Problem 16 Add. Do not use the number line ... [FREE SOLUTION]

91影视

Chapter 1: Problem 16

Add. Do not use the number line except as a check. \(-8+(-12)\)

Short Answer

Expert verified

-20

Step by step solution

Identify the Numbers

The first number is -8 and the second number is -12.

Combine the Numbers

Since both numbers are negative, add their absolute values. The absolute value of -8 is 8 and the absolute value of -12 is 12. Adding 8 and 12 gives 20.

Apply the Negative Sign

Since we added two negative numbers, the result will also be negative. Therefore, -8 + (-12) is -20.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Absolute Value

When working with negative numbers, understanding absolute value is crucial. The absolute value of a number is its distance from zero on the number line, regardless of direction. So, whether the number is positive or negative, its absolute value is always positive.
For example, the absolute value of -8 is 8, and the absolute value of -12 is 12. This means -8 and -12 are each 8 and 12 units away from zero, respectively.
When adding negative numbers, we use their absolute values to simplify our calculations and combine them later with the appropriate sign.

Combining Like Terms

Combining like terms is a helpful algebraic process used to simplify expressions. In the context of adding negative numbers, we combine terms that are alike (both being negative in this case).
To illustrate, consider the problem \(-8 + (-12)\). In this problem:

Both numbers are negative.
We add their absolute values (\[ |鈭�8| = 8 \] and \[ |鈭�12| = 12 \]).
The sum of 8 and 12 is 20.

Finally, since we were adding two negative numbers, the result is also negative, making the final result -20. Combining like terms helps us to efficiently handle operations involving similar components in mathematics.

Negative Integers

Negative integers are numbers less than zero and are often encountered in various mathematical problems. They are represented with a minus sign (鈭�) in front of the number.
When adding negative integers, it is helpful to remember:

Adding two negative integers will give a negative result. The absolute values of the numbers are summed up and the negative sign is kept.
Negative integers represent a move left on the number line.

In, \(-8 + (-12)\), we are effectively moving left from zero by 8 units and then a further 12 units. This combined movement lands us at -20 on the number line.
Understanding these properties of negative integers helps us to navigate through and solve such problems more easily.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Add. Do not use the number line except as a check. \(-8+(-12)\)

Short Answer

Step by step solution

Identify the Numbers

Combine the Numbers

Apply the Negative Sign

Key Concepts

Absolute Value

Combining Like Terms

Negative Integers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.