Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 21

Write down the reciprocal of the following: (a) \(\frac{1}{3}+\frac{1}{2}\) (b) \(\frac{x+y}{13}\) (c) \(\frac{2 R+1}{R-1}\) (d) \(4 !\)

Short Answer

Expert verified
Question: Find the reciprocals of the following expressions: a) \(\frac{1}{3}+\frac{1}{2}\) b) \(\frac{x+y}{13}\) c) \(\frac{2R+1}{R-1}\) d) \(4!\) Solution: a) The reciprocal of \(\frac{1}{3}+\frac{1}{2}\) is \(\frac{6}{5}\). b) The reciprocal of \(\frac{x+y}{13}\) is \(\frac{13}{x+y}\). c) The reciprocal of \(\frac{2R+1}{R-1}\) is \(\frac{R-1}{2R+1}\). d) The reciprocal of \(4!\) is \(\frac{1}{24}\).

Step by step solution

01

(a) Simplify the given expression

First, we should simplify the given expression: \(\frac{1}{3}+\frac{1}{2}\). To add fractions with different denominators, we first find a common denominator, which is the lowest common multiple (LCM) of the given denominators. The LCM of 3 and 2 is 6. Now we rewrite each fraction with the common denominator and then add them together: $$\frac{1}{3}\times \frac{2}{2} + \frac{1}{2} \times \frac{3}{3} = \frac{2}{6} + \frac{3}{6}$$
02

(a) Add the fractions

Now that the fractions have the same denominator, we can add them together: $$\frac{2}{6}+\frac{3}{6}=\frac{2+3}{6}=\frac{5}{6}$$
03

(a) Calculate the reciprocal

We have simplified the expression to \(\frac{5}{6}\). Its reciprocal will be found by inverting the fraction: $$\frac{1}{\frac{5}{6}}=\frac{6}{5}$$
04

(b) Calculate the reciprocal

The expression is given as \(\frac{x+y}{13}\). Its reciprocal will be found by inverting the fraction: $$\frac{1}{\frac{x+y}{13}}=\frac{13}{x+y}$$
05

(c) Calculate the reciprocal

The expression is given as \(\frac{2R+1}{R-1}\). Its reciprocal will be found by inverting the fraction: $$\frac{1}{\frac{2R+1}{R-1}}=\frac{R-1}{2R+1}$$
06

(d) Evaluate factorial

In this expression, \(4 !\) denotes "4 factorial," which is the product of all positive integers up to 4. Therefore, we first need to evaluate \(4 !\): $$4!=4\times3\times2\times1=24$$
07

(d) Calculate the reciprocal

We have simplified the expression to \(24\). Its reciprocal will be found by inverting the fraction: $$\frac{1}{24}$$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Simplify \(\frac{2 x-5}{10}-\frac{3 x-2}{15}\)

Factorise (a) \(m n+11 m\), (b) \(3 p q-2 p\), (c) \(11 p q-3 q r\), (d) \(4 z x+20 y z\)

Calculate the maximum and minimum values of the following resistances defined by their tolerance bands: (a) \(35 \Omega \pm 5 \%\) (b) \(470 \Omega \pm 10 \%\)

Simplify (a) \(5(3 x)\), (b) \(4(2 x)\), (c) \(8(-7 x)\)

Simplify \(\frac{x+2}{x^{2}+3 x+2} .\)
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Waves Physics

Read Explanation

Thermodynamics

Read Explanation

Electromagnetism

Read Explanation

Particle Model of Matter

Read Explanation

Radiation

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.

Sign-up for free