Counting Secrets Fast Arithmetic Series

How do I calculate a series Fast Arithmetic

Sample questions, 1. Sum the series is how fast, 1, 2, 3, 4, 5, 200 ...... Confusing?, Usually we count one-one, 1 +2 +3 +4 +5 +....+ 200. This way over time. How to calculate quickly the way, adding the first number with the last number, then add the number to two with the two last numbers, and so on. The first number, 1 + the last number, 200, amount = 201, turns the value of the number 201 of the above series there is 100 times repetition. Mean number of runs in the top = 201 x 100 = 20 100 it's easy?

Example 2, Sum this series quick, 3, 7, 11, 15, 19, 23, 27, 31 Problem above can be dealt with as a matter of the above. The first number, 3 + last number, 31 number = 34 it turns out there are 4 repetitions value 34 then the total number of runs in the top = 34 x 4 = 136

Posted by Ir. H. Hanan at 9:37 PM 0 comments Links to this post

Wednesday, April 28, 2010 How to Quickly Calculate the Power of Two

Power of two represented by the sign ^ 2, which means that number multiplied by two times. Eg 25 ^ 2 means 25 x 25. 35 ^ 2 means 35 x 35. Usually multiplying the rank is always multiplying downward. Like HOW TO CONVENTIONAL below.

35

35

____x

175

105

_____+

1225

This step is too long. How To Quickly Calculate rank: As above Problem?

A. Numbers the same tens digit and units digit 5

How to calculate:

1. Tens digit rises one digit x digit tens of

does not rise

2. Unit x unit

3. Results diimpitkan with the results of step 1 step 2

Sample questions:

1. 15 ^ 2 = .... 2. 35 ^ 2 = .... 3. 125 ^ 2 = ....

Discussion 1. 15 ^ 2 = 15 x 15

!------!

2 x 1 = 2 -----> step 1

!------! ]

steps 1 & 2 diimpitkan 5 x 5 = 25 ----> step 2

How to calculate:

Step 1, 2 x 1 = 2

Step 2, 5 x 5 = 25, then the results of steps 1, 2

diimpitkan with 2, 25 became 225, then 15 x 15 = 225

Discussion 2. 35 ^ 2 = 35 x 35

How to calculate:

1. 4 x 3 = 12

2. 5 x 5 = 25, the results of step 1, 12 diimpitkan with

the results of step 2, 25 became 225, then 35 x 35 = 1225

Discussion 3. 125 ^ 2 = 125 x 125

How to calculate:

1. 13 x 12 = 156

2. 5 x 5 = 25, the results of step 1, 156 diimpitkan with

the results of step 2, 25 so 15 625,

then 125 x 125 = 15 625

B. Numbers with digits puluhannya number 5

and the same unit

How to calculate:

1. (5 x 5) + unit

2. Units of x units,

3. Impitkan results of step 1 with the results of step 2.

Note: If the result of multiplying the units of x units

less than ten, the number 0 in front impitkan

Like, 1. 52 x 52 = .... 2. 54 x 54 = ....

Discussion 1. 52 ^ 2 = 52 x 52 = ...

1. (5 x 5) + 2 = 27

2. Unit x unit = 2 x 2 = 4, impitkan front

with 0, so 04

3. The result of step 1, 27 diimpitkan with

the results of step 2, 04, finished 2704

then 52 ^ 2 = 52 x 52 = 2704

Discussion 2. 54 ^ 2 = 54 x 54 = ...

1. (5 x 5) + 4 = 29

2. 4 x 4 = 16

3. The result of step 1, 29 diimpitkan with

the results of step 2, 16 finished in 2916,

then 54 ^ 2 = 54 x 54 = 2916

C. Rank Approaching 10

1. Multiplication rank below 10

How to calculate:

a. Summing the numbers which multiplied

with figures friend

b. friend x friend

The result of step a diimpitkan with the result b

This method is applicable for a friend x friend less

of 10

Example 1. 9 x 9 = ...

