/*! 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 2 Adding and Subtracting Signed Nu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 2

Adding and Subtracting Signed Numbers Combine as indicated. $$274+(-412)$$

Short Answer

Expert verified
-138

Step by step solution

01

Understanding the Numbers

Identify that 274 is a positive number and -412 is a negative number. When adding a negative number to a positive number, the operation turns into subtraction.
02

Performing the Subtraction

Subtract the absolute value of the negative number from the positive number: 274 - 412.
03

Calculate the Difference

Calculate the difference between the absolute values. Since the absolute value of 412 is greater than 274, the result will be negative.
04

Find the Result

Subtract the numbers: 274 - 412 = -138. The result is a negative number because the number with the larger absolute value (412) 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.

Understanding Positive and Negative Numbers
When we talk about numbers, each one comes with a sign: either positive or negative. Think of a number line stretching in both directions; positive numbers go to the right and negative numbers to the left of zero. Positive numbers represent quantities we have, while negative numbers often represent a lack or deficit of something.
Absolute Value
The absolute value of a number refers to its distance from zero on the number line, without considering its direction. To visualize, if you have the number -5, it is 5 units away from zero. Similarly, the number +5 is also 5 units away from zero. Both numbers have an absolute value of 5. In mathematical terms, the absolute value of a number is always non-negative.
Subtraction of Integers
Subtracting integers can be trickier than adding them because you must pay attention to their signs. To subtract a negative number is the same as adding its positive counterpart. So if you have to subtract -3 from 5, you're actually adding 5 + 3, resulting in 8. This switch is due to the concept that subtracting a deficit is akin to gaining that amount.
Arithmetic Operations
Arithmetic operations with signed numbers follow specific rules. With addition, like signs result in adding the absolute values and keeping the shared sign. With unlike signs, subtract the smaller absolute value from the larger one and assign the sign of the number with the larger absolute value. This is why in the example 274 + (-412), we end up with a negative result. The absolute value of -412 is larger than that of 274, and since -412 is negative, so is our result.

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

Perform the following computations. Display your answer in scientific notation. $$\left(1.58 \times 10^{2}\right)\left(9.82 \times 10^{3}\right)$$

Convert each number to engineering notation. $$26,940$$

Divide without using a calculator. Give your answer in scientific notation. $$49,000 \div\left(7.0 \times 10^{-2}\right)$$

Combined Operations with Approximate Numbers Perform each computation, keeping the proper number of digits in your answer. $$\left(\frac{45.3-8.34}{8.74-5.62}\right)^{2.5}$$

Divide the following powers of 10 $$10^{-2} \div 10^{-4}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.