/*! 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 266 Multiply. $$ -3 \cdot 9 $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 266

Multiply. $$ -3 \cdot 9 $$

Short Answer

Expert verified
-27

Step by step solution

01

Understand the Problem

The problem requires multiplying two numbers: - The first number is \(-3\) - The second number is \(9\) We need to find the product of these two numbers.
02

Multiply the Absolute Values

First, multiply the absolute values of the numbers involved. The absolute value of \(-3\) is \(3\) and the absolute value of \(9\) is \(9\). Calculate \(3 \times 9 = 27\).
03

Determine the Sign of the Product

Since we are multiplying a negative number by a positive number, the product will be negative. So the product of \(-3 \times 9\) is \(-27\).

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 can be a bit tricky, but they're simply numbers less than zero. They are often used to represent loss, decrease, or opposite directions. When multiplying with negative numbers, it's crucial to understand their behavior:
  • When you multiply a positive number by a negative number, the product is always negative.
  • If both numbers are negative, the product will be positive because a negative times a negative equals a positive.
In our problem, \(-3\) is our negative number.
absolute value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always positive. For instance:
  • The absolute value of \(-3\) is \(3\).
  • The absolute value of \(9\) is \(9\).
In the given exercise, we first find the absolute values of \(-3\) and \(9\), which simplify our multiplication.
product of numbers
The product is the result you get when you multiply two numbers. The process involves the following:
  • Multiply the absolute values: \(3 \times 9 = 27\).
  • Then determine the sign of the product based on the multiplication rules of negative and positive numbers.
So, in our example, we first calculate \(3\) times \(9\) to get a product of \27\ before considering the final sign.
multiplication rules
There are simple rules to remember when multiplying numbers, especially negatives:
  • A positive times a positive equals a positive.
  • A positive times a negative equals a negative.
  • A negative times a positive equals a negative (like in our example \(-3 \times 9 = -27\)).
  • A negative times a negative equals a positive.
In our problem, because \-3\ is negative and \9\ is positive, the product is \-27\.

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

Make the unit conversions. Round to the nearest tenth. Bill is 75 inches tall. Convert his height to centimeters.

Convert the units. JJ's cat, Posy, weighs 14 pounds. Convert her weight to ounces.

Trader Joe's grocery stores sold a bottle of wine they called "Two Buck Chuck" for $$\$ 1.99 .\( They sold a case of 12 bottles for \)\$ 23.88\(. To find the cost of 12 bottles at \)\$ 1.99,\( notice that 1.99 is \)2-0.01\( (a) Multiply 12(1.99) by using the distributive property to multiply \)12(2-0.01)$$. (b) Was it a bargain to buy "Two Buck Chuck" by the case?

Solve. Matthias is 1.8 meters tall. His son is 89 centimeters tall. How much taller is Matthias than his son?

Convert the units. Estrella is 1.55 meters tall. Convert her height to centimeters.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.