/*! 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 124 Explain how to determine the sig... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 124

Explain how to determine the sign of a product that involves more than two numbers.

Short Answer

Expert verified
The final sign of a product involving more than two numbers is dependent on the number of negatively signed numbers present. An even number of negative signs will result into a positive product, while an odd number of negative signs will lead to a negative product.

Step by step solution

01

Identify the signs of all numbers

Count how many negative numbers are in the set to be multiplied. Remember, positive numbers will not affect the final sign of the product.
02

Testing if the number of negatives is even or odd

If the count of negative numbers is even, the final product will have a positive sign. If the count is odd, the final product will have a negative sign.
03

Determining the sign

Apply these rules and finalize the sign of your final product. If you have an even number of negatives, your product is positive. If you have an odd number of negatives, your product 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 that are less than zero. These are represented with a minus sign (-) before the number. For example, -3 is a negative number. Negative numbers often appear in everyday life, such as temperatures below freezing or when calculating financial debt.

The presence of negative numbers complicates multiplication because they affect the sign of the resultant product. Knowing how to manipulate these numbers is crucial to solving problems accurately.
  • Multiplying two negative numbers results in a positive product. For example, \(-3 \times -2 = 6\).
  • Multiplying a positive number by a negative number results in a negative product, such as \(5 \times -2 = -10\).
Mastering negative numbers will greatly help in determining the sign of a product when multiple numbers are involved.
Positive Numbers
Positive numbers are any numbers greater than zero. They do not have a sign in front or are sometimes marked with a plus sign (+). Examples include 1, 2, 3, etc.

In multiplication, positive numbers do not affect the sign of the result. That is because multiplying any number by a positive number keeps the sign of the other number.
  • For instance, multiplying two positive numbers, such as \(3 \times 4\), always results in another positive number, \(12\).
  • If you multiply a positive and a negative number, like \(2 \times -5\), the outcome will be negative: \(-10\).
Understanding positive numbers is essential in predicting the sign of a product when they mix with negative numbers in a calculation.
Multiplication
Multiplication is one of the basic arithmetic operations that combines numbers to yield a product. It can be visualized as repeated addition. For example, instead of adding 3 four times, \(3 + 3 + 3 + 3\), you can multiply \(3 \times 4 = 12\).

When working with multiple numbers, understanding the effect of multiplication on both negative and positive numbers is key.
  • The commutative property of multiplication states that the order of numbers doesn't affect the product: \(a \times b = b \times a\). This applies to both positive and negative numbers.
  • Multiplication by zero, \(a \times 0 = 0\), always results in zero, regardless of other numbers involved.
  • In chain multiplication, the sign of the final product depends chiefly on the number of negative factors.
Therefore, multiplication isn't just about the numbers themselves but rather how they interact through their signs.
Counting Negatives
Counting negatives is a crucial skill when determining the sign of a product involving multiple numbers. Start by identifying each number's sign in the problem. Negative numbers should be counted and noted separately from positive numbers.

Once all negative numbers are counted, it's essential to see if their count is even or odd:
  • If the count of negative numbers is even, the negatives cancel each other out, resulting in a positive product. For instance, \((-2) \times (-3) \times 4 = 24\).
  • If the number of negatives is odd, there will be one negative number left unpaired, making the entire product negative. As an example, \((-2) \times 3 \times 4 = -24\).
To efficiently find the sign, remember this simple approach: even makes it positive, odd makes it negative. It provides a quick method for checking your final results in multiplication problems.

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

Describe how the inverse property of addition $$a+(-a)=0$$ can be shown on a number line.

Use a calculator to find a decimal approximation for each irrational number, correct to three decimal places. Between which two integers should you graph each of these numbers on the number line? $$-\sqrt{12}$$

Why is it that 0 has no multiplicative inverse?

Explain how to find the multiplicative inverse of a number.

Express each sentence as a single numerical expression. Then use the order of operations to simplify the expression Cube \(-5 .\) Subtract this exponential expression from \(-100 .\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.