9 friends -1

a. 9 + (-1) = 8

b. -1 X -1 = 1, the results of a step, 8 diimpitkan

with the results of step b, 1 be 81 then

9 x 9 = 81

Example 2. 8 x 8 = ...

8 apartment -2

a. 8 + (-2) = 6

b. -2 X -2 = 4, the results of a step, 6 diimpitkan

with the results of step b, 4, so 64 then

8 x 8 = 64

If a friend x friend equal to 10 or more

How to Calculate:

a. friend x friend, written in units, tens

saved

b. number that multiplied + friends, then +

saved tens digit, the result

diimpit with the results of a step

unit only.

Example 1. 6 x 6 = ....

6 -4 friend

a. -4 X -4 = 16, written 6, dozens of 1 is stored

b. 6 + (-4) = 2, then + 1 = 3, the end result

diimpitkan with the results of step a, 6, so 36,

the 6 x 6 = 36

2. Multiplication rank in top 10

If a friend x friend less than 10

How to calculate:

a. Summing the numbers

will be multiplied by the number of friends

b. friend x friend, the results of a step

diimpitkan with the results of step b

Example 1. 13 x 13

13 friends 3

a. 13 + 3 = 16

b. 3 x 3 = 9, lagkah a result, 16 diimpitkan

with the results of step b, 9 then 13 x 13 = 169

If a friend x friend = 10 or more

How to calculate:

1. friend x friend, write unit, stored puluhannya

2. number that multiplied added with a friend,

results plus the number that is stored step 1

3. the results of step 2, diimpitkan with unit step 1.

For example, 14 x 14 = ...

14 friends 4

1. friend x friend, 4 x 4 = 16, written 6, 1 saved

2. (14 + 4) + 1 = 19

3. 19 diimpitkan with 6, so 196 then 14x14 = 196

D. Approaching 100 rank

1. Multiplication rank below 100

How to calculate:

a. Figures add up to be multiplied

with figures friend

b. X's friend, if the result is less than 10,

result front diimpitkan with 0,

then the result of step with a diimpitkan

the results of step b

Example 1. 99 x 99 = ...

His 99 -1

a. 99 + (-1) = 98

b. -1 X -1 = 1, because less than 10, written in 2001,

outcome measures with a diimpitkan

the results of step b, 01, finished 9801

then 99 x 99 = 9801

Example 2. 96 x 96 = ...

96 -4 friend

a. 96 + (-4) = 92

b. -4 X -4 = 16, the results of a step, 92 diimpitkan

with the results of step b, 16, finished 9216

then 96 x 96 = 9216

2. Multiplication rank in the Top 100

How to calculate:

a. The figures will be multiplied coupled with Friends

b. friend x friend, if the result is less than 10,

impitkan previously with 0 then

impitkan results with the results of a step b step

Example 1. 103 x 103 = ....

103 friends 3

a. 103 + 3 = 106

b. 3 x 3 = 9, as less than 10, written in 2009 and then

the results of a step, 106 diimpitkan with

the results of step b, 09, so 10 609

then 103 x 103 = 10 609

E. Rank Approaching 1000

1. Multiplication rank in the bottom 1000

How Calculations

a. The figures add up the numbers multiplied friend

b. X's friend, if the result is less than 10,

front coupled with 00 then

results of step with the results of a diimpitkan step b.

If a friend x friend, is greater or

equal to 10 in front diimpitkan 0

Example 1. 999 x 999 = ....

-1 999 friends

a. 999 + (-1) = 998

b. -1 X -1 = 1, because less than 10 written 001,

outcome measures with a diimpitkan

the results of step b, 998 001, then 999 x 999 = 998 001

Example 2. 996 x 996 = ....

996 -4 friend

a. 996 + (-4) = 992

b. -4 X -4 = 16, the results of a, 992 diimpitkan with

the results of step b, 16 a 992 016

then 996 x 996 = 992 016

2. Multiplication rank: At above 1000

How Calculations:

a. The figures will be multiplied plus friends

b. X's friend, if the result is less than 10,

diimpitkan with 00. If the results are more or

equal to 10, with 0 diimpitkan

Example 1. 1003 x 1003 = ....

