MYTUTOR SUBJECT ANSWERS

481 views

Prove that between every two rational numbers a/b and c/d, there is a rational number (where a,b,c,d are integers)

Attempting to find the average of a/b and c/d, we have: 

(a/b+c/d)/2 = [(ad+bc)/bd]/2 = (ad+bc)/2bd

As a,b,c,d are integers, we know that ad+bc and 2bd are also integers, as the addition and multiplication of integers will always lead to another integer. 

Therefore, we can write x=ad+bc and y=2bd, where x and y are integers.

It follows that the average between a/b and c/d is now equal to x/y

As x and y are integers, x/y will be a rational number situated between a/b and c/d. 

This proof applies to any integers a,b,c,d where b and d are non-zero integers

Andra-Lorena G. A Level Maths tutor, GCSE Maths tutor

1 year ago

Answered by Andra-Lorena, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

257 SUBJECT SPECIALISTS

£20 /hr

Henry T.

Degree: Economics (Bachelors) - Leeds University

Subjects offered: Maths, Economics

Maths
Economics

“About me: I am a 20 year old third year economics student, currently achieving a first class degree at the Univesity of Leeds. Economics and Maths are two subjects that genuinely excite me. My degree allows me to study economics but al...”

MyTutor guarantee

£24 /hr

Osian S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I'm Osian, a Master's student at the University of Warwick. I've had fun with mathematics from a young age, and I hope to be able to instill this passion for mathematics in you, through my tutorials! Throughout my time at Warwick,...”

£20 /hr

Sam H.

Degree: Physics (Masters) - Bristol University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“Top Maths and Physics tutor from the renowned university of Bristol, ready to help you improve your grades!”

MyTutor guarantee

About the author

Andra-Lorena G.

Currently unavailable: until 23/12/2015

Degree: BSc Mathematics with Finance (Bachelors) - Exeter University

Subjects offered: Maths

Maths

“My passion for Mathematics has been easily noticeable since primary school. In the next few years it became familiar territory, so applying for Mathematics...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Differentiate y = √(1 + 3x²) with respect to x

A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?

How do you find the minimum of the equation sin^2(x) + 4sin(x)?

How do you find the inverse of a function?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok