Three smart mathe tricks made easy to calculate

Three smart mathe tricks made easy to calculate
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.