1003 friend 3

a. 1003 + 3 = 1006

b. 3 x 3 = 9, written in 009 and then the results of step a, 1006

diimpitkan with the results of step b, 009, so 1,006,009

then 1003 x 1003 = 1006009

F. Designation By The unit 1, such as 11, 21, 31, etc.

How to calculate:

1. Previous number multiplied by

thereafter numbers

2. The result of step 1 plus 1

Example 1. 11 x 11 = ...

Number 11 in between the numbers 10 and 12

Numbers before 11, 10

Numbers after 11, 12

How to calculate:

11 x 11 = (10 x 12) + 1 = 121

Example 2. 21 x 21 = ...

Figures 21 to lie between 20 and 22

Numbers before 21, 20

Numbers after 21, 22

How to calculate 21 ^ 2 =

21 x 21 = (20 x 22) + 1 = 441

Example 3. 31 x 31 = ...

Figures 31 to lie between 30 and 32

How to calculate 31 ^ 2 = ...

31 x 31 = (30 x 32) + 1 = 961

Another way to calculate a unit of rank: 1 (one).

If a number is a unit of one raised

assumed by (a + 1) ^ 2, then rank that value

equal to a ^ 2 + 2a + 1.

Let us exercise some power by way of example problems

as set forth above.

Example 1. 21 x 21 = ....

21 = (20 + 1), means the value of a = 20, then:

21 ^ 2 = 20 x 20 + 2 x 20 + 1 = 441

Example 2. 31 x 31 = ....

31 = (30 + 1), means the value of a = 30, then:

31 ^ 2 = 30 x 30 + 2 x 30 + 1 = 961

G. The calculation of rank, unit 9, such as 9, 19, 29, 39,

89, and so on.

Here are discussed the calculation of the rank of a pattern

multiplying the previous number with digits after

then added 1.

For the 9 square = 9 x 9, figures prior to 9 is

8, while the number after 9 is 10,

then the difference 9-8 = 1, or 10-9 = 1dapat calculated

by the way (8 x 10) + 1 = 81

For the square of the number 19 = 19 x 19, can be calculated

manner (18 x 20) + 1 = 361

To figure the square of 29 = 29 x 29, can be calculated

manner (28 x 30) + 1 = 841

For the figure of 39 square = 39 x 39, can be calculated

manner (38 x 40) + 1 = 1421

Way over to about 9 x 9 is similar to

Pattern Approach 10.

9 friends -1

9 friends -1

___________ X

8 coupled with a

Stages of the calculation:

1. 9 + (-1) = 8

2. -1 X -1 = 1, step 1 diimpitkan with step 2,

so 81, then 9 x 9 = 81

Another way by using the formula: a ^ 2 - 2a + 1

The formula above results reappointment of (a -1) ^ 2

To the rank of 9 was calculated by converting 9

a = (10-1), means the value of a = 10,

then 9 ^ 2 = (10-1) ^ 2 = 10 ^ 2 - 2x10 + 1 = 100-20 +1 = 81

Power of 19 to 19 = (20 -1), the value of a = 20,

19 ^ 2 = (20-1) ^ 2 = 20 ^ 2 - 2x20 + 1 = 461

Rank 29 to 29 = (30-1), the value of a = 30,

29 ^ 2 = (30-1) ^ 2 = 30 ^ 2 - 2x30 + 1 = 841

Rank 39 to 39 = (40 -1), the value of a = 40,

39 ^ 2 = (40-1) ^ 2 = 40 ^ 2 - 2x40 + 1 = 1521

H. Rank with unit 2, such as 12, 22, 32, 42, and so on

How fast,

1. Two figures behind x two digits after

2. Squared difference

3. The result of step 1 + step 2 results

Example 1. 12 ^ 2 = 12 x 12 = ...

