Not sure about "quick" mental maths... what sort of time limit are you facing?
But I generally find that for these sorts of exercises, you often need to spot the "short cuts" to get the figures into nice round numbers... usually, this is due to converting values from "hours" to "minutes" or recognising that 12 minutes = 1/5th of an hour etc... or decimals into whole numbers by removing the decimal point and adding back later on... and a lot of the values given will be evenly divisible by 60 to give you "per minute" values etc... then a bit of pencil/paper multiplication will usually give you the answer. Sometimes I find that breaking the multiplication or division down into smaller parts helps to calculate it mentally... ie. 3960 / 360... => 3600 / 360 = 10... 360 left over... 360 / 360 = 1... 10 + 1 = 11... so 3960 / 360 = 11
A man exchanges 368 pounds for dollars at an exchange rate of 1 pound=1:72 dollars. How many dollars does he get in return? (answer to the nearest dollar)
Is straight multiplication if you remove the decimal point... 368 * 172 = 63292, then put the decimal point back in => 632.92... rounded to nearest dollar = 633
If you travel 1248 miles, how much fuel will you need if you burn 4500 kgs per hour and are travelling at 72O mph?
convert the "per hour" figures into "per minute"... wouldn't you know it, 720 mph is divisible by 60
720 / 60 = 12 miles a minute....
1248 miles / 12 = 104 minutes... (1200 / 12 = 100... 48 / 12 = 4... 100+4)
What about the fuel burn? huh, look at that 4500 kg/hr is also cleanly divisible by 60 (4200 / 60 = 70, 300 / 60 = 5)
4500 / 60 = 75kg/minute...
Then you're left with basic multiplication:
104 * 75 = 7800 kg
The basic multiplication can also be done in chunks... 100 * 75 = 7500... 75 * 4 = 300... 7500+300 = 7800 etc
A 737 flies 930 miles in 75 minutes. How many miles does it fly in 4 hours 45 minutes assuming as constant speed?
What I'm seeing here is "15 minute" chunks... 75 = 5x 15 minute chunks... 4 hrs 45 = 19x 15 minute chunks...
930 / 5 = 186 (pro tip: dividing by 5 is the same as dividing by 10 and then doubling the answer)... 930 / 10 = 93... *2 = 186
You're then left with "easy" multiplication of 186 * 19 = 3534...
You could also do 186 * 20 = 3720... then subtract the 186 to give 3534.
If an aircraft departed an airfield and headed directly south for 16 miles and then turned onto a heading of 27O degrees for 12 minutes at an average speed of 80 miles per hour, how many miles is it (in a straight line) from its original destination?
Ok... so 12 minutes = 1/5th of an hour... 80 / 5 = 16 miles...
south then west is a right angle triangle with two sides of 16 miles and 16 miles... I'm not sure this is solvable with mental math... but I know with a 45-45-90 triangle like this... the hypotenuse is x* sqrt(2)...
maybe the a-squared + b-squared = c-squared? Honestly, I'd probably just guess knowing that sqrt(2) is around 1.4... 16 * 1.4 ~= 22.5 miles.
How many nautical miles can an aircraft travel if it is carrying 288O kgs of fuel and burns 240 kgs an hour averaging a speed of 375 knots?
need to get total endurance... fuel onboard / fuel burn... 2880 / 240... well 2400 / 240 = 10... leaving 480... 480/240 = 2... so 2880 / 240 = 12...
so we have 12 hours of fuel on board... again we're doing "simple" multiplication in a speed/time/distance calc... 375 kts * 12 hrs = 4500 nm
Again, you can always do 375 * 10 = 3750... 375 * 2 = 750... 3750 + 750 = 4500...
You'll find that as you practice, practice, practice... you'll start to notice the "short cuts"
