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Chapter 1: Problem 66

Subtract. $$ 0-(-1) $$

Short Answer

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Step by step solution

01

Identify the Operation

Look at the problem and identify that you need to subtract -1 from 0, which can be rewritten as follows: 0 - (-1).
02

Understand Double Negatives

Realize that subtracting a negative number is the same as adding the absolute value of that number. Therefore, 0 - (-1) becomes 0 + 1.
03

Perform the Addition

Now, perform the addition: 0 + 1 = 1.

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Key Concepts

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

Understanding Double Negatives
When we come across double negatives in math, it can initially seem confusing. The term 'double negative' refers to having two negative signs in a row. In this problem, we have the expression 0 - (-1). The two negative signs here change the operation.
Instead of subtracting, double negatives indicate that we need to add. In this case, subtracting -1 from 0 is the same as adding 1 to 0. Why? Because subtracting a negative number effectively becomes addition. Think of it as turning the direction of subtraction around.
This leads to our next step: 0 - (-1) which simplifies to 0 + 1. The concept of double negatives is key to solving such problems easily.
Understanding Absolute Value
The absolute value of a number is its distance from zero on the number line, without considering the sign. In other words, the absolute value of any number is always positive. The absolute value of -1 is written as \(|-1|\) and equals 1.
So in the problem 0 - (-1), when we change the operation from subtraction of a negative number to addition, we focus on the absolute value. Subtracting -1 from 0 becomes adding the absolute value of -1, which is 1.
Applying this, we get 0 + 1. Absolute values help us see numbers without their signs and simplify our calculations.
Performing Simple Addition
Once we understand that 0 - (-1) becomes 0 + 1 using the concepts of double negatives and absolute value, our task is to perform a simple addition.
Let's break it down: Adding 0 and 1 is straightforward. We start at 0 on the number line and move one step to the right, which lands us at 1.
Therefore, 0 + 1 equals 1. It's important to understand each part of the process, but in the end, being comfortable with addition helps us quickly reach the correct answer.

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