/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 Find each sum. $$ 6+[2+(-13)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 22

Find each sum. $$ 6+[2+(-13)] $$

Short Answer

Expert verified
-5

Step by step solution

01

Identify the Expression Inside the Brackets

First, look at the expression inside the brackets: \(2 + (-13)\).
02

Simplify Inside the Brackets

Simplify \(2 + (-13)\). When you add a positive number to a negative number, you subtract the absolute value of the smaller number from the absolute value of the larger number and apply the sign of the larger number. So, \(2 + (-13) = -11\).
03

Replace and Simplify the Entire Expression

Replace the simplified bracket expression back into the original equation: \(6 + (-11)\). Then, simplify \(6 + (-11)\). Since adding a negative number is the same as subtracting, it becomes \(6 - 11 = -5\).

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
The absolute value of a number is the distance between that number and zero on a number line, regardless of direction. It's always a non-negative number, even for negative values. For example, the absolute value of both 5 and -5 is 5.

If you're dealing with \(2 + (-13)\), recognize the absolute values: |2| = 2 and |-13| = 13.
This helps in visualizing the operation since we are subtracting the smaller absolute value from the larger one.
Additive Inverse
The additive inverse of a number is what you add to it to get zero. For example, the additive inverse of 7 is -7 because \(7 + (-7)=0\).
The same rule applies in reverse, making -7鈥檚 additive inverse 7.

Understanding additive inverses simplifies the process of solving equations like \(2+(-13)\). Here, \-13\ is the additive inverse that helps simplify the addition process. This understanding helps you see that adding a negative number is essentially subtracting its absolute value.
Negative Numbers
Negative numbers are values less than zero, found to the left of zero on a number line. Negative numbers are crucial in various math operations and concepts.

When you're adding positive and negative numbers, you can think of it as moving on the number line:
  • Adding a negative number (like \(-11)\) is the same as subtracting its absolute value.
  • Combining \(6 + (-11)\) means moving 11 steps left from 6, which results in -5.
.
Correctly managing negative numbers helps in mastering fundamental math problems like our example.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 6 if it is divisible by both 2 and \(3,\) and not otherwise. Show that (a) \(1,524,822\) is divisible by 6 and \((b) 2,873,590\) is not divisible by 6

Write a numerical expression for each phrase and simplify. 19 less than the difference between 9 and \(-2\)

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. \(23,18,13,-4,\) and \(-8\)

Perform each indicated operation. $$ 6-(-8+3) $$

Perform each indicated operation. $$ -9.1237+[(-4.8099-3.2516)+11.27903] $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.