Being able to perform arithmetic
quickly and mentally can greatly boost your self-esteem, especially if you
don’t consider yourself to be very good at Math. And, getting comfortable with
arithmetic might just motivate you to dive deeper into other things mathematical.
This article presents nine ideas that
will hopefully get you to look at arithmetic as a game, one in which you can
see patterns among numbers and pick then apply the right trick to quickly doing
the calculation.
The tricks in this article all involve
multiplication.
Don’t be discouraged if the tricks
seem difficult at first. Learn one trick at a time. Read the description,
explanation, and examples several times for each technique you’re learning.
Then make up some of your own examples and practice the technique.
As you learn and practice the tricks
make sure you check your results by doing multiplication the way you’re used
to, until the tricks start to become second nature. Checking your results is
critically important: the last thing you want to do is learn the tricks
incorrectly.
1. Multiplying
by 9, or 99, or 999
Multiplying by 9 is really multiplying
by 10-1.
So, 9×9 is just 9x(10-1) which is
9×10-9 which is 90-9 or 81.
Let’s try a harder example: 46×9 =
46×10-46 = 460-46 = 414.
One more example: 68×9 = 680-68 = 612.
To multiply by 99, you multiply by
100-1.
So, 46×99 = 46x(100-1) = 4600-46 =
4554.
Multiplying by 999 is similar to
multiplying by 9 and by 99.
38×999 = 38x(1000-1) = 38000-38 =
37962.
2. Multiplying
by 11
To multiply a number by 11 you add
pairs of numbers next to each other, except for the numbers on the edges.
Let me illustrate:
To multiply 436 by 11 go from right to
left.
First write down the 6 then add 6 to
its neighbor on the left, 3, to get 9.
Write down 9 to the left of 6.
Then add 4 to 3 to get 7. Write down
7.
Then, write down the leftmost digit,
4.
So, 436×11 = is 4796.
Let’s do another example: 3254×11.
The answer comes from these sums and
edge numbers: (3)(3+2)(2+5)(5+4)(4) = 35794.
One more example, this one involving
carrying: 4657×11.
Write down the sums and edge numbers:
(4)(4+6)(6+5)(5+7)(7).
Going from right to left we write down
7.
Then we notice that 5+7=12.
So we write down 2 and carry the 1.
6+5 = 11, plus the 1 we carried = 12.
So, we write down the 2 and carry the
1.
4+6 = 10, plus the 1 we carried = 11.
So, we write down the 1 and carry the
1.
To the leftmost digit, 4, we add the 1
we carried.
So, 4657×11 = 51227 .
3. Multiplying
by 5, 25, or 125
Multiplying by 5 is just multiplying
by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end
of the number.
12×5 = (12×10)/2 = 120/2 = 60.
Another example: 64×5 = 640/2 = 320.
And, 4286×5 = 42860/2 = 21430.
To multiply by 25 you multiply by 100
(just add two 0’s to the end of the number) then divide by 4, since 100 = 25×4.
Note: to divide by 4 your can just divide by 2 twice, since 2×2 = 4.
64×25 = 6400/4 = 3200/2 = 1600.
58×25 = 5800/4 = 2900/2 = 1450.
To multiply by 125, you multipy by
1000 then divide by 8 since 8×125 = 1000. Notice that 8 = 2×2x2. So, to divide
by 1000 add three 0’s to the number and divide by 2 three times.
32×125 = 32000/8 = 16000/4 = 8000/2 =
4000.
48×125 = 48000/8 = 24000/4 = 12000/2 =
6000.