1. Two figures before 12, 10 x two points after 12, 14, 10 x 14 = 140

2. The difference, 12-10 = 2 squared = 4

3. 140 + 4 = 144

How to count:

(10 x 14) + 2 ^ 2 = 140 + 4 = 144

Example 2. 22 ^ 2 = 22 x 22 = ...

1. Two figures before 22, 20 x two points after 22, 24, 20 x 24 = 480

2. The difference, 22-20 = 2 squared = 4

3. 480 + 4 = 484

How to count:

(20 x 24) + 2 ^ 2 = 480 + 4 = 484

Example 3. 32 ^ 2 = 32 x 32 = ...

Two figures before 32, 30

Two digits after 32, 34

The difference is 32-30 = 2

How to count:

(30 x 34) + 2 ^ 2 = 1024

Example 4. 42 ^ 2 = 42 x 42 = ...

Two figures before 42, 40

The two numbers after 42, 44

The difference is 42-40 = 2

How to count:

(40 x 44) + 2 ^ 2 = 1744

I. Rank with the unit 8, such as 8, 18, 28, 38 and so on

How to Calculate the speed with which:

1. Two x two-digit number before it afterwards

2. Squared difference

3. The result of step 1 + step 2 results

Example 1. 8 ^ 2 = 8 x 8 = ...

Two figures before 8, 6

Two digits after 8, 10

The difference, 8-6 = 2 or 10-8 = 2, squared

How to count:

(6 x 10) + 2x2 = 64

Example 2. 18 ^ 2 = 18 x 18

Two figures before 18, 16

Two digits after 18, 20

The difference, 18-16 = 2 or 20 - 18 = 2, then

squared, 2 x 2 = 4

How to count:

(16 x 20) + 4 = 324

Example 3. 28 ^ 2 = 28 x 28

Two figures before 28, 26

Two digits after 28, 30

The difference, 28-26 = 2 or 30-28 = 2

then squared, 2 x 2 = 4

How to count:

(26 x 30) + 4 = 784

Posted by Ir. H. Hanan at 07:19 1 comments Links to this post

Saturday, April 17, 2010 Calculate Fast Multiplication in the top 20

The value of the Multiplication friend above 20, positive. Results Multiplication friend anyone under ten and have the same or more than ten. Multiplication under ten friends, such as 3 x 3, 3x 2, 3 x 1,, 2 x 2, 2 x 1, 1 x 1, 1 x 4, 1 x 6, 1 x 7, 1 x 8, 1 x 9 and 2 x 4. Multiplication of friends, the result is above or equal to 10. Like, 2 x 5, 2 x 6, 2 x 7, 2 x 8, 2 x 9, 3 x 4, 3 x 5, 3 x 6, 3 x 7, 3 x 8, 3 x 9, 4 x 4, 4 x 5, 4 x 6, 4 x 7, 4 x 8, 4 x 9, 5 x 5, 5 x 6, 5 x 7, 5 x 8, 5 x 9. How To Calculate Faster Perkaliannya? A. If the x's friend, the result is less than ten

Stages: 1. Values are multiplied, add up diagonally with a friend, choose one only. Then the result x 2 2. X's friend, then the result of step 1 diimpitkan with the results of step 2 Example: 1. 21 x 23 = .... 21 friends 1 23 friends 3 __________ X 48 diimpitkan 3 = 483 Step work: 1. 21 or 23 add up to a diagonal way, 21 + 3 = 24 or 23 + 1 = 24 then x 2 = 48 2. friend x friend, 1 x 3 = 3, the results of step 2 impitkan with the results of step 3, 483 so 21 x 23 = 483

Example 2. 22 x 23 = ... 22 friends 2 23 friends 3 ___________ X

Step work: 1. 22 or 23 add up to a diagonal way, 22 + 3 = 25 or 23 + 2 = 25 then x 2 = 50 2. friend x friend, 2 x 3 = 6, the results of step 2 impitkan with the results of step 2, 506 so 22 x 23 = 506

