The Magic Number
1. Have your friend think of a number between 1 and 100, and to keep it a secret.
2. Now, using your calculator, take your age, multiply by 2, add 5, multiply by 50, and
subtract 365.
3. Next, keep that number from the last step on the calculator, hand the calculator
to your friend, and tell them to add their secret number, then add 115.
4. The first half of the resulting number is your age, and the other part of the
number is your friend's secret number!
Gimme 5!
1. Ask a friend to pick a number.
2. Add the next higher number to it.
3. Add 9 and divide by 2, and then subtract the original number.
Is it 5?!
Guess the Number
1. Write a number on a piece of paper equal to the current year times two. (example:
1999 x 2 =3998).
2. Fold the paper and put it in your pocket.
3. Give your friend a piece of paper and a pencil.
4. Tell your friend to write down the following:
A. The year he was born
B. The year he started school
C. How old he will be at the end of this year
D. The number of years he has been in school by the end of this year.
Make sure he doesn’t' t tell you any of these numbers!
5. Tell your friend to add up all of his numbers.
6. Now, take out the piece of paper in your pocket and amaze your friend by showing
him the same number he just wrote!
If you are using this trick for your parents, or someone finished with school, you will
have to change the questions to the following:
A. The year he was born
B. The year he graduated high school
C. How old he will be at the end of this year
D. The number of years since graduation, by the end of this year.
Number's Game
Effect: Through math, you can find out two cards that a person has chosen.
Preparation: Make sure all Tens, Jacks , Queens, and Kings have been removed from
the deck. (Aces serve as one.)
Trick:
Have the person you are showing the trick shuffle the cards. Take a group of cards
and hold them in your hand, spread out in a fan shape. Ask him/her to pick a card
from among them. Tell the person to remember it and to put it back in the deck.
Ask them to double the value of the card they picked, then to add 5. Now have them
multiply that number by 5. Tell them not to forget this number.
Instruct them to look at another card in the deck, and to add its value to the total
that they had computed before. They are to tell you the final total of everything.
In your head, subtract 25 from the total. The two digits you get are the same as the
two cards they chose. Example: they choose a Five, then a Three.
5(doubled) = 10 plus 5 = 15. Multiply times 5 = 75.
Three added to total = 78. You subtract 25 = 53.
They picked a Five and a Three!
Cancelling Digits
When you're faced with a difficult math problem, you always try to reduce the
complexity before actually doing any calculations. Here's another trick for helping.
We all know that you can remove common terms from the top and bottom of a
fraction. Did you realize that individual digits count as terms?
Disbelief! Then perhaps you need to see an example. Consider the fraction
16/64
If you cancel out the 6's, you are left with
1/4
Go ahead. Get out your calculator and try it. Sure enough 16/64 is 1/4.
But does this work in general? Let's try some more:
19/95
cancel the 9's to get
1/5
Looks good so far. But maybe it only works when the top number starts with a 1. Let's
try
26/65
cancel the 6's to get
2/5
Again, it's correct.
The Easy Way To Find More Primes
Here's another one. We all know that 11 and 13 are prime, but 15 isn't. When we get
much higher, it gets more difficult. But here's a trick for quickly finding more
primes.
Did you know you can simply reverse the digits of a prime to get a new prime?
Obviously, this won't help with 3, 5, and 7, since reversing the digits just leaves you
with the same thing.
But let's carry on to two digits. Well, 11 is pretty boring. If we reverse the digits of
13, we get 31, which is certainly prime. And, to check ourselves, if we reverse the
digits of 15 (not a prime), we get 51, which is 3 times 17, so it is not prime. Continuing,
17 gives 71, and 19 gives 91, so it all looks good.
Telling the Total.
Let a person write down a row of six figures. Then write something on a piece of
paper and lay it aside.
Another person writes six figures beneath the first row. Then you write a number of
six figures. Another person obliges with a number of six figures, and you do the same.
When the sum is added, a total is reached. Your paper is unfolded, and there is the
answer!
Method: Note the first number written. Add to it 2,000,000, and subtract 2. That is
what you write on the piece of paper. Just put down 2 less than the number written,
and put a figure 2 in front of it!
