- Thulasi XI B -
1.
Multiply Up to 20X20 In Your Head
In just FIVE minutes you should learn to quickly multiply up to
20x20 in your head.
With this trick, you will be able to multiply any two numbers from 11 to
19 in your head quickly, without the use of a calculator.
Try this:- Take
15 x 13 for an example.
- Always
place the larger number of the two on top in your mind.
- Then
draw the shape of
- First
add 15 + 3 = 18
- Add
a zero behind it (multiply by 10) to get 180.
- Multiply
the covered lower 3 x the single digit above it the "5" (3x5=
15)
- Add
180 + 15 = 195.
You likely all know the 10 rule (to multiply by 10, just add a 0
behind the number) but do you know the 11 rule? It is as easy! You should be
able to do this one in you head for any two digit number.
To multiply any two digit number by 11: - For this
example we will use 54.
- Separate
the two digits in you mind (5__4).
- Notice the
hole between them!
- Add the 5
and the 4 together (5+4=9)
- Put the
resulting 9 in the hole 594. That's it! 11 x 54=594
For this example we will use 25
- Take the
"tens" part of the number (the 2 and add 1)=3
- Multiply
the original "tens" part of the number by the new number (2x3)
- Take the
result (2x3=6) and put 25 behind it. Result the answer 625.
55 squared = 5x6=30 ... put 25 behind it ... is 3025.
Square a 2 Digit Number, for this example 37:
- Look for
the nearest 10 boundary
- In this
case up 3 from 37 to 40.
- Since you
went UP 3 to 40 go DOWN 3 from 37 to 34.
- Now
mentally multiply 34x40
- The way I
do it is 34x10=340;
- Double it
mentally to 680
- Double it
again mentally to 1360
- This 1360
is the FIRST interim answer.
- 37 is
"3" away from the 10 boundary 40.
- Square
this "3" distance from 10 boundary.
- 3x3=9
which is the SECOND interim answer.
- Add the
two interim answers to get the final answer.
- Answer:
1360 + 9 = 1369
5. The 11 Rule Expanded
You can directly write down the answer to any number multiplied
by 11.
- Take for
example the number 51236 X 11.
- First,
write down the number with a zero in front of it.
051236
The zero is necessary so that the rules are simpler.
- Draw a
line under the number.
- It is
simple if you work through it slowly. To do this, all you have to do this
is "Add the neighbor". Look at the 6 in the "units"
position of the number. Since there is no number to the right of it, you
can't add to its "neighbor" so just write down 6 below the 6 in
the units col.
- For the
"tens" place, add the 3 to the its "neighbor" (the 6).
Write the answer: 9 below the 3.
- For the
"hundreds" place, add the 2 to the its "neighbor" (the
3). Write the answer: 5 below the 2.
- For the
"thousands" place, add the 1 to the its "neighbor"
(the 2). Write the answer: 3 below the 1.
- For the
"ten-thousands" place, add the 5 to the its "neighbor"
(the 1). Write the answer: 6 below the 5.
- For the
"hundred-thousands" place, add the 0 to the its
"neighbor" (the 5). Write the answer: 5 below the 0.
That's it ... 11 X 051236 = 563596
6. Guess Your Birthday!
Here's
a fun trick to show a friend, a group, or an entire class of people. Step 1) Have them take the month number from their birthday: January = 1, Feb = 2 etc.
Step 2) Multiply that by 5
Step 3) Then add 6
Step 4) Then multiply that total by 4
Step 5) Then add 9
Step 6) Then multiply this total by 5 once again
Step 7) Finally, have them add to that total the day they were born on. If they were born on the 18th, they add 18, etc.
Have them give you the total. In your head, subtract 165, and you will have the month and day they were born on!
How It Works: Let M be the month number and D will be the day number. After the seven steps the expression for their calculation is:
5 (4 (5 M + 6 ) + 9 ) + D = 100 M + D + 165
Thus, if you subtract off the 165, what will remain will be the month in hundreds plus the day!
