mind game maths

37 x 3 .= 111
37 x 6 .= 222
37 x 9 .= 333
37 x 12 .= 444
37 x 15 .= 555
37 x 18 .= 666
37 x 21 .= 777
37 x 24 .= 888
37 x 27 .= 999

15873 x 7 .= 111111
15873 x 14 .= 222222
15873 x 21 .= 333333
15873 x 28 .= 444444
15873 x 35 .= 555555
15873 x 42 .= 666666
15873 x 49 .= 777777
15873 x 56 .= 888888
15873 x 63 .= 999999

--
A.M.Abdul Malick

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squaring-2-digit-numbers-that-end-in-5.html
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multiplying-by-5-25-or-125.html
multiplying-by-11.html
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Wednesday, September 1, 2010

Maths Game 18

Maths Game

Make use of any 3 different maths operators to generate the number 18.

Rule of the game: The last maths operator has to be the first for the next person to continue, and no numbers in the operation are to be the same.

Start: 18 ==> 40 / 2 - 5 + 3 ==> .......

Happy thinking

Saturday, August 28, 2010

Maths Game - "Reversity"

This is a maths game that I strongly recommend to anyone who like to keep their brain active.

You will find it wonderful and importantly, it is free and requires only a piece of paper and a pencil to go with it.

This activity is not new. I have seen many with deviation.

Here I will share with you the concept.

CONCEPT: The target ( a list of number from 1 to 10, or similar list) is to be produced using a set of pre-defined numbers, or a certain number only. Any mathematical operation can be utilised to achieve the target.

Example:

To produce a list of number from 0 to 10 using ALL the numbers 1, 2, 3 and 4, with any of the mathematics operators, + , -, /, x, ) ( and exponential.

Here it goes...

0 = 4 - 3 - ( 2 - 1 )
1 = (4 - 2 )/ (3 - 1 )
2 = (4 + 2¹) / 3
3 = 4¹ + 2 -3
4 = 4 x 2 - 3 - 1
5 = 4 x 2 - 3¹
6 = 4 + 2 / 1³
7 = 4 + 3 / 1²
8 = 4 x 2 / 1³
9 = 4 x 2 + 1³
10 = 4 x 2 + 3 - 1

This is a simple maths game, but it involves the application of the basic principle of mathematics to achieve the targeted number for a given set of constraints.

"Reversity" - a reversal of the mathematical procedure.

Another tougher Reversity game is to have only the number 4 used.

Any deviation can be created to generate different levels of difficulties. Explore it!

Keep your mind in reverse gear ....... ! s r e e h C (reversed)

http://mathsisinteresting.blogspot.com/search/label/mental%20maths

3 squire Total = 15



8	1	6
3	5	7
4	9	2

1241/9=137.80

1 1+2 3+4 7+1

1 3 7 8

123

123 add 123

123123

Divide by 7, 11, 13 ( 1001 )

= 123

Use Match sticks

456

4 = 4 sticks

5 = 5 sticks

6 = 6 sticks

671 x 992

329 x 008 = 2 632

( 6+3=9 7+2=9 1+9=10, 9+0=9 9+0=9 2+8=10 )

671 + 2 - 8 = 665

665632

356x532


3	5	6
1/5	2/5	3/0	5
0/9	1/5	1/8	3
0/6	1/0	1/2	2

multiply 3

103 x 104 = 10712

103 + 4 = 107

3 x 4 = 12

= 107 12

multiply 2

7 x 8 = 56

7 8

3 2 ( 7+3=10, 8+2=10 )

_________

10 10

7 - 2 = 5

3 x 2 = 6

2 digit even num multiply

41 x 41 = 1681

40 x 40 = 1600

40 + 40 = 80

+ 1 = 1

= 1681

Wednesday, November 19, 2008

Multiplying by a power of 2

To multiply a number by 2, 4, 8, 16, 32, or some other power of 2 just keep doubling

the product as many times as necessary. If you want to multiply by 16 then double the

number 4 times since 16 = 2×2x2×2.

15×16: 15×2 = 30. 30×2 = 60. 60×2 = 120. 120×2 = 240.23×8: 23×2 = 46. 46×2 = 92.

92×2 = 184.54×8: 54×2 = 108. 108×2 = 216. 216×2 = 432.