When the second number is written, you write your number. Just add enough to each
number in the second row to make each figure total 9.
When the fourth row is written, you write the fifth, and make the fourth row total 9
for every figure. That will bring your, answer.
Example: A person writes 347,628. On your paper write 2,347,626.
Now the addition may appear like this:
First row............... 347,628
Second row............. 312,799
Your row............. 687,200
Fourth row............. 810,204
Your row............. 189,795
Total............. 2,347,626
Number Tricks and Mental Math
Introduction: Squaring a number means you multiply the number by itself. It is easy
to square small numbers. For example, 72 = 7(7) = 49. Other squares are harder to
calculate in your head. Trying to solve 432 would be hard to do in your head. You can
find the answer using a pencil and paper or it is easily found using a calculator. In this
problem you will learn and use a "trick" to let you solve 432 and some other tough
questions in your head.
Problem:
Before you learn the "trick", you must know how to and become quick at squaring the
numbers between 1 and 9. Find a partner and take turns asking questions such as 52,
22, 92, 42, 12, 82, and so on. Try to give instant answers.
1. Now, here is a "trick" to square numbers between 41 and 59 in your head. In
this "trick" 25 and 50 act like "magical" numbers. The two examples below show
how the "trick" is used.
On paper, show how the "trick" would be used to solve 562. Show how it would
be used to solve 492.
2. Now take turns with your partner posing and answering questions where you
square numbers between 41 and 59 in your head. See how quickly you can
answer the questions.
3. Write down, in words, the steps of the "trick" shown in the two examples
above.
4. Can you use the "trick" to square numbers such as 382 or 662? Would you have
to make any changes to the "trick"? Is it harder to use? Explain.
5. Try to find a "trick" using 25 and 50 as "magical" numbers that helps you
multiply any two numbers between 41 and 49. For example, can you find a
"trick" that helps you multiply 43(47) in your head. Explain your "trick" and
show a few examples of it working
Number Tricks
1.
Here is a very interesting number trick.
it works.
Instructions
Try the trick out first and show why
My Example
Think of a Number
12
Add 3
15
Double your answer
30
Add 4
34
Divide the result by 2
17
Take away the original number
5
The answer is always (ta da) 5!
By golly! It works!
Your Example
2.
Now use algebra to show why this trick works. The first few steps are done for
you.
Instructions
My Example
The Algebra
Think of a number
13
n
Double it
26
2n
Add 10
36
2n + 10
Take away 6
30
Halve your answer
15
Take away 2
13
The answer is the original number!
3.
By gum! It works!
And show why this number trick always works.
Instructions
Example
The Algebra
Think of a number
Take away 1
Multiply by 5
Add 15
Divide by 5
Take away the original number
The answer is always 2!
4.
What a trick!
I’ll start this next trick for you. Your task is to figure out a set of instructions
that will finish it. You may need a bit of trial and error. Use algebra to explain
the trick.
(Hint: because you multiplied by 3, you will eventually have to divide by 3.)
Instructions
Think of a number
Example
The Algebra
4
n
Add 5
Multiply by 3
5.
9
n+5
27
3(n+5) = 3n+15
Finish off this trick also. Use algebra to explain how it works.
Instructions
Example
The Algebra
Think of a number
Double your answer
Take away 3
6.
You decide to make up a number trick as a present for a 21st birthday. Make up
a number trick that always ends in 21. (This will take a bit of planning. Good
luck!)
7.
Here is a trick that is a bit different. Explain why this trick works, using
algebra.
Instructions
Write down your house number
Double it
Add 5
Multiply by 50
Add your age
Add 365, the number of days in a year
Subtract 615
Divide by 100
The whole number is your house number, the decimal is your age.
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.
I will assume that you know your multiplication table reasonably well up to 10x10.
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 Africa mentally so it covers the 15 and the 3 from the
13 below. Those covered numbers are all you need.
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.
The 11 Rule
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. Practice it on paper first!
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
The only thing tricky to remember is that if the result of the addition is greater than
9, you only put the "ones" digit in the hole and carry the "tens" digit from the
addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1
from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627
Practice it on paper first!