Problem 113 Perform the indicated operation ... [FREE SOLUTION] (2024)

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Chapter 1: Problem 113

Perform the indicated operation and, if possible, simplify. If a quotient isundefined, state this. $$ \frac{14}{-9} \div \frac{0}{3} $$

Short Answer

Expert verified

The quotient is undefined because division by zero is not allowed.

Step by step solution

Understand the Problem

The given problem is the division of two fractions: $ \frac{14}{-9} \div \frac{0}{3} $. To solve this, it's important to recognize that division by zero is undefined.

Identify Division by Zero

The fraction $ \frac{0}{3} $ has a numerator of zero. In a division operation, having zero in the numerator (of the divisor) makes the problem division by zero, which is undefined.

Stating the Result

Since division by zero is undefined, the original problem does not have a valid numerical result.

Key Concepts

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

undefined quotient

In mathematics, dividing by zero is a big no-go. If you try to divide any number by zero, you will end up with an undefined quotient. This means there's no meaningful or valid result. Think of it like trying to share something with no one; it just doesn't make sense! In our example, we have $\frac{14}{-9} $ divided by $\frac{0}{3} $. Here, $\frac{0}{3} $ is essentially zero, leading us to division by zero. We quickly recognize that this operation is undefined.

division of fractions

Dividing fractions may look complicated, but it's pretty straightforward once you get the hang of it. Normally, when you divide one fraction by another, you multiply by the reciprocal. For example, to divide $\frac{1}{2} $ by $\frac{3}{4} $, you multiply $\frac{1}{2} $ by the reciprocal of $\frac{3}{4} $, which is $\frac{4}{3} $. This would look like \[ \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3} \].
But in our given problem, we can't follow this rule because the reciprocal of $\frac{0}{3} $, which is $\frac{3}{0} $, also involves division by zero – making the entire operation undefined.

numerator and denominator

To fully grasp division problems like ours, you need to understand numerators and denominators. In any fraction, the numerator is the number above the line, representing how many parts we have. The denominator is the number below the line, showing into how many parts the whole is divided.

In $\frac{14}{-9} $, 14 is the numerator and -9 is the denominator.
In $\frac{0}{3} $, 0 is the numerator and 3 is the denominator.

In our fraction $\frac{0}{3} $, having a zero in the numerator means we can't divide it further. When this fraction is the divisor, it leads to an undefined quotient scenario. Always pay special attention to the numerator and denominator to see if division by zero could occur!

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Most popular questions from this chapter

Explain the different uses of the symbol "-". Give examples of each use of thesymbol.Simplify. $5 t-\\{7 t-[4 r-3(t-7)]+6 r\\}-4 r$Given that $0.3 \overline{3}=\frac{1}{3}$ and $0.6 \overline{6}=\frac{2}{3},$express each of the following as a ratio of two integers. $$7.7 \overline{7}$$Brianna insists that if you can add real numbers, then you can also subtractreal numbers. Do you agree? Why or why not?Simplify. $$ 5 t^{3}+t+3\left(t-2 t^{3}\right) $$

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