \(+x\).
  • This transformation makes complex expressions simpler and easier to solve. For example, \(-21 - (-3)\) simplifies to \(-21 + 3\).
Understanding and applying the concept of a double negative is crucial for solving mathematical problems accurately and efficiently.
Arithmetic Operations
Arithmetic operations encompass the basic mathematical procedures used for calculations: addition, subtraction, multiplication, and division. Each of these operations follows specific rules, particularly when negative numbers are involved.
  • For subtraction, it's essential to remember the effect of removing values. Hence, subtracting a larger number from a smaller one results in a negative outcome.
  • Addition, conversely, often involves combining quantities or values. When adding a smaller positive number to a larger negative number, the result will still be negative, but closer to zero.
In the exercise \(-21 - (-3)\), we initially deal with subtraction, but the manipulation of the double negative turns it into an addition problem: \(-21 + 3\). Calculating further, we find that the result of subtracting these values actually involves simple addition due to the double negative rule, yielding \(-18\). Understanding these basic operations and their rules allows for easier and more accurate problem-solving.

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Most popular questions from this chapter

Without using a number line, describe how to add two numbers with different signs. Give an example.

Write each phrase as an algebraic expression. a loss of half of an investment of \(d\) dollars

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. 8 added to the product of 4 and \(-10\)

In Exercises \(147-149,\) perform the indicated operation. \(-6+(-3)\) (Section \(1.7,\) Example 4 )

In each exercise, determine whether the given number is a solution of the equation. $$4 x+2=3(x-6)+8 ;-11$$
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