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Chapter 10: Problem 49

Add. Do not use the number line except as a check. $$ 76+(-15)+(-18)+(-6) $$

Short Answer

Expert verified
37

Step by step solution

01

Grouping the Numbers

First, separate the positive and negative numbers to simplify the addition process.Positive numbers: 76Negative numbers: -15, -18, -6
02

Adding the Positive Numbers

Add the positive number(s) together. In this case, we only have one positive number.So, 76 remains 76.
03

Adding the Negative Numbers

Add the negative numbers together:\[(-15) + (-18) + (-6) = -15 - 18 - 6 = -39\]
04

Combine Positive and Negative Sums

Now, combine the positive sum with the negative sum:\[76 + (-39) = 76 - 39 = 37\]
05

Verify with Number Line

As a check, consider using a number line where you start at 76, move back 15, 18, and 6 units step by step. This should land you on 37.

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Key Concepts

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

Integer Addition
Adding integers involves combining both positive and negative whole numbers. Understanding how to handle these additions is vital for mastering integer operations.
When adding integers follow these steps:
  • Group positive and negative integers separately.
  • Add the numbers in each group.
  • Combine the results from both groups to get the final sum.
In our exercise:
We have positive: 76
We also have negative: -15, -18, -6
First, add the negative numbers: \[-15 + (-18) + (-6) = -39\] Then, combine with the positive number:\[76 + (-39) = 37\] Getting comfortable with these steps will make integer addition simpler!
Positive and Negative Numbers
Positive numbers are greater than zero, while negative numbers are less than zero. Think of a positive number as moving to the right on a number line and a negative number as moving to the left.
When adding negative numbers, it is like combining debts. For example, \(-15 + (-18) + (-6) = -39\).
This simply means you're adding up the total debt.
For positive numbers, it鈥檚 standard addition, and so 76 remains 76.
Combining these results, you subtract the total debt from the positive number: \76 + (-39)\. This simplifies to \76 - 39 = 37\.
Understanding the nature of positive and negative numbers will help you handle integer operations confidently!
Number Line Check
A number line is a valuable tool for visualizing addition and subtraction. Imagine a line with zero in the middle, positive numbers to the right, and negative numbers to the left.
For checking our work, we start at 76 on the number line.
Move 15 units left: lands us at 61.
Move another 18 units left: lands us at 43.
Move 6 more units left: lands us at 37.
This confirms our calculated result.

Using a number line this way can help verify your integer addition and ensure you understand each step of the process.

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