Author name: Jason

Articles, Maths

Maths. The truth about adding or subtracting mixed numbers!

What is The truth about adding or subtracting mixed numbers?
It is a common misconception that one needs to convert mixed numbers into top heavy fractions to add or subtract them. Unlike with multiplication or division of mixed numbers we can leave them as mixed numbers.
Example 1
158 7/8 +23 23/24.
This means 158 + 7/8 + 23 + 23/24 so, of course we can add the whole number parts and fraction parts separately.
We get 181 + 44/24
= 181 + 11/6
= 182 5/6
It would have been very time consuming to have turned them into top heavy fractions, which not only would have been a waste of time in an exam but would also have increased the chance of making mistakes.
Example 2
68 1/4 – 25 1/3.
This means (68 + 1/4) – (25 + 1/3)
= 68 +1/4 – 25 – 1/3
= 43 + (3 – 4)/12
= 42 + (3 + 12 -4)/12
= 42 11/12
Again, we subtracted the whole number and fraction parts separately, but when the fraction part becomes negative we make the whole number part one less and add one back in terms of the lowest common denominator to keep the overall value the same.

Articles, French

French Tutor North London | The French Subjunctive!

The French Subjunctive

As a French Tutor I have always been fascinated by the French grammar and its logic that is on the whole so similar to Maths. I find the subjunctive opens up so many possibilities.

Usage

There are many cases but the general and easiest case will be dealt with here.(A lesson will be needed for full details). It can often be used when infinitives in English cannot be used in French where the subject is different. Think of the example “I want to drink”. The infinitive can be used in French in the same way as in English as there is only one subject involved here ie “Me”.(Je veux boire).

It becomes interesting when one wants to say for example “I want him to drink”. There are now two subjects here ie “Him and me”. The infinitive now must not be used in French. We now have to translate ” I want that he drinks” with one small change beyond that. The subjunctive is used in the subordinate clause “He drinks” but not in the main clause “I want”. Therefore, the whole sentence will read “Je veux qu’il boive”, instead of “Je veux qu’il boit” (which would be incorrect). The technical reason why a subjunctive is used is because “Wanting” conveys a significant uncertainty and therefore the “Drinking” may never become reality (It is hypothetical). (That is NOT to say that “Maybe” sentences are allowed a subjunctive). This now leads us to how the subjunctive is formed.

Formation

Apart from the seven irregular or semi irregular verbs in the present subjunctive the rule is as follows:

Take the the “Ils” form of the present tense and remove the “Ent” for the first column only and add the present tense “ER” verb endings. In the second column the “Nous” and “Vous” forms will be identical to the imperfect tense and the “Ils” form will be identical to its present tense counterpart. Here is “Boire” in the present subjunctive:

Je boive Nous buvions

Tu boives Vous buviez

Il boive Ils boivent

Other Tenses

Please note that the imperfect subjunctive and the pluperfect subjunctive are extremely rarely used in conversational French and rarely in written French nowadays. They need to be recognised at A- Level and beyond. The perfect subjunctive is used still as it just requires the present subjunctive of “Avoir” or “Être” + the Past Participle.

Miscellaneous

One could be forgiven for thinking that “Espérer que” clauses would be followed by a subjunctive, but this would not be correct. It could be because “Hope” is thought to be something likely which requires an indicative in French. However, Spanish does not take the same view here.

Articles, Spanish

Spanish tutoring lessons in London | El pretérito grave

El pretérito grave
El pretérito grave is an irregular form of the preterite tense but with a pattern nonetheless. In fact, the only difficulty is having to memorise the irregular stem which is different from the infinitive stem. You just add the following endings to the stem:
e imos
iste isteis
o ieron
You may have noticed that the endings are identical to the ER and IR preterite endings except the 1st person singular and the 3rd person singular forms are like the AR preterite endings but without the accents.
Example with Poner
Puse Pusimos
Pusiste Pusisteis
Puso Pusieron
So, instead of the stem being Pon as usual, you have to remember it is Pus and then simply add the above endings which are easy to remember once you are proficient in the regular preterite endings.

