Problem 53 Simplify. $$ -(-43) $$... [FREE SOLUTION]

Chapter 2: Problem 53

Simplify. $$ -(-43) $$

Short Answer

Expert verified

The simplified form is 43.

Step by step solution

Understand the Problem

The problem asks us to simplify the expression $-(-43)$. This is a multiplication of a negative sign by a negative number, based on the rule of integers.

Apply the Rule of Double Negation

In mathematics, the rule of double negation states that a double negative makes a positive. Therefore:$-(-43) = 43$ This is because negating a negative number results in a positive number.

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Key Concepts

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

Double Negation

Double negation is a fascinating concept in mathematics. It refers to the rule that two negative signs will cancel each other out and result in a positive.
When you see the expression $-(-43)$, you apply the double negation rule by changing the double negative into a positive.
This is because the first "-" changes the number to its opposite, and then the second "-" flips it back again. Essentially, you're just reversing the reversal, bringing you back to the original positive number.

Example: $-(-x) = x$
Another Example: $-(-5) = 5$

This concept is important and frequently used in algebra and arithmetic to simplify expressions efficiently.

Simplification

Simplification is the process of reducing an expression to its simplest form. This often means performing operations to make an expression more concise.
In the given exercise, simplification involves understanding the operation and applying the rule effectively.
For instance, when simplifying $-(-43)$, we focused on reducing the negative signs to their simplest form, which is a single positive sign.
This helps in making calculations easier and more understandable.

Aim for the least number of operations.
Focus on clear and direct outcomes, like changing $-(-a)$ to $a$.

Through simplification, we achieve clarity and precision in solving mathematical problems.

Negative Numbers

Negative numbers are values less than zero, often represented with a "-" sign ahead of them. They are an essential part of mathematics, often used to represent debt, temperatures below zero, and other sub-zero conditions.
Understanding operations involving negative numbers is crucial.
When you negate a negative number, like in $-(-43)$, the two negations create a positive number.

Negative and positive numbers obey certain rules.
For instance, adding a negative is like subtracting a positive of the same value.
Multiplying two negative numbers results in a positive product.

Mastering these rules and understanding their applications can make working with integers seamless and straightforward.

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91影视

Simplify. $$ -(-43) $$

Short Answer

Step by step solution

Understand the Problem

Apply the Rule of Double Negation

Key Concepts

Double Negation

Simplification

Negative Numbers

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