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Chapter 6: Problem 95

What is the product of any whole number and 0 ?

Short Answer

Expert verified
The product of any whole number and 0 is always 0.

Step by step solution

01

- Understand the Problem

Identify what the exercise is asking for. It asks for the result of multiplying any whole number by 0.
02

- Recall the Property of Multiplication

Remember the multiplication property that states any number multiplied by 0 equals 0. This is one of the basic properties of multiplication.
03

- Apply the Property

Apply this property to any whole number. No matter the whole number chosen, multiplying it by 0 will result in 0.
04

- Verify Your Understanding

Choose a few whole numbers, for example, 3, 125, and 0 itself, and multiply each by 0 to verify the result: 3 脳 0 = 0, 125 脳 0 = 0, 0 脳 0 = 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Whole Numbers
Whole numbers are basic building blocks in math, and they are the numbers you probably first learned to count with. They include 0, 1, 2, 3, and so on. Whole numbers do not include fractions or decimals.
聽Understanding whole numbers is crucial because they are used in everyday life, like counting objects or representing quantities.
Whole numbers are simple and easy to work with, especially when learning new concepts like multiplication.
Properties of Multiplication
Multiplication has several important properties that make math easier to understand and use. Here are a few key properties:
  • Commutative Property: Changing the order of the numbers does not change the product. For instance, 3 脳 4 is the same as 4 脳 3.
  • Associative Property: Changing the grouping of the numbers does not change the product. For example, (2 脳 3) 脳 4 is the same as 2 脳 (3 脳 4).
  • Identity Property: Multiplying any number by 1 leaves it unchanged. For instance, 5 脳 1 = 5.
  • Multiplication by Zero: Any number multiplied by 0 equals 0. This property states that no matter what whole number you choose, if you multiply it by 0, the result will always be 0.
These properties are powerful tools that help simplify problems and verify answers.
Basic Arithmetic Operations
Arithmetic operations form the foundation of math. The basic operations you will use the most are addition, subtraction, multiplication, and division.
  • Addition: Combining two or more numbers to get a total. For instance, 2 + 3 = 5.
  • Subtraction: Taking one number away from another. For example, 5 - 2 = 3.
  • Multiplication: Adding a number to itself a certain number of times. For instance, 4 脳 3 is the same as 4 + 4 + 4, which equals 12.
  • Division: Splitting a number into equal parts. For example, 12 梅 3 = 4 means dividing 12 into three equal parts of 4.
Multiplication by 0 is a specific case of multiplication, and it shows how special rules help simplify math. Understanding these operations is key to mastering more complex math concepts in the future.

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(a) solve. (b) check. $$ w^{3}+6 w^{2}+8 w=0 $$

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