Question

Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check. In our definition of division for $$ \frac{P}{Q} \div \frac{R}{S} $$ we stated that $Q \neq 0, S \neq 0,$ and $R \neq 0 .$ Explain why $R$ cannot equal 0.

Name: Problem 95, Chapter 6: Intermediate Algebra
Uploaded: 2020-07-16T21:36:37-08:00
Duration: 23 s
Channel: Amy Jiang
Description: Solve. For Exercises 83 and 84, see the second Concept Check in this section, for Exercises 85 and 86, see the third Concept Check. In our definition of division for (P)/(Q) ÷(R)/(S) we stated that Q ≠0, S ≠0, and R ≠0 . Explain why R cannot equal 0.

   Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check.
In our definition of division for
$$
\frac{P}{Q} \div \frac{R}{S}
$$
we stated that $Q \neq 0, S \neq 0,$ and $R \neq 0 .$ Explain why $R$ cannot equal 0.

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 6, Problem 95

Instant Answer

Solved by Expert Amy Jiang

07/16/2020

Step 1

The expression given is $$ \frac{P}{Q} \div \frac{R}{S} $$ where it is stated that $ Q \neq 0 $, $ S \neq 0 $, and $ R \neq 0 $. The operation involved is division of two fractions. Show more…

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Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check. In our definition of division for $$ \frac{P}{Q} \div \frac{R}{S} $$ we stated that $Q \neq 0, S \neq 0,$ and $R \neq 0 .$ Explain why $R$ cannot equal 0.

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Key Concepts

Reciprocal and Undefined Division by Zero

The reciprocal of a fraction is obtained by interchanging its numerator and denominator. For the operation to be valid, the numerator of the original divisor must be nonzero because it becomes the denominator in the reciprocal. If this numerator were zero, it would result in a division by zero, an undefined operation. Thus, the condition that the numerator of the divisor (R in the example) must not equal zero is essential to avoid undefined mathematical expressions.

Division of Fractions

Dividing one fraction by another is carried out by multiplying the first fraction (dividend) by the reciprocal of the second fraction (divisor). This method relies on the idea that division is the inverse of multiplication, and it requires all parts of the fractions to be valid, meaning that none of the denominators or numerators that become denominators in the reciprocal process are zero.

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