Another way: 1. Figures add up to be multiplied by a diagonal with friends choose one, then x 20 2. X's friend, then add up the results of step 1 with the results of step 2

Example 1. 21 x 23 = ... 21 friends 1 23 friends 3 ____________x

Stages: 1. 21 + 3 = 24 or 23 + 1 = 24 then x 20 = 480 2. Friend x friend = 1 x 3 = 3, add up the results of steps 1, 3 + 480 = 483, so 21 x 23 = 483

Example 2. 22 x 23 = ... 22 friends 2 23 friends 3 ___________ X

Stages: 1. 22 + 3 = 25 or 23 + 2 = 25, then multiplied by 20 = 500 2. Friend x friend = 2 x 3 = 6, add up the results of steps 1, 6 + 500 = 506, so 22 x 23 = 506

B. If a friend x friend, the result is 10 or more

Example 1. 22 x 25 = .... Tahapann 1. The numbers multiplied, add up with friends diagona way, then x 2 2. X's friend, written units, tens digit numbers stored 3. The result of step 1 digit numbers add up to tens of step 2 4. The result of step 3 diimpitkan with the results of step 2 units

22 friends 2 25 friends 5 ___________ X

Step work: 1. 22 or 25 add up in a way diagoal, 22 + 5 = 27 or 25 + 2 = 27 multiply by 2 = 54 2. friend x friend, 2 x 5 = 10 units are written only 0, 1 saved 3. The result of step 1 add up to tens of step 2 the numbers 1, 54 + 1 = 55 4. The result of step 3 diimpitkan with hasill unit step 2, 550 so 22 x 25 = 550

You can also 21 23 __x 483 Stages count: 1. unit x unit = 1 x 3 = 3 2. Multiply the diagonal, then total, (2 x 3) + (2 x 1) = 6 + 2 = 8 3. tens x tens digit digits, (2 x 2) = 4, the final result 483 About both the way the process the same as no. 1

Problem no. 3. 22 25 __x

1. unit x unit = 2 x 5 = 10 is written 0, 1 saved 2. 1 + {(2 x 5) + (2 x 2)} = 1 + 14 = 15 written 5, 1 saved 3. 1 + (2 x 2) = 5, then 22 x 25 = 550

Posted by Ir. H. Hanan at 16:52 AM 0 comments Links to this post

Monday, April 12, 2010 Fast Multiplication Approach 20

The material will be discussed now, Fast Multiplication Under 20 with Approach 20. For any number below 20 has multiplied his value minus (-). Like his friend 19 -1, 18 -2 friends, 17 friends -3, 16 -4 friend, the calculation step is similar to the way the previous multiplication. Complete the following multiplication using Approach 20. Example: 1. 19 x 19 = ....., 19 friends -1 19 friends -1 __x __ x

Process stages: 1. number 19 add up diagonally, select one, 19 + (-1) = 18 multiply by 2 = 36 2. Friend x friend = -1 x -1 = 1 3. The result of step 1 diimpitkan with the results of step 2, 361, so 19 x 19 = 361

Example 2, 16 x 16 = ...., 16 -4 friend 16 -4 friend __x ___x

Process stages: 1. number 16 add up diagonally, select one, 16 + (-4) = 12 multiply by 2 = 24 2. X's friend, -4 x -4 = 16, written alone unit 6, 1 puluhannya saved 3. Tens digits add up with the results of step 2 step 1, 1 + 24 = 25 4. The result of step 3 diimpitkan with the unit step 2, 256 so 16 x 16 = 256.

Another way: 1. totalizing way diagonal, then the outcome x 20 2. X's friend, then add the results of step 1 with the results of step 2.

