Math can be terrifying for many people. This list will
hopefully improve your general knowledge of mathematical tricks and
your speed when you need to do math in your head.
So here's 9 super mental math tricks...
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.
