/*! 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 26 Find each sum. $$4+(-6)$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 26

Find each sum. $$4+(-6)$$

Short Answer

Expert verified
The sum is -2.

Step by step solution

01

Identify the Numbers

We start with the numbers given in the exercise: 4 and -6. Recognize that 4 is a positive number and -6 is a negative number.
02

Understand the Operation

The operation to perform is addition, as indicated by the plus sign between the two numbers: \(4 + (-6)\). Since one number is positive and the other is negative, this becomes a subtraction operation.
03

Convert to Subtraction

When adding a negative number, convert the operation to subtraction: \(4 + (-6)\) is the same as \(4 - 6\).
04

Perform the Subtraction

Subtract 6 from 4. This can be expressed as \(4 - 6 = -2\). Since 6 is greater than 4, the result is negative.

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 less than zero and are usually expressed with a minus sign (-) in front of them. They represent values that are opposite to positive numbers.
Negative numbers are often used to denote:
  • Temperatures below zero degrees.
  • Depths below sea level.
  • Financial losses or liabilities.
Understanding negative numbers is crucial when dealing with real-world situations where values can decrease or be opposite, like spending money which decreases your account balance, often expressed as a negative number if you go into debt. When working with negative numbers in mathematics, it's essential to pay attention to the operation signs and know that they can change how you approach problems.
Addition as Subtraction
Addition can sometimes feel confusing when negative numbers are involved. When we add a negative number to a positive one, it is equivalent to subtracting the positive value of that negative number.
For example, if you have 7 and add -3, you are effectively subtracting 3 from 7. This process is represented mathematically as:
  • From a positive number, moving left on a number line. Thus, 7 + (-3) becomes 7 - 3.
This concept also allows us to simplify expressions in algebra by recognizing that the addition of negative numbers can be directly converted into subtraction, streamlining computations and helping to prevent mistakes. Understanding that addition can transform into subtraction when dealing with negatives is key to mastering integer operations.
Subtraction of Integers
Subtraction with integers, both positive and negative, involves considering the direction and magnitude of the numbers. When you subtract a larger number from a smaller integer, the result is negative.
Let's use the example of the exercise where you subtract 6 from 4:
  • First, know that 6 is greater than 4.
  • When subtracting 6 from 4 (\(4 - 6\)), we essentially need to find how far 4 is from 6 in the opposite direction on the number line, resulting in -2.
To avoid errors, remember:
  • If both integers are positive, traditional subtraction rules apply.
  • If you subtract a negative number, you're effectively adding the absolute value of that integer.
  • Results depend significantly on the relative sizes of the integers involved.
Being comfortable with these rules helps solve real-world problems correctly, considering both direction and magnitude when subtracting different types of integers.

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

Evaluate each expression if \(a=-2, b=-6,\) and \(c=14\). $$c-a+b$$

Evaluate each expression. \(9 s,\) if \(s=-11\)

Evaluate each expression if \(a=0, b=3,\) and \(c=-4\) $$a+b+|c|$$

Translate each phrase into an algebraic expression. a number divided by 5

Evaluate each expression if \(a=6, b=10,\) and \(c=3\) $$a b-a c$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.