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Chapter 3: Problem 23

How should the real numbers be read ? (Write in words.) $$ -(-1) $$

Short Answer

Expert verified
Answer: The expression -(-1) can be read as "the negative of negative one" or "the opposite of negative one." The simplified form of the expression is 1.

Step by step solution

01

Understanding the expression

In the given expression, -(-1), we have a double negation. The negative sign inside the brackets is applied to -1, and the negative sign outside the brackets is applied to the whole expression.
02

Reading the expression in words

The expression $$-(-1)$$ can be read as "the negative of negative one" or "the opposite of negative one." In either case, the meaning is that we are negating the negative value, which results in a positive value.
03

Simplifying the expression

Since a double negative results in a positive value, the simplified expression is $$1$$.

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Key Concepts

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

Understanding Double Negation
Double negation in mathematics might seem tricky at first, but it's actually quite simple. When you have two negative signs applied to a number or variable, they cancel each other out. This is commonly encountered in expressions like \(-(-1)\).

In this expression, the first negative sign turns a positive into a negative, while the second negative changes a negative back into a positive.
Think of it as the mathematical equivalent of reversing direction twice on a road: you end up going the original way you started.

Key details to remember:
  • Two negatives make a positive.
  • Applicable to real numbers and variables.
  • Think of it as "undoing" a negation.
Approaching double negation with these points in mind can help demystify complex expressions and provide clarity in solving problems.
Simplifying Expressions
Expression simplification is a crucial skill in algebra. It involves transforming an expression into a simpler or more concise form. In the case of expressions like \(-(-1)\), simplifying is about recognizing patterns and applying rules.

The expression begins with a double negation, which we previously noted cancels itself out, leaving us with a positive result: 1.
Steps to simplify any expression include:
  • Identify and resolve any double negations.
  • Perform arithmetic operations as necessary.
  • Combine like terms, if applicable.
  • Check and verify the simplified expression is equivalent to the original.
Facilitating these steps helps make complex equations manageable, ensuring accuracy and enhancing problem-solving skills.
Working with Negative Numbers
Negative numbers are integral to mathematics. They extend the number line below zero and are essential in various contexts, from accounting to physics.

When dealing with negative numbers, it鈥檚 important to understand the effect of negative signs. A single negative sign changes a positive number to its opposite, a negative one. For example, the number \(-1\) is simply negative one.
Double negatives, as mentioned before, will revert the number to its positive form.

Important facts about negative numbers:
  • Represent a loss or absence of quantity.
  • Used in temperature scales, elevation measurements, etc.
  • Follow specific arithmetic rules (e.g., multiplying two negatives results in a positive).
Handling negative numbers confidently enables you to solve a wide range of mathematical problems effectively.

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Most popular questions from this chapter

Convert the following numbers to standard form. $$ 1.2 \times 10^{-1} $$

Find the value of each of the following expressions. $$ \frac{-1(3+2)+5}{-1} $$

Find the value of each of the following expressions. $$ 3(4-6) $$

Perform the following operations. $$ \left(6 \times 10^{14}\right)\left(6 \times 10^{-10}\right) $$

For the following problems, convert the numbers from scientific notation to standard decimal form. Rubik's cube has about \(4.3 \times 10^{19}\) different configurations.
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