Problem 50 - Beginning and Intermediate Algebra

Question

Find each quotient. \(\frac{0}{-9}\)

Step-by-Step Solution

Answer

0

Step 1 - Understand the Problem

The problem involves dividing zero by a negative number. The expression given is \(\frac{0}{-9}\).

Step 2 - Apply the Rules of Division

Recall that dividing zero by any non-zero number results in zero. This is because zero divided into any number of parts is still zero.

Step 3 - Determine the Quotient

Given \(\frac{0}{-9}\), apply the rule from Step 2. The result is zero, because any number divided by zero is zero.

Key Concepts

dividing zero

When we talk about dividing zero by another number, it simply means we are distributing 'nothing' into parts. Imagine you have zero candies and you want to share them with nine friends. Well, each friend would still get zero candies because there's nothing to share! Such an expression in math is represented by \( \frac{0}{\text{non-zero number}} \). Whether the divisor is positive or negative doesn't change the result: it will always be zero. Therefore, \( \frac{0}{-9} = 0 \).

rules of division

Division is an essential arithmetic operation. The basic rules of division help us apply this operation correctly. Here are some key rules to remember:

• Any number divided by 1 is the number itself (e.g., \( \frac{a}{1} = a \)).
• Any number divided by itself is 1 (e.g., \( \frac{a}{a} = 1 \) for \( a \e 0 \)).
• Zero divided by any non-zero number is 0 (e.g., \( \frac{0}{a} = 0 \) for \( a \e 0 \)).
• Division by zero is undefined (e.g., \( \frac{a}{0} ot= \) any real number).
• A negative number divided by a positive number results in a negative quotient (e.g., \( \frac{-a}{b} = - \frac{a}{b} \)). Likewise, a positive number divided by a negative number also results in a negative quotient (e.g., \( \frac{a}{-b} = - \frac{a}{b} \)).

These rules are fundamental to solve division problems efficiently.

negative numbers

Negative numbers might seem tricky, but once you understand them, you'll see they follow simple patterns. Here's a quick guide to negative numbers in division:

• A negative divided by a positive is a negative. For example, \( \frac{-10}{2} = -5 \).
• A positive divided by a negative is also a negative. For instance, \( \frac{10}{-2} = -5 \).
• A negative divided by a negative gives a positive result. So, \( \frac{-10}{-2} = 5 \).

When dividing, keep track of the signs, and use the rules of division to determine the correct outcome.
In our original problem, \( \frac{0}{-9} \), although we are dividing by a negative number, remember the rule that any zero divided by a non-zero number results in zero.