How about the settlement of the above: 19 friends -1 19 friends -1 __ X

Stages: 1. {19 + (-1)} x 20 = 360 2. {(-1) X (-1)} + 360 = 361, then 19 x 19 = 361

The next Problem: 16 -4 friend 16 -4 friend ___________x

Stages: 1. {16 + (-4)} x 20 = 240 2. {(-4) X (-4)} + 240 = 256, then 16 x 16 = 256

Label: emann

Posted by Ir. H. Hanan at 7:58 PM 0 comments Links to this post

Wednesday, April 7, 2010 How to Calculate Fast Multiplication Between 10 and 20 with 10 Approach

Friends of the multiplication value between 10 and 20 with the Pattern Approach 20, positive. Like, 11 friends 1, 12 his second, 13 his 3, 14 4 friends, 15 friends 5, 16 friends 6, 17 friends 7, 18 friend 8, 19 friends 9. How To Quickly Calculate Perkaliannya?

This part of the first, Results multiplication friend x friend, less than 10

Example 1. 13 x 12 = ... Steps: 13 friends 3 12 friends 2 __x __x 15 diimpitkan 6, so 156 Stages: 1. Number 13 or 12 diagonal add up with friends, 13 + 2 = 15 or 12 + 3 = 15 2. The result of step one diimpitkan by multiplying friend x friend, 3 x 2 = 6, 15 diimpitkan with 6, so 156. 13 x 12 = 156

Example 2, 11 x 19 = ... Steps: 11 friends 1 19 friends 9 ___________x 20 diimpitkan 9 = 209 Stages: 1. number 11 or 19 add up diagonally with friends, 11 + 9 = 20 or 19 + 1 = 20. 2. The result of step 1 diimpitkan with the friend x friend = 1 x 9 = 9, 20 diimpitkan 9, 209 so 11 x 19 = 209.

Another way: 1. The numbers multiplied, add up diagonally add up with friends, then the results x 10 2. The result of step 1, computed with the friend x friend Examples of multiplication: 11 x 19 = .... 11 friends 1 19 friends 9 __________ X 200 + 9 = 209 Steps: 1. 11 or 19, + with diagonal friends, 11 + 9 = 20 or 19 + 1 = 20 then x 10 = 200 2. The results with the results of step 1 Sum friend x friend, 200 + (1 x 9) = 209

The second part, Results Multiplication friend x friend, more than 10 Example: 1. 13 x 14 = .... 2. 16 x 14 = .... The first way: 1. 13 + 4 = 17 or 14 + 3 = 17 select one only, then the results x 10 = 170 2. 3 x 4 = 12, then add up the results of step 1, 12 + 170 = 182, so 13 x 14 = 182 Problem the second: 1. 16 + 4 = 20 or 14 + 6 = 20 select one only, then the results x 10 = 200 2. 6 x 4 = 24, then add up the results of step 1, 24 + 200 = 224, so 16 x 14 = 224

Another way to question no. 1: 1. 3 x 4 = 12, written 2, digits puluhannya saved, 1 2. 13 + 4 = 17, kemudin digits add up tens step 1, to 17 + 1 = 18 3. The result of step 2, 18 diimpitkan with one unit of outcome measures, 2 so 182, 13x14 = 182 Problem the second: 1. 6 x 4 = 24, write 4, number 2 is stored 2 16 + 4 = 20 or 14 + 6 = 20 select one, then + the numbers that are stored 20 + 2 = 22, then step diimpitkan with unit number 1, 224, so 16 x 14 = 224

Special Bilangane multiplication between 10 and 20. Multiplication special number between 10 and 20 there are three types: 1. Type the number that multiplied by 11 multiplication 2. Multiplication number, the puluhannya same and the number of units 10 3. Multiplication Using Middle Value Explanation 1: How Settlement Multiplication number multiplied by 11 above the number 10 Example 16 x 11 = ..., Steps: 1. numbers 1 and 6 are added, 1 + 6 = 7 stored in the middle between the numbers 1 and 6, a 176, so 16 x 11 = 176.

