Problem 62 Multiply or divide as indicated.... [FREE SOLUTION]

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Chapter 2: Problem 62

Multiply or divide as indicated. See Examples 1 through 14. $$ \frac{0}{-14} $$

Short Answer

Expert verified

The result of $ \frac{0}{-14} $ is 0.

Step by step solution

Understand the Problem

The expression given is $ \frac{0}{-14} $, which means we need to divide 0 by -14.

Division Property of Zero

Any number divided by zero is always zero. This is because zero divided by any non-zero number always results in zero.

Apply the Division Property

Based on the division property of zero, we have $ \frac{0}{-14} = 0 $. The denominator does not affect the result as long as it is non-zero.

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Key Concepts

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

Division by Zero

Division is one of the four fundamental arithmetic operations, along with addition, subtraction, and multiplication. It involves splitting a quantity into equal parts. However, when it comes to dividing by zero, things get tricky. Dividing any number by zero, symbolically represented as $ \frac{a}{0} $, leads to an undefined expression. This is because there is no number that can multiply with zero to give a non-zero number. If we think about division as the inverse operation of multiplication, no viable answer satisfies our equations when the divisor is zero.Think of it like this:

If $0 \times x = a$, where $a eq 0$, there is no real solution for $x$.
This is why dividing by zero is undefined and should be avoided in equations.

Understanding this concept is important to prevent mathematical errors in calculations.

Zero Property

The zero property of multiplication states that any number multiplied by zero yields a product of zero. This principle also closely relates to division involving zero as the numerator. When a zero is divided by any non-zero number, the quotient is always zero. This is represented as $ \frac{0}{b} = 0 $ where $b$ is any number other than zero. Let's break this down:

Zero acts as a kind of neutral element in multiplication and division.
In multiplication, it's like having no items to count, so the product is zero.
In division, if there is nothing to be distributed (numerator is zero), the result comes out as zero, regardless of how many parts it could be split into.

Thus, when dividing 0 by a non-zero number, the answer is always 0, demonstrating the simplicity and reliability of the zero property.

Negative Numbers

Negative numbers are values less than zero and are typically used to represent loss, debt, or a decrease in some quantity. They play a vital role in various mathematical computations, including division.Here's what you need to know:

A negative number is denoted by a minus sign (-) before the number.
When dividing a positive number by a negative number or vice versa, the result is always negative.
However, if both dividend and divisor are negative, their division yields a positive quotient. This is essential in maintaining the balance of equations involving negative terms.

The exercise example $ \frac{0}{-14} = 0 $ highlights that even when the divisor is negative, the zero property renders the quotient zero, showing that negatives do not affect the zero outcome.Understanding how negative numbers interact with other numbers helps simplify complex expressions and solve equations effectively.

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91影视

Multiply or divide as indicated. See Examples 1 through 14. $$ \frac{0}{-14} $$

Short Answer

Step by step solution

Understand the Problem

Division Property of Zero

Apply the Division Property

Key Concepts

Division by Zero

Zero Property

Negative Numbers

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