I am still struggling with calculating efficiently.
Are there any shortcuts to this calculation or do I just have to get quicker with my pen&paper math (long multiplications). Even if I summarize the calculation to 23 * 1760 * 35, I feel that I still need long multiplication to solve it.
Do I miss the obvious here? Or is long multiplication indeed intended for this calculation?
With multiple-factor multiplications like these it is often a good idea to change the order of operations and group the numbers more efficiently.
As a first step, I would propose the following:
((25 * 8) * 1.4) * 220 * 23 = (200*1.4) * 220 * 23 = 280 * 220 * 23
As a second step, the 280 * 220 can be simplified using the distance-of-squares method. Both numbers are 30 away from 250, so you can calculate the result as follows:
280 * 220 = 250^2 - 30^2 = 62500 - 900 = 61600
Please note that there is a shortcut for squares ending in 5 that I've used here - basically, if you square a number ending in 5, take the non-unit digit, multiply it with itself + 10, and add 25.
And now the calculation boils down to 61600 * 23, which I would treat as such:
61600 * 23 = 61600 * 20 + 61600 * 3 = 1232000 + 184800 = 1416800
Hope this helps!
Hello!
I would:
Hope it helps!
Cheers,
Clara
Hi,
I recommend this video to learn how to multiply double-digit numbers really fast. In my opinion it's the biggest contributor to the speed of calculations:
Learn how to multiply double digit numbers (https://www.youtube.com/watch?v=6ndkkPZYJHo)
Best
I agree with Alexander. It is always easy to change the order and calculate. Preference should be given to those that result in round numbers. I would proceed in the following way:
First multiply 8*25 and then multiply the result 200 with 1,4. Till that it's quite simple. Multiplying 280 with 220 and 23 is the hard part. You can break 220 and 23 into 200+20 and 23. If you notice multiplying by 2 is not that difficult. So multiplying (200+20) with (23) would yield 4600+460 = 5060. Now multiply 280 by (10000/2 + 60) = 1,400,000+16,800 = 1,416,800
(25*8)*(1.4)*(200+20)(23) = 200*1.4*(4600+460) = 280*(5000+60) = 280*(10,000/2 + 60) = 1,400,000 + 16,800 = 1,416,800. If you find multipluying with 60 is hard, then you can break it into (100/2 + 10).
Hope this helps!
