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Chapter 1: Problem 92

Multiply. $$ 15.2 \times 0 $$

Short Answer

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Step by step solution

01

Understand the Multiplication Property of Zero

The Multiplication Property of Zero states that any number multiplied by zero equals zero. This means if you multiply any value by zero, the result will always be zero.
02

Apply the Property to the Given Multiplication

Apply the property to the given problem \(15.2 \times 0\). According to the Multiplication Property of Zero, the result is zero.

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Key Concepts

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

Multiplication
Multiplication is one of the basic operations in arithmetic. It involves combining groups of equal sizes to find the total number of items. In mathematical terms, when you multiply two numbers, you are adding a number (called the multiplicand) to itself a certain number of times (this number is called the multiplier). For example, multiplying 3 by 4 means adding the number 3 a total of 4 times (3 + 3 + 3 + 3), which equals 12.
Multiplication can be thought of using several models, such as:
  • Repeated Addition
  • Arrays
  • Area Models
Each approach helps to visualize and understand the concept more deeply. The result of multiplying two numbers is called the product.
Zero Property
The Zero Property of Multiplication is a special rule that simplifies calculations. This property states that any number multiplied by zero is always zero. Mathematically, this is expressed as:
\(a \times 0 = 0\)
Here, 'a' can be any number, and the result is always 0, regardless of the value of 'a'.
This property also makes solving certain arithmetic problems a lot quicker. No matter how large or complex the number is, multiplying it by 0 instantly gives the result zero, saving time and effort in more complicated calculations. Understanding and using this property is key to mastering basic arithmetic operations.
Basic Arithmetic
Basic arithmetic includes the fundamental operations of addition, subtraction, multiplication, and division. These operations form the foundation for all higher mathematical concepts. Here's a brief look:
  • Addition: Combining two or more numbers to get a sum.

  • Subtraction: Finding the difference between two numbers.`

  • Multiplication: Adding a number to itself a certain number of times (the focus of our problem).

  • Division: Splitting a number into equal parts.

Being comfortable with these operations helps in solving more complex problems in areas like algebra, geometry, and calculus. For instance, knowing that any number multiplied by zero gives zero (as per the Zero Property) simplifies calculations and helps avoid errors in various mathematical contexts.

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Most popular questions from this chapter

Solve and check. The symbol \(\sqsubseteq\) indicates an exercise designed to be solved with a calculator. $$ 6 x-\\{5 x-[7 x-(4 x-(3 x+1))]\\}=6 x+5 $$

Calculate using the rules for order of operations. Use the commutative, associative, and distributive laws to show that \(5(a+b c)\) is equivalent to \(c(b \cdot 5)+a \cdot 5 .\) Use only one law in each step of your work.

To the student and the instructor: Writing exercises, denoted by \([\%,\) are meant to be answered using sentences. Because answers to many writing exercises will vary, solutions are not listed at the back of the book. Charlie insists that \(15-4+1 \div 2 \cdot 3\) is \(2 .\) What error is he making?

Write an equivalent expression using the distributive law. $$ 9 a(b-c+d) $$

Translate to an algebraic expression. \(\\{x | x=3 n, n \text { is a natural number }\\}\)
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