/*! 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 27 In Exercises \(1-34,\) perform t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 27

In Exercises \(1-34,\) perform the indicated multiplication. $$-2(-3)(-4)(-1)$$

Short Answer

Expert verified
The solution to the multiplication -2(-3)(-4)(-1) is 24.

Step by step solution

01

Multiplication of the First Two Numbers

We start the process by multiplying the first two numbers together, which are -2 and -3. Applying the rule that the multiplication of two negative numbers is a positive number, we get -2 multiplied by -3 equals 6.
02

Multiplication of the Result with the Third Number

Next, we multiply the result of the first step, which is 6, with the third number, which is -4. Multiplying a positive number by a negative number yields a negative number, this yields -24.
03

Multiplication of the Result with the Fourth Number

Finally, we multiply the result of the second step, which is -24, with the fourth number, -1. Applying the rule that negative multiplied by a negative is positive, this yields a final result of 24.

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 in Multiplication
Negative numbers play a crucial role in multiplication. They can change the outcome's sign depending on the number of negative numbers you multiply. Let's explore how that works:

Recall that a negative number can be thought of as an opposite or direction on the number line. For example, -3 is three units away from zero, but in the opposite direction to 3.

When multiplying negative numbers, observe these key rules:
  • Multiplying two negative numbers results in a positive number, because reversing direction twice brings us back to a positive.
  • Multiplying a negative number by a positive number yields a negative result. This means we continue to move in the negative direction.
Using these principles helps us anticipate the result of arithmetic involving negatives, ensuring that our calculations are on track.
Basic Multiplication Rules
Understanding multiplication rules is essential to solve arithmetic problems, particularly involving multiple numbers. Multiplication is essentially repeated addition, but with its specific rules.

When you're multiplying several numbers together, consider these multiplication rules:
  • If you multiply two positives, the product is always positive.
  • The product of two negative numbers is positive.
  • Multiplying a positive and a negative number results in a negative.
  • The order doesn't matter in multiplication, due to its commutative property \(a \times b = b \times a\).
These rules help simplify expressions and guide you in calculating the right product of numbers, no matter their sign.
Combining Arithmetic Operations
Arithmetic operations such as addition, subtraction, multiplication, and division are fundamental in mathematics. Integrating these operations, especially multiplication, can be tricky when negative numbers are involved.

When performing arithmetic operations, it's important to follow an order of operations (PEMDAS/BODMAS), which stands for:
  • Parentheses or Brackets
  • Exponents or Orders
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
When you're multiplying several numbers, focusing on two at a time while following the sign rules ensures accuracy. Always keep an eye on the number signs, as this affects the intermediate results and the final outcome. Proper handling of the arithmetic operations allows you to streamline solving complex problems with confidence.

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

From here on, each exercise set will contain three review exercises. It is essential to review previously covered topics to improve your understanding of the topics and to help maintain your mastery of the material. If you are not certain how to solve a review exercise, turn to the section and the worked example given in parentheses at the end of each exercise. Determine whether 18 is a solution of \(16=2(x-1)-x\) (Section 1.1, Example 4)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every fraction has infinitely many equivalent fractions.

Explain how to simplify an algebraic expression in which a negative sign precedes parentheses.

In Exercises \(139-142\), write an algebraic expression for the given English phrase. The fraction of people in a room who are women if there are 40 women and \(x\) men in the room

Simplify using a calculator: $$ 0.3(4.7 x-5.9)-0.07(3.8 x-61) $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.