If say, I subtract 10% from 165 I am left with 148.5. 10% being 16.5.

In your books you suggest to simplify things to divide by 1.1.

165/1.1= 150

In the world I get that, that should suffice but does it hold up the exam standard?

Thanks in advance
Mike

Hi Mike,

The tolerances in the CASA exams regarding calculations tend to be tight. For example, when calculating contingencies and fixed reserves, it's important to understand the difference between adding and removing 10% with that particular formula.

Multiplying a given value by 1.1 precisely adds 10%. For example, 100 × 1.1 = 110.

Dividing a given value by 1.1 to remove 10% is an approximation and not mathematically precise. For example, 100 ÷ 1.1 = 90.91.

Sometimes one question might be the difference between a pass and fail. While there might be some lenience on either side of the true value in the exam, if you perform your calculations mathematically correctly, your answer will always be accurate.

It's worth noting that dividing by 1.1 is the correct way to reverse a 10% increase, making it useful for working out what a given quantity of fuel equals with the VR or FR removed. However, if you're adding 10%, multiplying by 1.1 remains the best approach

If say, I subtract 10% from 165 I am left with 148.5. 10% being 16.5.

That's fine and quite correct ........ but it has absolutely NOTHING to do with the standard fuel calculations. What you have done is figure 10% of the (flight fuel + contingency) subtotal and then subtract that value from the subtotal. The flight fuel process calculates 10% of the flight fuel and then adds that to the flight fuel. Two quite different calculations. The required calculation is to start with flight fuel and then figure 10% of that for the contingency.

For a total of (flight fuel + contingency fuel) = 165, we would have arrived at that figure by starting with 150, calculating 10% of 150, and then adding that fraction to the 150 starting position to get 150 + 15 = 165. In effect, what this does is

= 150 + 150 x (10/100)
= 150 x 1 + 150 x 0.1
= 150 x ( 1 + 0.1 )
= 150 x 1.1
= 165

To run this in the reverse direction, the algebraic process required is to do a bit of cross multiplication (you might see the term "literal operation") -

165 = 1.1 x 150. Divide both sides by 1.1 to get

165/1.1 = (1.1 x 150) /1.1 = 150

So far as the exam is concerned, if you were to run your suggested calculation, the resulting output is incorrect and you would be marked wrong. End of story, I'm afraid.

The tolerances in the CASA exams regarding calculations tend to be tight

Quite irrelevant. Mike's suggested process is incorrect and would be marked wrong.

Dividing a given value by 1.1 to remove 10% is an approximation and not mathematically precise.

I'm afraid that that is absolute arithmetic nonsense. It is, on the other hand, dead accurate.

For example, 100 ÷ 1.1 = 90.91

Absolutely correct but not a great deal of use to the discussion. Were we to use your initial example

100 x 1.1 = 110

then we can run the sum the other way to get

110/1.1 = 100

No approximation, dead accurate.

It's worth noting that dividing by 1.1 is the correct way to reverse a 10% increase,

Is this not the reverse of your earlier statement ?