/*! 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 138 Explain how to add integers.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 138

Explain how to add integers.

Short Answer

Expert verified
You can add integers by following these rules: when adding two positive integers or two negative integers, the result is positive or negative respectively. The magnitude of the result is the sum of absolute values. When adding a positive and a negative integer, the process is like subtracting the smaller number from the larger one and the resulting sign depends on the sign of the number with larger absolute value.

Step by step solution

01

Define Integers

Integers are whole numbers that can be either greater than zero (positive), less than zero (negative), or exactly zero. They don't have fractional or decimal parts.
02

Rule for Adding Positive Integers

When two positive integers are added together, the result is always positive. If we're adding a positive integer and zero, the result is the positive integer itself. For example, \(5+2=7\) or \(5+0=5\). This can also apply for larger integers as well.
03

Rule for Adding Negative Integers

If two negative integers are added, the result is always negative. For example, \(-3+(-2) = -5\). The magnitude of the result is the sum of the absolute values of the numbers.
04

Rule for Adding Negative and Positive Integers

When a positive and a negative integer are added, the process is similar to subtracting the smaller absolute value from the larger one. The sign of the number with the larger absolute value is the sign of the result. For instance, \(3+(-5) = -2\) and \(-3+5=2\).

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!

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

You will develop geometric sequences that model the population growth for California and Texas, the two most populated U.S. states. The table shows the population of Texas for 2000 and 2010 , with estimates given by the U.S. Census Bureau for 2001 through \(2009 .\) $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 0} & \mathbf{2 0 0 1} & \mathbf{2 0 0 2} & \mathbf{2 0 0 3} & \mathbf{2 0 0 4} & \mathbf{2 0 0 5} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 20.85 & 21.27 & 21.70 & 22.13 & 22.57 & 23.02 \\ \hline \end{array} $$ $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Year } & \mathbf{2 0 0 6} & \mathbf{2 0 0 7} & \mathbf{2 0 0 8} & \mathbf{2 0 0 9} & \mathbf{2 0 1 0} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 23.48 & 23.95 & 24.43 & 24.92 & 25.15 \\ \hline \end{array} $$ a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that Texas has a population increase that is approximately geometric. b. Write the general term of the geometric sequence modeling Texas's population, in millions, \(n\) years after \(1999 .\) c. Use your model from part (b) to project Texas's population, in millions, for the year 2020 . Round to two decimal places.

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=12, r=\frac{1}{2}\).

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{5}\), when \(a_{1}=4, r=3\).
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.