Did you know you can easily multiply 86 x 74 in
your head?
The answer is 6,364.
Here's how you do it:
Any time you multiply two numbers that are equidistant (the same
distance) from another number (86 and 74 are each 6 away from 80), then all you
have to do is multiply the middle number (80 in this case) by itself and then
subtract the distance (6) multiplied by itself (36). In our example problem you
would do the following:
1.) 80 x 80 = 6,400
2.) 6,400 - (6 x 6) =
6,400 - 36
3.) 6,400 - 36 = 6,364
Here are a few other examples:
9 x 11 = ___
1.) 10 x 10 = 100
use 10 because it is in the middle of 9 and 11
2.) 100 - (1 x 1) = 100 - 1
subtract the distance times itself (9 and 11 are
each 1
away from 10)
3.) 100 - 1
= 99
42 x 38 = ___
1.) 40 x 40 = 1,600
use 40 because it is in the middle of 42 and
38
2.) 1,600 - (2 x 2) = 1,600 - 4
subtract the distance times itself (42 and 38
are
each 2 away from 40)
3.)
1,600 - 4 = 1,596
67 x 53 = ___
1.) 60 x 60 =
3,600 use 60 because it is in
the middle of 67 and 53
2.) 3,600 - (7 x 7) = 3,600 - 49
subtract the distance times
itself (67 and 53
are each 7 away from 60)
3.) 3,600 - 49 = 3,551
Try this one on your own: 24 x 16
A final note: This trick doesn't just work with numbers that are
equidistant from a number ending in zero, as in the problems above, but these
are the easiest examples of problems where you could use this trick. The reason
for this is that numbers ending in zero are the easiest to multiply by
themselves (e.g. 60 x 60 = 3,600; 90 x 90 = 8,100; etc.). However, you could
use the trick when this situation doesn't come up. For instance, look at 8 x
16. Both of those numbers are 4 away from 12. So multiply 12 by itself (you
should get 144) and then subtract (4 x 4). You'll end up with 144 - 16 = 128.
Pretty easy, huh?
I hope you're learning some neat tricks yourself (and
history lessons too)! |
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