Problem 39 Multiply or divide as indicated.... [FREE SOLUTION]

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Chapter 2: Problem 39

Multiply or divide as indicated. See Examples 1 through 14. $$ -14(0) $$

Short Answer

Expert verified

The result of $-14 \times 0$ is 0.

Step by step solution

Understand the Operation

In this exercise, we need to multiply the number $-14$ by zero $0$. Multiplying any number by zero results in zero.

Apply the Multiplication Rule

Multiply $-14$ by $0$. According to the rule of multiplication involving zero, any number multiplied by zero gives zero.

Conclude the Operation

After performing the multiplication, the result of $-14 \times 0$ is $0$.

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Key Concepts

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

Multiplication with Zero

In basic arithmetic, multiplication is one of the core operations. When a number is multiplied by zero, we encounter a special case which simplifies the entire process. The rule here is very simple: any number multiplied by zero results in zero. This happens because the zero represents the absence of a quantity. Essentially, if you were to multiply five groups of zero marbles, you would end up with zero marbles. Therefore, zero "consumes" every number it multiplies with, reducing it to zero. This principle is straightforward and saves time when working with mathematical problems.

Here are important points to remember:

Zero times anything is zero.
It doesn't matter if the number is positive, negative, an integer, or a fraction鈥攝ero wins.
This property is universal across all numbers and helps in quickly evaluating expressions and solving equations.

Integer Multiplication

Integer multiplication refers to the process of multiplying whole numbers. In this context, integers can be positive, negative, or even zero. The steps involved in integer multiplication are simple. First, you multiply the numerals (or absolute values) like in basic arithmetic.

The challenge lies in applying the correct sign.

If both integers have the same sign, the result is positive.
If the integers have different signs, the result is negative.

For example, multiplying $-14$ by $3$ involves multiplying $|-14| = 14$ and $3$, giving us $42$, and then applying a negative sign since one number is negative. Thus, the final result is $-42$. This fundamental understanding is crucial for higher-order mathematics and real-world problem-solving.

Zero Property of Multiplication

The zero property of multiplication is a fundamental principle in mathematics that states that any number multiplied by zero results in zero. This property simplifies calculations and is used frequently in algebra and calculus. The zero property is significant because:

It acts as a neutralizing agent in multiplication.
It allows mathematic equations, especially those involving algebraic expressions, to simplify easily.
It illustrates the concept of annihilation in various mathematical applications.
It is foundational in solving equations where variables may be equal to zero.

This property works the same for any numeric system: whether dealing with real numbers, fractions, or mixed numbers, multiplying by zero always leads to zero. Thanks to the zero property, equations like $-14 \times 0 = 0$ are quickly resolved, demonstrating its efficacy and reinforcing a consistent operational rule.

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91影视

Multiply or divide as indicated. See Examples 1 through 14. $$ -14(0) $$

Short Answer

Step by step solution

Understand the Operation

Apply the Multiplication Rule

Conclude the Operation

Key Concepts

Multiplication with Zero

Integer Multiplication

Zero Property of Multiplication

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