7. Strange Properties of 666, "The Number of the Beast"
The last book of the Bible, Revelation, brings up the number 666 as being the number of the beast connected with the end of this age and the coming of the Messiah. You will find the direct reference in Chapter 13, verse 18 of Revelation. Besides that cataclysmic reference, the number 666 has quite a few very interesting properties.
666 = 3^6 - 2^6 + 1^6
666 = 6^3 + 6^3 + 6^3 + 6 + 6 + 6
(Mike Keith mentions that there are only five other positive integers that exhibit this property...
666 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2
666 = 1 + 2 + 3 + 4 + 567 + 89 = 123 + 456 + 78 + 9 = 9 + 87 + 6 + 543 + 21
Moreover, 666 is equal to the sum of the cubes of the digits in its square (666^2 = 443556, and the sum of the cubes of these digits is 4^3 + 4^3 + 3^3 + 5^3 + 5^3 + 6^3 = 621) plus the sum of the digits in its cube (666^3 = 295408296, and 2+9+5+4+0+8+2+9+6 = 45, and 621+45 = 666).
Incredibly, the number 666 is equal to the sum of the digits of its 47th power, and is also equal to the sum of the digits of its 51st power. That is,
666^47 = 5049969684420796753173148798405564772941516295265
4081881176326689365404466160330686530288898927188
59670297563286219594665904733945856
666^51 = 9935407575913859403342635113412959807238586374694
3100899712069131346071328296758253023455821491848
0960748972838900637634215694097683599029436416
and the sum of the digits on the right hand side is, in both cases, 666. In fact, 666 is the only integer greater than one with this property. (Also, note that from the two powers, 47 and 51, we get (4+7) (5+1) = 66.)
Mr. Keith also points out that if we assign numerical values for the letters of the alphabet starting with A = 36, B = 37, and so on, we find that the letters in the word
SUPERSTITIOUS = 666!!!
8. What Day of the Week Were You Born On?
Even though you were there at the moment of your birth, you may not remember exactly what day of the week it was. In fact, not only will this method help you find that out, you can find out the day of the week for any date you want in the 1900's. Here is a little trick to help you figure what day that was:
Step 1) Write the last two digits of the year you were born. Call it A.
Step 2) Divide that number, that is, divide A by four. Drop the remainder if there is one.
Call this answer, without the remainder, B.
Step 3) Find the month number corresponding to the month you were born in from the table below. Call it C.
Step 4) Oh, the date you were born on, call it D. (If you were born on the 12th, call D 12.)
Step 5) Now add A + B + C + D. Divide this sum by 7. The remainder you get is the key to the day of the week.
Step 6) In the table of days below, match the remainder with the day of the week you were born on.
NOTE: This trick will work for any date in the 20th century.
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TABLE OF MONTHS
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TABLE OF DAYS
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Sunday = 1
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January = 1 (0 in leap yr)
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July = 0
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Monday = 2
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February = 4 (3 in leap yr)
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August = 3
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Tuesday = 3
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March = 4
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September = 6
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Wednesday = 4
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April = 0
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October = 1
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Thursday = 5
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May = 2
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November = 4
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Friday = 6
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June = 5
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December = 6
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Saturday = 0
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The prime number 73,939,133 has a very strange property. If you keep removing a digit from the right hand end of the number, each of the remaining numbers is also prime. It's the largest number known with this property. Take a look: 73,939,133 and 73, 939, 13 and 73, 939, 1 and 73,939 and 7,393 and 739 and 73 and 7 are all prime!
10. Multiply by 5
Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex – or does it? This trick is super easy.
Take any number, then divide it by 2 (in other words, halve the number). If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works every time:
2682 x 5 = (2682 / 2) & 5 or 0
2682 / 2 = 1341 (whole number so add 0)
13410
Let’s try another:
5887 x 5
2943.5 (fractional number (ignore remainder, add 5)
29435
.
11. Tough Multiplication
If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:
32 x 125, is the same as:
16 x 250 is the same as:
8 x 500 is the same as:
4 x 1000 = 4,000
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