Practice these tricks and you’ll get good at solving many different kinds of arithmetic

problems in your head, or at least quickly on paper. Half the fun is identifying which

trick to use. Sometimes more than one trick will apply and you’ll get to choose which

one is easiest for a particular problem.

Multiplication can be a great sport! Enjoy.

Multiplying by doubling and halving

There are cases when you’re multiplying two numbers together and one of the

numbers is even. In this case you can divide that number by two and multiply the

other number by 2. You can do this over and over until you get to multiplication this

is easy for you to do.

Let’s say you want to multiply 14 by 16. You can do this:

14×16 = 28×8 = 56×4 = 112×2 = 224.

Another example: 12×15 = 6×30 = 6×3 with a 0 at the end so it’s 180.

48×17 = 24×34 = 12×68 = 6×136 = 3×272 = 816. (Being able to calculate that 3×27 =

81 in your head is very helpful for this problem.)

Squaring other 2-digit numbers

Let’s say you want to square 58. Square each digit and write a partial answer. 5×5

= 25. 8×8 = 64. Write down 2564 to start. Then, multiply the two digits of the

number you’re squaring together, 5×8=40.

Double this product: 40×2=80, then add a 0 to it, getting 800.

Add 800 to 2564 to get 3364.

This is pretty complicated so let’s do more examples.

32×32. The first part of the answer comes from squaring 3 and 2.

3×3=9. 2×2 = 4. Write down 0904. Notice the extra zeros. It’s important that every

square in the partial product have two digits.

Multiply the digits, 2 and 3, together and double the whole thing. 2×3x2 = 12.

Add a zero to get 120. Add 120 to the partial product, 0904, and we get 1024.

56×56. The partial product comes from 5×5 and 6×6. Write down 2536.

5×6x2 = 60. Add a zero to get 600.

56×56 = 2536+600 = 3136.

One more example: 67×67. Write down 3649 as the partial product.

6×7x2 = 42×2 = 84. Add a zero to get 840.

67×67=3649+840 = 4489.

Multiplying together 2-digit numbers where the first digits are the same and the last digits sum to 10

Let’s say you want to multiply 42 by 48. You notice that the first digit is 4 in both

cases. You also notice that the other digits, 2 and 8, sum to 10. You can then use this

trick: multiply the first digit by one more than itself to get the first part of the answer

and multiply the last digits together to get the second (right) part of the answer.

An illustration is in order:

To calculate 42×48: Multiply 4 by 4+1. So, 4×5 = 20. Write down 20.

Multiply together the last digits: 2×8 = 16. Write down 16.

The product of 42 and 48 is thus 2016.

Notice that for this particular example you could also have noticed that 42 and 48

differ by 6 and have applied technique number 4.

Another example: 64×66. 6×7 = 42. 4×6 = 24. The product is 4224.

A final example: 86×84. 8×9 = 72. 6×4 = 24. The product is 7224

Squaring 2-digit numbers that end in 5

If a number ends in 5 then its square always ends in 25. To get the rest of the product

take the left digit and multiply it by one more than itself.

35×35 ends in 25. We get the rest of the product by multiplying 3 by one more than 3.

So, 3×4 = 12 and that’s the rest of the product. Thus, 35×35 = 1225.

To calculate 65×65, notice that 6×7 = 42 and write down 4225 as the answer.

85×85: Calculate 8×9 = 72 and write down 7225.

Multiplying together two numbers that differ by a small even number

This trick only works if you’ve memorized or can quickly calculate the squares of

numbers. If you’re able to memorize some squares and use the tricks described later

for some kinds of numbers you’ll be able to quickly multiply together many pairs of

numbers that differ by 2, or 4, or 6.

Let’s say you want to calculate 12×14.

When two numbers differ by two their product is always the square of the number in

between them minus 1.

12×14 = (13×13)-1 = 168.

16×18 = (17×17)-1 = 288.

99×101 = (100×100)-1 = 10000-1 = 9999

If two numbers differ by 4 then their product is the square of the number in the

middle (the average of the two numbers) minus 4.

11×15 = (13×13)-4 = 169-4 = 165.

13×17 = (15×15)-4 = 225-4 = 221.

If the two numbers differ by 6 then their product is the square of their average minus

9.

12×18 = (15×15)-9 = 216.

17×23 = (20×20)-9 = 391.

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.

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 .

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.