Problem 70 - Elementary and Intermediate Algebra

Question

Divide, if possible, and check. If a quotient is undefined, state this. $$ \frac{(-4.9)(7.2)}{0} $$

Step-by-Step Solution

Answer

The quotient is undefined.

Step 1 - Understand the problem

Given the expression \(\frac{(-4.9)(7.2)}{0}\), we are asked to perform the division if possible and check the quotient. If the division is undefined, we must state this.

Step 2 - Define division by zero

Recall that division by zero is undefined in mathematics. Any number divided by zero does not yield a meaningful result.

Step 3 - Apply the rule to the given problem

Since the denominator of the expression is 0, the division \(\frac{(-4.9)(7.2)}{0}\) is undefined.

Step 4 - State the conclusion

The quotient of the given expression is undefined.

Key Concepts

undefined quotient

Let's dive into why some divisions result in something called an 'undefined quotient'.
In math, division is about splitting a number into equal parts.
Take any number and try dividing it by zero.
You'll quickly see it's not possible.
For example, in the exercise, when you try to divide \(\frac{(-4.9)(7.2)}{0}\), it's like asking, 'How many times does zero fit into this number?' The answer is, it doesn't.
Zero cannot split anything into parts. This results in what is known as an 'undefined quotient'.
This means the operation doesn't work within our usual math rules.

mathematical rules

Now, let's focus on the mathematical rules that make division by zero undefined.
Normally, math has very clear rules for operations.
These help us perform operations consistently and correctly.
Division has a rule that says you can't divide by zero.
Why? Because dividing by zero leads to contradictions and undefined results.
Imagine trying to find how many times zero fits into a number.
You can't measure it.
Remember: the rule is simple—never divide by zero.
In any math problem, check if the division involves zero.
If it does, the answer is always undefined.

problem solving in algebra

Finally, let's look at how these rules help in problem solving in algebra.
Algebra often involves working with variables and equations.
Following math rules is critical.
When given an algebraic problem, always analyze carefully.
For instance, in the given exercise, determining if the division is possible is the first step.
Once you recognize the denominator is zero, you can conclude the quotient is undefined.
This kind of detailed analysis helps solve even more complex algebra problems.
Remember: identify all key parts of the problem first.
Then, use the applicable math rules to find a solution.