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Chapter 2: Problem 129

Perform the indicated operations. $$ -8-20 $$

Short Answer

Expert verified
-28

Step by step solution

01

Understanding the Expression

The given expression is \(-8 - 20\). This is a subtraction expression where you subtract 20 from -8.
02

Rearrange the Expression

Rewrite the expression by thinking of subtraction as adding a negative. This gives us: \(-8 + (-20)\).
03

Perform the Addition

When adding two negative numbers, you add their absolute values and the result is negative. Calculate: \(8 + 20 = 28\); Thus, the result is \(-28\).

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Key Concepts

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

Subtraction of Integers
Subtraction of integers is a fundamental arithmetic operation that involves finding the difference between two numbers. When subtracting, it is often helpful to think of subtraction as the addition of a negative number. For instance, the expression
  • \(-8 - 20\) can be thought of as \(-8 + (-20)\).

This helps simplify the operation to a point where only addition is involved. In doing so, you just need to add the negative number to the first, making it easier to calculate the difference. This alternate view is especially useful when handling negative operands.
Remember:
  • Subtracting a positive number is the same as adding its negative equivalent.
Addition of Negative Numbers
Adding negative numbers follows a straightforward procedure. It involves combining the absolute values then attaching a negative sign to the result. Consider two numbers, both less than zero. Their absolute values are simply the positive measures of those numbers without considering the negative sign. In essence, you sum the absolute values and then make the result negative again.
For example:
  • Add \(-8\) and \(-20\).
  • The absolute values are 8 and 20.
  • Thus, \(8 + 20 = 28\).
The result of adding \(-8\) and \(-20\) is therefore \(-28\). This method allows you to treat complex numbers as simpler positive values before reassessing their overall negative status.
Absolute Values in Arithmetic
Absolute values represent the magnitude of a number without considering its sign. It is denoted by two vertical bars, for example, \(|-8| = 8\). Absolute values are crucial in handling operations involving negative numbers as they provide a framework for measuring distance from zero on a number line.
  • The absolute value of any number removes the negative sign.
  • In calculations, always convert negative numbers to positive when seeking their absolute value.

Using absolute values helps clarify calculations, particularly in complex arithmetic operations. They are especially useful in determining the size of the difference when working with subtraction and addition of negative numbers. By focusing on the size (absolute value) of the numbers, arithmetic operations become less prone to errors.

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Most popular questions from this chapter

Graph each integer in the list on the same number line. $$ 0,3,10,11 $$

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Simplify. $$ -|-18| $$

Evaluate: \((-|-(-7)|)\)
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