Explanation 2: How fast multiplication puluhannya same numbers and the number of units = 10 Sample questions: 1. 12 x 18 = ..... 2. 14 x 16 = ... 3. 15 x 15 Discussion 1. 12 friends 2 18 friends 8 __x __x 2 diimpitkan with 16, so 216 Steps: 1. One of dozens of fox-digit rises one digit, then multiply to the tens digit is not changed. 2 x 1 = 2 2. X's friend, 2 x 8 = 16 3. The result of step 1 impitkan with the results of step 2, 216 so 12x18 = 216. To exercise no. 2 and 3 do the same as above

Explanation 3: can be done by finding the middle value, about 14 x 16 = ..., the middle 15, the middle and then squared to 15 x 15 = 225, then find the difference between the middle with the initial value will be multiplied, the value of the difference , 15 -14 = 1. Then the difference is squared. The final step, the square median values minus the square of the difference. 14 x 16 = (15 x 15) - (1 x 1) = 225-1 = 224. For about 12 x 18 = ..., can be done by way of the above. Middle value between 12 and 18, is = 15 Difference in median values with the first value will be multiplied, 15-12 = 3 12 x 18 = (15 x 15) - (3 x 3) = 225-9 = 216.

Select Use The Easy Only .............. Good luck.

Posted by Ir. H. Hanan at 20:10 AM 0 comments Links to this post

Tuesday, March 30, 2010 How to Calculate Fast Multiplication Between 5 and 10 with 10 Approach

Figures friend to multiplication under 10 with a pattern of negative values approach 10 (-). What is the rapid multiplication of 9 x 8 = ....? Figures 9 and 8 below 10, meaning nine minus 1 and Figures 8 or less 2 to near 10, 9 friend -1, 8 friend -2. What about the friends 6, and 7? 6 friend -4, Number 7 friends -3. A quick way to multiply is the same as the previous multiplication.

The first material, friend x friend if the result is less than 10. What is the result of multiplication of the 9 x 8 = ... ? Answer: 9 friends -1 8 friend -2 __ X __x 7 diimpitkan with 2, 72 Step calculation: 1. Number 9 or 8 summed diagonal with the number of friends, 9 + (-2) = 7 or 8 + (-1) = 7 2. X's friend, -1 x -2 = 2, the results of step 1 diimpitkan with the results of step 2, 72, so 9x8 = 72

Alternatively: 9 friends -1 8 friend -2 ___________x 70 + 2 = 72 1. Number 9 or 8 add up diagonally with a friend, 9 + (-2) = 7 or 8 + (-1) = 7 then x 10 = 70 2. X's friend, -1 x -2 = 2, add up the results of step 1 with the results of step 2, 70 + 2 = 72

Material into two, friend x friend if the results are more than 10 What is the result of multiplying 6 x 7 = .... ? Answer: 6 -4 friend 7 -3 friend __ X __ x 30 + 12 = 42 Step calculation: 1. 6 or 7 digits add up diagonally with a friend, 6 + (-3) = 3 or 7 + (-4) = 3 then x by 10, 3 x 10 = 30 2. X's friend, -4 x -3 = 12, total the results of step 1 + step 2 results, 30 + 12 = 42

Another way: 6 -4 friend 7 -3 friend __________x 4 diimpitkan 2 = 42 1. friend x friend, -4 x -3 = 12, written in unit 2, dozens of 1 is stored 2. 6 or 7 add up diagonally with a friend, 6 + (-3) = 3 choose one only 3. The result of step 2 add up to tens result of step 1, 3 + 1 = 4 then impitkan with the unit step 1, 4 diimpitkan 2, 42 so 6 x 7 = 42.

To understand the material above the train about the following. 1. 6 x 6 = 2. 6 x 7 = 3. 6 x 8 = 4. 6 x 9 = 5. 7 x 7 = 6. 7 x 8 = 7. 7 x 9 = 8. 8 x 8 = 9. 8 x 9 = 10. 9 x 9 =

Posted by Ir. H. Hanan at 4:35 PM 0 comments Links to this post

Sunday, March 28, 2010 How to Calculate Fast Multiplication under 5 and over 5 with 5 Approach

In previous studies we know the quick multiplication, multiplication by 5. In order not to forget us repeat again that material. To that end we try to train some problems.

