/*! 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 44 Find each sum. $$|-27+19|$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 44

Find each sum. $$|-27+19|$$

Short Answer

Expert verified
The sum is 8.

Step by step solution

01

Add the Numbers

First, we need to add the numbers given within the absolute value symbols: \(-27 + 19\). To simplify this, think of it as subtracting 19 from 27 due to the negative sign. Therefore, \(-27 + 19 = -8\).
02

Apply the Absolute Value

The problem requires finding the absolute value of the result in Step 1. Absolute value makes any negative number positive:\(|-8| = 8\).

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.

Integer Addition
Adding integers means combining whole numbers, considering their signs鈥攚hether they're positive or negative. It isn't always straightforward, especially when negative numbers are involved.
When you add a negative number to a positive one, you are essentially performing a subtraction. This is because adding a negative is the same as moving left on a number line, which decreases the value.
For instance, with \(-27 + 19\), you first subtract the smaller absolute value (19) from the larger absolute value (27). Since -27 is more negative than +19 is positive, the result is negative, yielding -8.
  • Remember: Add two numbers with the same sign by adding their absolute values and giving the result the common sign.
  • Add numbers with opposite signs by subtracting their absolute values and giving the result the sign of the larger absolute value.
Negative Numbers
Negative numbers are numbers less than zero, represented with a minus sign. They are crucial in representing losses, debts, or any deficiency in numerous fields. In basic arithmetic, negative numbers demand special attention.
When working with negatives, it is crucial to remember that they invert the direction of movement on a number line.
Let's consider an example: Adding -27 to 19 can be seen as moving 27 units left from zero, then moving 19 units right.
  • Negative plus negative is more negative: \(-b + (-c) = -(b+c)\).
  • Negative plus positive reduces the absolute value, depending on which has the greater value.
Understanding these basics ensures that handling operations involving negative numbers feels effortless.
Arithmetic Operations
Arithmetic operations involve basic procedures like addition, subtraction, multiplication, and division. These form the foundation of mathematics and are routinely used in various types of problems.
Within arithmetic operations, signs are crucial: Positive signs traditionally represent gain or increase, while negative signs represent loss or decrease.
Let's break down how this works with expressions:
  • Addition: Different signs? Subtract! Same signs? Combine!
  • Subtraction: Think of it as adding the opposite; instead of subtracting a number, add its negative equivalent.
When dealing with symbols like absolute values, the outcome is always positive or zero, adding another layer of understanding to arithmetic operations.

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

Find each product. $$5 \cdot 15$$

Graph each set of integers on a number line. $$\\{-2,-4,-5,-8\\}$$

Simplify each expression. $$4(6 h)$$

In the newspaper, Ruben read that the low temperature for the day was expected to be \(-5^{\circ} \mathrm{F}\) and the high temperature was expected to be \(8^{\circ} \mathrm{F}\). What was the difference in the expected high and low temperatures?

Find the value of each expression. $$96 \div(6 \times 8) \div 2$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.