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Chapter 1: Problem 5

Multiply. See Example \(1 .\) $$ 8 \cdot 0 \cdot 9 $$

Short Answer

Expert verified
The product is 0.

Step by step solution

01

Identify the Operation

The exercise requires multiplication of three numbers: 8, 0, and 9. Remember, multiplication involves finding the product of the numbers.
02

Apply the Multiplication Property of Zero

In multiplication, any number multiplied by zero results in zero. Here, we have the number 0 as one of the factors, which means the entire product will be zero.
03

Calculate the Product

Starting with the expression: \[ 8 \cdot 0 \cdot 9 \]From Step 2, since one of the numbers is 0, multiplying any number by 0 results in 0. Therefore, the product is:\[ 8 \cdot 0 = 0 \] and further,\[ 0 \cdot 9 = 0 \]So, the final result is 0.

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Key Concepts

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

Multiplication Property of Zero
The multiplication property of zero is a fundamental rule in mathematics that every student should understand. When you multiply any number by zero, the result is always zero. This is true regardless of how large or complex the other number is. In the provided exercise, the statement \( 8 \cdot 0 \cdot 9 \) illustrates this property perfectly. Since the number zero is included in the multiplication, the entire product becomes zero. This property simplifies many mathematical operations and helps us deal with larger equations by quickly determining outcomes when zero is involved.
Mathematical Operations
Mathematical operations, such as addition, subtraction, multiplication, and division, are the basic building blocks of arithmetic. They allow us to manipulate numbers to achieve desired results. In the context of the exercise, we are specifically focusing on multiplication. Multiplication involves finding the total of one number taken a specified number of times.
  • In the expression \( 8 \cdot 0 \cdot 9 \), multiplication is used.
  • Unlike addition, where the order of numbers does not matter, multiplication sequences can include properties like the multiplication property of zero which influence results.
Understanding how these operations work and interact is crucial for solving more complex mathematical equations and problems.
Prealgebra Concepts
Prealgebra involves basic arithmetic operations and an introduction to more advanced topics like algebraic expressions. It is designed to prepare students for algebra by solidifying their understanding of fundamental math concepts. Applying prealgebra concepts involves recognizing mathematical patterns and properties.
  • Grasping the multiplication property of zero is a key prealgebra concept.
  • Understanding order of operations, represented by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is crucial.
By mastering these concepts, students form a solid foundation for algebra and subsequent math courses, fostering confidence and competence when dealing with more advanced topics.

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Most popular questions from this chapter

In your own words, explain the commutative property of addition.

Write each phrase as a variable expression. Use \(x\) to represent "a number." Twelve subtracted from a number

Write each phrase as a variable expression. Use \(x\) to represent "a number." A number subtracted from 11

Perform each indicated operation. $$ \begin{array}{r} 128 \\ +\quad 7 \\ \hline \end{array} $$

The following table shows a few of the airports in the United States with the largest volumes of passengers. Complete this table. The first line is completed for you. (Source: Airports Council International) $$ \begin{array}{|l|c|c|c|c|} \hline & \text { Total passengers in 2015 } & \text { Amount Written } & \text { Standard Form } & \text { Standard Form } \\ & \text { (in hundred-thousands } & \text { in Standard } & \text { Rounded to the } & \text { Rounded to the } \\ \text { City Location of Airport } & \text { of passengers) } & \text { Form } & \text { Nearest Million } & \text { Nearest Ten-Million } \\ \hline \text { Atlanta, GA } & 1015 & 101,500,000 & 102,000,000 & 100,000,000 \\\ \hline \text { New York JFK } & 568 & & & \\ \hline \end{array} $$
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