What is 27 x 5 = .., 34 x 5 = ..., 123 x 5 = ..., 12 x 5 = ... ? Answer: 27 x 5 = ..... 1. Item 27 to change into (26 + 1) 2. Figures genapnya 26: 2 = 13, number 1 is identical with 5. 3. The result of the division of even numbers diimpitkan with 5, so 135 So, 27 x 5 = 135

34 x 5 = .... 1. Figures 34 divided by 2, 34: 2 = 17 then diimpitkan with 0, 170 So, 34 x 5 = 170

123 x 5 = .... 1. Figures 123 was changed to (122 + 1) 2. Figures genapnya 122: 2 = 61, number 1 identical 5, 3. The result of the division of even numbers diimpitkan with 5, so 615, So 123 x 5 = 615

12 x 5 = ... 1. Number 12 divided by 2, 12: 2 = 6 then diimpitkan with 0, 60 So, 12 x 5 = 60.

How Fast Multiplication Counting Down 5

Multiplication under 5, such as 4 x 4, 4 x 3, 4 x 2, 3 x 3, can be done by way of Approach 5. Number 4 approximately 5, then 4 short one digit, 3 short 2 digits, 2 deficiency 3 figures, for lack of numbers we put a (-). The word shortage we agree with the word friends. -1 4 friends, 3 friends -2, 2 friends -3. How to step calculation? Follow the steps below workmanship.

How to do calculations downward. a. 4 x 4 = .... 4 friends -1 4 friends -1 __ X __x 15 + 1 = 16

Stages of the process: 1. diagonally summed number 4, 4 + (-1) = 3 then x 5 = 15 2. friend x friend = -1 x -1 = 1, the results of step 1 + step 2 results, 15 + 1 = 16

b. 4 x 3 = ... 4 friends -1 3 friends -2 __ X __ x 10 + 2 = 12

The steps are: 1. number 4 or 3 summed diagonally 4 + (-2) = 2 or 3 + (-1) = 2 multiply by 5 = 10 2. friend x friend = -1 x -2 = 2, the results of step 1 + step 2 results, 10 + 2 = 12.

For other questions such as: 4 x 2, and 3 x 3 how the calculation is the same as the work about the above.

How to Calculate Fast Multiplication in top 5

Multiplication above 5, such as 6 x 6, 7 x 8, 8 x 9 can be done by way of Approach 5. To multiplication above 5, the value of a positive friend, in practice these signs do not need to be written. 6 friends 1, 7 friends 2, 8 friends 3, 9 friend 4. Step work is almost the same as multiplication arithmetic to calculate how fast multiplication under 5.

How to step calculation? Follow the construction phase the following:

1. 6 x 6 = ... 6 friends 1 6 friends 1 __ X __x 35 + 1 = 36 Stages: 1. number 6 diagonal sum with the number of friends, 6 + 1 = 7, then x 5 = 35 3. friend x friend, 1 x 1 = 1, then the result of step 1 + step 2 results, 35 + 1 = 36

Next we discuss the question no. 3, count toward the bottom. 8 x 9 = .... 8 friend 3 9 friends 4 __ X __x 60 + 12 = 72

Stages: 1. number 8 or 9 digits add up diagonally with friends, 8 + 4 = 12 then x 5 = 60 2. friend x friend, 3 x 4 = 12, then the result of step 1 + step 2 = 60 + 12 = 72

How workmanship question no. 2 the same as no. 1 and 3.

Exercise Problem Approach 5 below 5 and above five. Compute the question below. 1. 4 x 4 = ... 2. 4 x 3 = ... 3. 4 x 2 = ... 4. 3 x 3 = ... 5. 6 x 6 = ... 6. 6 x 7 = ... 7. 6 x 8 = ... 8. 6 x 9 = ... 9. 7 x 7 = .. 10. 8 x 9 =...

## Saturday, May 22, 2010

### Counting Secrets Fast Arithmetic Series

Posted by Ir. H. Hanafi at 9:37 AM 0 comments Links to this post

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