/*! 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 114 Can the sum of two negative deci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 114

Can the sum of two negative decimals ever be a positive decimal? Why or why not?

Short Answer

Expert verified
No, the sum of two negative decimals cannot be a positive decimal.

Step by step solution

01

Understanding Negative Decimals

Negative decimals are numbers less than zero but expressed in decimal form like -0.5, -2.3, etc. They represent values below zero on the number line.
02

Rule for Adding Negative Numbers

When you add two negative numbers, they combine to create a larger negative number. This is because you are essentially moving further in the negative direction on the number line.
03

Test with Example

Let's add two negative decimals, such as -1.5 and -2.3. Adding these gives \[ (-1.5) + (-2.3) = -1.5 - 2.3 = -3.8 \]. This result is still a negative number.
04

Conclusion from the Rule and Example

Since adding two negative decimals results in a larger negative number, the sum of two negative decimals cannot be positive.

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.

Decimal Numbers
Decimal numbers, including negative ones, are a way to represent fractions or parts of whole numbers using the decimal point. When you see a number like -0.5 or 2.75, it's a decimal number. The decimal point separates the whole number part from the fractional part. For instance, in -0.5, the number is less than zero by a half.
Decimal numbers are convenient because they give us precision to depict values such as heights, weights, and financial amounts. Understanding decimals is crucial, especially when performing mathematical operations like addition or subtraction.
  • Important: Always pay attention to the sign in front of the decimal number.
  • Negative decimal numbers are below zero on the number line.
Number Line
Imagine a straight line stretching infinitely in both directions with zero in the middle. This is a number line鈥攁 visual tool for understanding numbers and their relationships. To the right of zero, you find positive numbers like 1, 2, 3. To the left, there are negative numbers such as -1, -2, -3.
Each point on the number line represents a real number. Decimal numbers fit perfectly on the number line as well. For example, 2.5 is between 2 and 3 on the right, while -2.5 is between -2 and -3 on the left.
  • A negative decimal, like -2.3, is found to the left of zero.
  • The further left you go, the smaller the number's value.
Using the number line, you can easily visualize adding numbers. When adding negative decimals, you move left, further into the negative zone.
Addition Rules
Adding numbers follows certain rules, especially for negative and decimal numbers. When you add two negative numbers, they together make a larger negative number. Think about them like debts; if you owe \(1.50 and borrow another \)2.30, your total debt is greater, now $3.80.
  • Rule: Adding two negative decimal numbers will always give you a more negative result.
  • Example: \[(-1.5) + (-2.3) = -3.8\]
These rules are consistent, meaning regardless of which negative decimals you choose, the sum will never flip into the positive. Awareness of these rules helps in correctly handling mathematical problems involving negative and decimal numbers.

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

Divide. \(\frac{23.8}{0.035}\)

Divide. \(-2.156 \div 0.98\)

The following pulse rates were recorded for a group of 15 students: $$ 78,80,66,68,71,64,82,71,70,65,70,75,77,86,72 $$ Find the mode

Divide. Round the quotients as indicated. Divide: \(68.39 \div 0.6\). Round the quotient to the nearest tenth.

Determine whether the given values are solutions of the given equations. \(\frac{x}{10}=0.23 ; x=23\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.