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Chapter 1: Problem 11

Find each sum. $$ -6+(-2) $$

Short Answer

Expert verified
-8

Step by step solution

01

Identify the Numbers

The problem is asking for the sum of two negative numbers: -6 and -2.
02

Combine the Negatives

When summing negative numbers, add their absolute values and keep the result negative. Here, the absolute values are 6 and 2.
03

Add the Absolute Values

Add 6 and 2: 6 + 2 = 8
04

Apply the Negative Sign

Since both original numbers were negative, the sum will also be negative. Thus, -6 + (-2) = -8.

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Key Concepts

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

Absolute Values
Absolute values are the distance a number is from zero on the number line, without considering the direction. For instance, the absolute value of -6 is 6, and the absolute value of -2 is 2. We denote the absolute value of a number 'a' as \( |a| \).
Here鈥檚 why understanding absolute values is important when dealing with negative numbers:
  • They help us focus on the size of the number without worrying about the sign.
  • When adding or subtracting numbers, absolute values make it easier to handle the calculation.
So, in our problem, the absolute values of -6 and -2 are 6 and 2 respectively.
Negative Numbers
Negative numbers are numbers less than zero, represented with a minus sign (-). These numbers can be a bit tricky, but here鈥檚 what you need to know:
  • When you add negative numbers, you essentially combine their absolute values and keep the sign negative.
  • Understanding how negative numbers behave is crucial in both basic arithmetic and advanced mathematics.
For example, if we have -6 and -2 and want to add them, we think of how far each number is from zero, add those distances, and then apply the negative sign back again. In our problem, -6 + (-2) requires us to first add their absolute values: 6 + 2 = 8. Since both numbers are negative, we finally make the sum negative, resulting in -8.
Sum of Integers
Summing integers involves combining the values of the numbers while considering their signs.
If the numbers have the same sign, like our problem with -6 and -2, the steps are:
  1. Identify the absolute values of the numbers.
  2. Add the absolute values together.
  3. Apply the common sign (in this case, negative) to the result.
If the numbers have different signs, you鈥檒l:
  1. Identify the absolute values.
  2. Subtract the smaller absolute value from the larger one.
  3. Use the sign of the larger absolute value for the result.
Practicing with different integer sums and getting familiar with their behavior will greatly improve your fundamental math skills.

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