Andra-Lorena G.

Currently unavailable: until 23/12/2015

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

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My passion for Mathematics has been easily noticeable since primary school. In the next few years it became familiar territory, so applying for Mathematics at university has been an obvious choice. I can think of no better way to spend my spare time than passing on my passion and understanding of this subject.

Being a student myself, I believe I can communicate with other students on the same level, eliminating the pressure of an older authority figure, thus making the student a lot more confortable in asking questions and not being afraid of making mistakes.

I have been a private tutor in the past, teaching both face-to-face and online. Additionally, during the last academic year I have worked in an adventure park on weekends and during summer I’ve been fundraising for charities. My part time work has highly increased my communication skills. However, these jobs did not prevent me from studying, as I have achieved a high 1st in my first year of university. I believe the practical skills acquired from work experience combined with my outstanding academic ability will set me up with the skills to make a success of every single lesson.

#### Subjects offered

SubjectLevelMy prices
Maths A Level £20 /hr
Maths GCSE £18 /hr

#### Qualifications

MathematicsA-LevelA*
Further MathematicsA-LevelA
BiologyA-LevelA
 CRB/DBS Standard No CRB/DBS Enhanced No

### 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...

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

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

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2 years ago

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