Maths

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.

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.

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.