/*! 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 Multiply. $$ -8(5) $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 2

Multiply. $$ -8(5) $$

Short Answer

Expert verified
The product of \(-8\) and \(5\) is \(-40\).

Step by step solution

01

Identify the Numbers

In the expression \(-8(5)\), the numbers involved are \(-8\) and \(5\). We need to multiply these two numbers.
02

Understand the Sign Rules

Recall that when multiplying two numbers, if one number is negative and the other is positive, the result will be negative.
03

Perform Multiplication

Multiply the absolute values of the numbers: \(8\times 5 = 40\). This gives us the magnitude of the result.
04

Apply the Sign

Since one of the numbers is negative, the result of \(-8(5)\) is \(-40\).

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 can be a bit tricky to work with when you're first learning about them, but once you understand their properties, they become much simpler to manage.
  • Negative numbers are often used to represent things like debt, temperatures below freezing, or elevations below sea level.
  • They are written with a minus sign in front, such as $-4$ or $-10$.
Adding and subtracting negative numbers can be confusing at first. For example, subtracting a negative number is the same as adding its absolute positive value. Multiplying and dividing them requires understanding sign rules, which we'll delve into below.
Absolute Value
The absolute value of a number is its distance from zero on the number line, without considering which direction from zero the number lies.
  • It is always non-negative. For example, the absolute value of $-8$ is $8$, written as $|-8| = 8$.
  • Similarly, the absolute value of $5$ is simply $5$, written as $|5| = 5$.
This property is especially useful when multiplying negative numbers, as it allows us to still use positive values to find the size of their product, before applying the appropriate sign using sign rules. Think of absolute value as the number without any sign - its plain, unadorned magnitude.
Sign Rules
Sign rules are essential when working with multiplication or division of integers. They determine the sign of the result based on the signs of the numbers you鈥檙e working with.
  • If both numbers are positive, the result is positive.
  • If both numbers are negative, the result is also positive because a negative times a negative gives a positive.
  • When you multiply a positive number by a negative number, the result is always negative. Similarly, if you multiply a negative by a positive, the result is still negative.
In the exercise $-8(5)$, we first multiplied $8$ by $5$ to get the absolute value result, $40$. Since $-8$ is negative and $5$ is positive, we applied the sign rule, resulting in $-40$. Understanding these rules is crucial for correctly solving problems that involve negative 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

Determine which pairs of actions are commutative. "putting on your left shoe" and "putting on your right shoe"

The perimeter of a figure is the distance around the figure. The expression \(2 l+2 w\) represents the perimeter of a rectangle when \(l\) is its length and \(w\) is its width. Find the perimeter of the following rectangle by substituting 8 for \(l\) and 6 for \(w\).

If \(a\) is a positive number and \(b\) is a negative number, determine whether each statement is true or false. \(|b-a|\) is always a positive number.

Much of New Orleans is below sea level. If George descends 12 feet from an elevation of 5 feet above sea level, what is his new elevation?

Perform the following operations. Write answers in lowest terms. $$ \frac{3}{4} \div \frac{7}{12} $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.