Problem 3 Find the value of \(-(-13)\) \... [FREE SOLUTION]

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Chapter 2: Problem 3

Find the value of \(-(-13)\) \(A .-13\) B. 0 c. \(-(+13)\) D. 13

Short Answer

Expert verified

The value of \(-(-13)\) is 13, answer D.

Step by step solution

Identify the Problem

The problem asks us to find the value of a double negative expression, specifically \(-(-13)\).

Understand Negative Signs

A negative sign in front of a number means the opposite of that number. Therefore, when you have a double negative, it just means the opposite of the opposite, which brings you back to the original value.

Apply Double Negative Rule

The double negative in \(-(-13)\) cancels out, so we simplify this to just \(13\).

Choose the Correct Answer

Based on the simplification, \(-(-13)\) is equivalent to \(13\). Therefore, the correct answer is option D. 13.

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Key Concepts

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

Understanding Negative Numbers

Negative numbers are pivotal in mathematics as they depict values less than zero. They are crucial in various mathematical operations and are represented with a minus sign (-) before a number. This characteristic implies a direction or position that opposes a positive value.
Negative numbers find common usage in contexts like temperatures below freezing, depths below sea level, or financial debts.

In the number line, negative numbers appear to the left of zero.
The further to the left a number is, the smaller its value.
Operations involving negative numbers must consider the basic arithmetic rules, specifically understanding that they can alter the direction or sense relative to positive values.

The Principle of Double Negatives

Double negatives can initially seem perplexing, but they present a straightforward concept: they cancel each other out. This means that two negative signs transform into a single positive sign, restoring the number to its original value. In expressions such as \(-(-13)\), the first negative sign indicates taking the opposite of what follows, while the second negative sign again indicates taking the opposite of that result.

This can be understood as the opposite of "the opposite of 13," leading us back to 13.
Visualize it like this: if facing south is negative and north is positive, then double negation implies returning to facing north.
In mathematical operations, resolving double negatives is essential in simplifying expressions effectively.

Opposite Values and Their Roles

Opposite values hold a key role in arithmetic operations, especially when dealing with integers. The concept of opposites is essential for mastering integer operations, zeroing in particularly on how numbers relate symmetrically around zero.
Every integer has an opposite, which is the same distance from zero on the number line but in the opposite direction.

If you take the opposite of a positive number, you get its negative counterpart and vice versa.
For example, the opposite of 13 is -13, and likewise, the opposite of -13 is 13.
Recognizing opposite values helps particularly in solving equations and simplifying expressions.

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91影视

Find the value of \(-(-13)\) \(A .-13\) B. 0 c. \(-(+13)\) D. 13

Short Answer

Step by step solution

Identify the Problem

Understand Negative Signs

Apply Double Negative Rule

Choose the Correct Answer

Key Concepts

Understanding Negative Numbers

The Principle of Double Negatives

Opposite Values and Their Roles

One App. One Place for Learning.

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