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Chapter 10: Problem 7

Subtract. $$ -10-(-10) $$

Short Answer

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Step by step solution

01

Understand the Given Expression

The given expression is \( -10 - (-10) \). It involves subtracting a negative number.
02

Simplify the Subtraction of a Negative Number

Subtracting a negative number is equivalent to adding its positive counterpart. So, \( -10 - (-10) \) becomes \( -10 + 10 \).
03

Perform the Addition

Now, add the numbers together: \( -10 + 10 = 0 \).

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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 numbers that are less than zero. They have a '-' sign in front of them, like -1, -2, and -10. These numbers are used to represent values below a baseline, like temperatures below freezing or losses in finances. When we subtract or add negative numbers, it鈥檚 important to keep track of these signs to get the correct result. For instance, -10 is 10 units below zero on the number line.
Simplifying Expressions with Negative Numbers
Simplifying expressions involves reducing them to a simpler form which is easier to work with. When working with negative numbers, we often use some key rules:
  • Subtracting a negative number is the same as adding the number's positive counterpart. For example, in the expression -10 - (-10), subtracting -10 is the same as adding 10, making it -10 + 10.
  • Combining like terms: When working with expressions, combine terms that have the same variable part. This does not specifically apply here, but it is a crucial part of simplification in algebra.
Addition of Integers with Different Signs
Adding integers with different signs might seem tricky, but it's quite straightforward if you follow these steps:
1. Determine the absolute values of the numbers (ignore the signs temporarily).
2. Subtract the smaller absolute value from the larger absolute value.
3. Give the result the sign of the integer with the larger absolute value.
Let's look at our example: -10 + 10. Here, both numbers have the same magnitude (absolute value) but opposite signs. On subtracting the smaller from the larger, we get 0, which is neutral. Hence, -10 + 10 equals 0.

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