/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 40 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 40

Perform the indicated operations. Final answers should be reduced to lowest terms. $$\frac{x^{2}}{10} \div\left(\frac{2}{x} \div \frac{x}{5}\right)$$

Short Answer

Expert verified
\[ \frac{x^{4}}{100} \]

Step by step solution

01

- Simplify the innermost division

First, simplify the innermost division which is \(\frac{2}{x} \div\frac{x}{5}\). To do this, multiply the first fraction by the reciprocal of the second fraction: \frac{2}{x} \div\frac{x}{5} = \frac{2}{x} \times\frac{5}{x} = \frac{2 \times\rm{5}}{x \times\rm{x}} = \frac{10}{x^2}\.
02

- Replace and simplify the outer division

Now replace the simplified expression back into the original problem: \(\frac{x^{2}}{10} \div \frac{10}{x^{2}}\). Again, multiply the first fraction by the reciprocal of the second fraction: \(\frac{x^{2}}{10} \times \frac{x^{2}}{10} = \frac{x^{2} \times \rm{x^{2}}}{10 \times \rm{10}} = \frac{x^{4}}{100}\).
03

- Simplify the final expression

Reduce \(\frac{x^{4}}{100}\) to its lowest terms. There are no common factors between the numerator and the denominator, so the fraction is already in its lowest terms.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Division of Fractions
When you see a division operation with fractions, the first step is to think about multiplying by the reciprocal instead of dividing directly. Let's take the example of \(\frac{2}{x} \div \frac{x}{5}\). Here, instead of dividing \(\frac{2}{x}\) by \(\frac{x}{5}\), we multiply \(\frac{2}{x}\) by the reciprocal of \(\frac{x}{5}\). The reciprocal of \(\frac{x}{5}\) is \(\frac{5}{x}\). So, the division becomes: \[\frac{2}{x} \times \frac{5}{x} \].

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve the equations and inequalities. $$\frac{t}{2}+\frac{t-1}{3}+\frac{t-6}{4}=t-2$$

Solve the equations and inequalities. $$3-\frac{a+1}{4}=\frac{a+4}{2}$$

Solve the equations and inequalities. $$0.06 x+0.04(5.000-x)=320$$

Solve the equations and inequalities. $$0.5(x+2)-0.3(x-4)=3$$

In each of the following exercises, perform the indicated operations. Express your answer as a single fraction reduced to lowest terms. $$\frac{3 x+2}{15}+\frac{x}{40}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.