Articles, Maths

What is an equation and what is an identity?

An Identity
An identity could be thought of as an equation where both sides are the same way or a different way of expressing the same thing. The interesting property about this is that it will hold true for no matter what values are chosen for the unknown(s). An identity could therefore be thought of as an equation with infinitely many solutions.
Example 1
a+a=2a
This will become 2a=2a when the left hand side is simplified. It is worth noting in simple English that this identity means when you add a number to itself like this, you will get two times that number.
A typical equation that is not an identity is an equation where the left hand side is not equal to the right hand side except when the correct value(s) of the unknown(s) is/are found, indeed if there is a solution.
Example 2
5c -9=4c +7
The left hand side is not another way of expressing the right hand side and vice versa, therefore it is not an identity.
c=16 is the solution and will make both sides equal to 71.

Articles, Maths

Maths tutoring

Even good schools get it so wrong about Maths

It is sadly a too common story that even good private schools, even in affluent areas are giving false praise about their pupils’ standard or progress in Mathematics. For example, if I am teaching Arithmetical Fractions in Year 10 or 11 it is a sign something is seriously wrong and the schools don’t seem to mind even in the run up to the new harder GCSEs.

It may seem attractive when a school offers coaching as it may well be all inclusive, but please remember it is cheap or free for a reason. It is far better to have a more expensive tutor who does the job properly and in fewer sessions than a cheaper tutor with very limited progress. It may even be better financially in the long term because of the shorter period of needing coaching. You will be very happy with my Maths tutoring or coaching.

Articles, Chess

Chess openings for beginners

King’s pawn openings or Queen’s pawn openings for beginners?
It is my very strong belief that beginners should play King’s pawn openings, in other words, 1.e4 because it is extremely important to familiarise oneself with tactics (Complications and combinations) more likely to arise from this opening because the light squared bishop’s diagonal is opened up ready to target potentially the f7 square next to the enemy’s king. Also, the e4 pawn for example is undefended by the queen making the game more of an exercise in both attacking and defending and of course not being able to ignore the opponent’s move.

With Queen’s pawn openings ie, 1.d4 the d4 pawn is already protected by the queen meaning there is more flexibility with move order, which may seem attractive but with the downside of not being trained to think as much. Also, the pieces eg the queen’s bishop can become more focused towards the c7 square next to the queen, making it a more indirect attack on the king eventually. Such positions of trying to accumulate small advantages are an important skill once the skill of playing tactically has been sufficiently developed from the other opening because it is no good having a positional advantage that you don’t know how to convert because of weak tactics. Tactics can eventually arise from any opening, so it is important to become good at the basics first from the King’s pawn opening.

Besides, Chess tactics are a great deal of fun and this is important for a beginner player with a game full of action, otherwise the game may not appear interesting to them. It is a win-win situation.

My Chess tutoring or coaching should help immensely with this too and if there is a good case for a Queen’s pawn opening instead I would be happy to explore that too.

Articles, Chess

Castling in Chess

King’s pawn openings or Queen’s pawn openings for beginners?

It is my very strong belief that beginners should play King’s pawn openings, in other words, 1.e4 because it is extremely important to familiarise oneself with tactics (Complications and combinations) more likely to arise from this opening because the light squared bishop’s diagonal is opened up ready to target potentially the f7 square next to the enemy’s king. Also, the e4 pawn for example is undefended by the queen making the game more of an exercise in both attacking and defending and of course not being able to ignore the opponent’s move.

With Queen’s pawn openings ie, 1.d4 the d4 pawn is already protected by the queen meaning there is more flexibility with move order, which may seem attractive but with the downside of not being trained to think as much. Also, the pieces eg the queen’s bishop can become more focused towards the c7 square next to the queen, making it a more indirect attack on the king eventually. Such positions of trying to accumulate small advantages are an important skill once the skill of playing tactically has been sufficiently developed from the other opening because it is no good having

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