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Chapter 1: Problem 58

In Exercises \(1-72\), compute the value of each expression. $$-6-(-6)$$

Short Answer

Expert verified
The value of the expression is 0.

Step by step solution

01

Understand the Problem

The exercise requires computing the value of the expression -6 - (-6). It involves basic arithmetic operations.
02

Recognize Double Negative

Notice there is a double negative in the expression. Subtracting a negative number is the same as adding its positive counterpart.
03

Simplify the Expression

Rewrite the expression by changing the subtraction of the negative number to addition: -6 - (-6) = -6 + 6.
04

Perform the Addition

Add the numbers together: -6 + 6 = 0.

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Key Concepts

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

Double Negative
When you see a negative sign in front of another negative number, it's called a 'double negative.' For example, when you see -(-6), it's like saying 'the opposite of negative 6.' Another way to think of it is that two negatives cancel each other out. Just like in real life where a 'no' to a 'no' often means 'yes,' in math, -(-6) becomes +6. Double negatives can be tricky at first, but with practice, they become easy to handle. Remember, when you subtract a negative number, it's the same as adding its positive counterpart.
Subtracting Negative Numbers
When you subtract a negative number, you're essentially adding a positive. This concept can be confusing but becomes clear with an example. Let's look at the problem -6 - (-6). As soon as you see the negative signs next to each other, replace it with a plus sign. So, -6 - (-6) turns into -6 + 6.Think of 'subtracting negative numbers' as actually 'adding' the positive version. If it helps, visualize it on a number line. Moving left for negative and right for positive. Subtracting a negative means you move to the right, just like adding.
Addition
Once you understand the impact of double negatives and subtracting negatives, the final step is addition. If your question turned into something like -6 + 6, then all you need to do is perform a simple addition.The rules of addition are straightforward. If both numbers are positive, their sum is positive. If both are negative, their sum is negative. In this case, we have -6 + 6. Since you are adding a positive to a negative of the same absolute value, they cancel each other out and total zero. This problem shows how addition can simplify seemingly complex operations. Understanding these concepts makes arithmetic clearer and even enjoyable. Happy calculating!

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$\frac{24-4 \cdot 5+8}{2+3 \cdot 6-4 \cdot 2}$$

In Exercises \(1-72\), compute the value of each expression. $$-561-412-(-678)$$

Evaluate the given expression. Remember to follow the order of operations. $$30-5(4-2)$$

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Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-6}{1.5}+\frac{21.6}{-1.2}$$
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