/*! 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 87 Explain in your own words why th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 87

Explain in your own words why the sum of two negative numbers is negative.

Short Answer

Expert verified
Adding two negatives sums their absolute values and keeps the minus sign, resulting in a negative number.

Step by step solution

01

Understanding Negative Numbers

Negative numbers are numbers less than zero. They are typically represented with a minus sign (-). For example, -3 and -5 are both negative numbers.
02

Adding Negative Numbers

When adding two negative numbers, we add their absolute values (ignore the minus signs) and then place a minus sign in front of the result. This is because adding negatives increases the magnitude in the negative direction (left on a number line). For example, adding -2 and -3 involves combining the digits 2 and 3 to get 5, then adding the minus sign to get -5.
03

Visualizing on a Number Line

Consider the number line where positive numbers are to the right of zero and negative numbers to the left. If starting at zero and moving left to reach -2, then moving further left by 3 more units, the result is -5. This visual shows why the sum of negative numbers is still negative and further left.
04

General Rule

Sum of negatives: Whenever two negative numbers are added together, the result will always be more negative. This means the sum will be a negative number.

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.

Negative Numbers
Negative numbers are numbers that are less than zero. They are represented with a minus sign (-). This means when you see -3 or -5, you know these numbers are below zero. It's like having a debt. If you owe someone 3 dollars, you can think of it as being at -3 dollars in your account. When we deal with negative numbers, we often talk about moving left on a number line, which represents going into more debt or having less than zero.
Sum of Negative Numbers
When you add two negative numbers, you're actually combining two debts. Imagine you owe 2 dollars and then borrow another 3 dollars. Adding these negative amounts means you now owe more money. Mathematically, you ignore the minus signs and add the absolute values together, then put the minus sign back on the result. For example, -2 + -3 becomes 2 + 3 which equals 5, then we add the minus sign back to get -5. Hence, the sum of two negative numbers will always be negative.
Number Line Visualization
A number line helps us understand negative numbers visually. Positive numbers go to the right of zero, and negative numbers go to the left. If you start at zero and move to the left to reach -2 (as if losing 2 dollars), then go further left by 3 more units (losing another 3 dollars), you end up at -5. This movement on the number line clearly shows that combining negative movements (debts) results in a larger negative, or a sum further left. This visualization helps in understanding why the sum of two negative numbers is always negative.
Absolute Value
The absolute value of a number is how far it is from zero, without considering its sign. For example, the absolute value of -3 is 3, because -3 is 3 units away from zero. This concept is crucial in adding negative numbers. When adding -2 and -3, we take the absolute values (2 and 3), add them to get 5, and then put the negative sign back to get -5. Understanding absolute value helps us easily find the sum of negative numbers by simplifying the process of combining their magnitudes.

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

Simplify. $$ 2 a+5 a-(6 a+8) $$

After five rounds of golf, a golf pro was 3 under par twice, 2 over par once, 2 under par once, and 1 over par once. On average, how far above or below par was the golfer?

Combine like terms. $$ 4 x-7 x $$

Find the reciprocal of each number, if it exists. $$ \frac{43}{-24} $$

Label each of the following numbers as prime, composite, or neither. $$ 4 $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

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.