The Magic Number



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.

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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. Try the trick out first and show why it works.

|Instructions |My Example |Your 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! | |

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! |By gum! It works! | |

3. 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! |What a trick! | |

4. 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 |Example |The Algebra |

|Think of a number |4 |n |

|Add 5 |9 |n+5 |

|Multiply by 3 |27 |3(n+5) = 3n+15 |

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| | | |

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5. 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!

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