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Chapter 1: Problem 13

Find each sum. $$ -5+(-7) $$

Short Answer

Expert verified
-12

Step by step solution

01

- Understand the Problem

The task is to find the sum of -5 and -7. Remember that adding negative numbers means moving further to the left on the number line.
02

- Combine the Numbers

When adding two negative numbers, you add their absolute values (ignore the negative signs for now) and then add the negative sign to the result. Here, combine 5 and 7.
03

- Calculate the Sum

Add 5 and 7 to get 12. Since both numbers were negative, the result will also be negative. Therefore, -5 + (-7) equals -12.

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Key Concepts

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

Negatives on Number Line
To understand how to add negative numbers, let's first look at the number line. A number line is a straight line with numbers placed at equal intervals along its length. Zero is at the center, positive numbers are to the right, and negative numbers are to the left.

When you add a negative number, you move to the left on the number line. For example, if you start at 0 and add -3, you move three steps to the left, landing on -3.
  • Adding -5 means moving 5 steps left from your starting point.
  • Adding another -7 means moving another 7 steps left.
So when you add -5 and -7, you move a total of 12 steps to the left, starting from 0. This is why -5 + (-7) equals -12.
Absolute Values
Understanding absolute values is crucial when adding negative numbers. An absolute value of a number is its distance from zero on the number line, regardless of direction or sign.

Here's how it works:
  • The absolute value of -5 is 5 because it is 5 steps away from zero.
  • Similarly, the absolute value of -7 is 7.
When you're asked to add -5 and -7, you can first consider their absolute values. Add these absolute values together: 5 + 7 = 12. This gives you the total distance moved on the number line.
Since both starting numbers were negative, your result also takes a negative sign, making the sum -12.
Combining Numbers
Now, let's talk about combining negative numbers. The key steps involve:
  • Identifying the absolute values of the numbers involved.
  • Combining these absolute values.
  • Applying the negative sign to the result.
In the exercise, we combined -5 and -7. Our first step was adding their absolute values: 5 + 7, which equals 12.
The final step is to bring back the negative sign to our combined result.
So, -5 + (-7) = -12.

By following these steps, you can easily handle adding negative numbers and working with their sums on a number line.

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Most popular questions from this chapter

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(-15,29,8,-6\)

Write a numerical expression for each phrase and simplify. 8 less than \(-2\)

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Perform each indicated operation. $$ |-4-2|-|-8-1| $$
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