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Chapter 5: Problem 562

In the following exercises, add or subtract. $$ -6.4+(-2.9) $$

Short Answer

Expert verified
-9.3

Step by step solution

01

- Understand the problem

The given exercise requires finding the sum of two negative numbers: -6.4 + (-2.9).
02

- Add the absolute values

Since both numbers are negative, add their absolute values together: Absolute value of -6.4 is 6.4 and absolute value of -2.9 is 2.9. So, 6.4 + 2.9 = 9.3.
03

- Apply the sign

Since both original numbers were negative, the sum will also be negative. Therefore, the sum of -6.4 and -2.9 is -9.3.

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Key Concepts

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

absolute values
When you see a negative number, you are looking at a value that's less than zero. These can be tricky at first. But breaking them down into absolute values makes things simpler.

The absolute value of a number is the distance from zero, ignoring its sign. For example, the absolute value of -6.4 is 6.4, and for -2.9, it is 2.9. This means that we only consider their magnitude or size without worrying about the negative sign.

Absolute values are always positive or zero. When we deal with negative numbers in calculations, understanding their absolute values helps simplify the process.
sum of negative numbers
Adding negative numbers can sometimes seem difficult, but it鈥檚 quite straightforward once you understand the rules.

When you are asked to add two negative numbers, focus on their absolute values first. Like in our exercise, we have -6.4 and -2.9.
  • First, find their absolute values: 6.4 and 2.9.
  • Then, add these absolute values together: 6.4 + 2.9 = 9.3.
So far, we鈥檝e added their magnitudes together.
The final step, which we will discuss next, involves applying the negative sign to the result.
negative sign
The role of the negative sign in addition is crucial to understand. When adding two negative numbers, their sum retains the negative sign.

In our example, we added the absolute values to get 9.3. Since both original numbers, -6.4 and -2.9, are negative, we apply the negative sign to our result. This gives us -9.3.

Always remember: When adding negative numbers, the result is always more negative because you are essentially combining two 'debts'. The more you add, the bigger the debt, hence the sum becomes more negative.

So in summary:
  • Find the absolute values
  • Add the magnitudes
  • Apply the negative sign to the result
This will give you the correct sum of the negative numbers.

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