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
Wednesday, April 28, 2010
Cara Cepat Menghitung Pangkat Dua
Pangkat dua dilambangkan dengan tanda ^2, artinya bilangan itu dikalikan dua kali.
Misal 25^2 artinya 25 x 25.
35^2 artinya 35 x 35.
Biasanya mengalikan pangkat selalu mengalikan ke arah bawah.
Seperti CARA KONVENSIONAL di bawah ini.
35
35
____x
175
105
_____+
1225
Langkah ini terlalu lama.
35^2 artinya 35 x 35.
Biasanya mengalikan pangkat selalu mengalikan ke arah bawah.
Seperti CARA KONVENSIONAL di bawah ini.
35
35
____x
175
105
_____+
1225
Langkah ini terlalu lama.
Bagaimana Cara Cepat Menghitung Pangkat Seperti Soal di atas ?
A. Bilangan yang digit puluhan sama dan digit satuan 5
A. Bilangan yang digit puluhan sama dan digit satuan 5
Cara menghitungnya :
1. Digit puluhan naik satu angka x digit puluhan yang
tidak naik
2. Satuan x satuan
3. Hasil langkah 1 diimpitkan dengan hasil langkah 2
1. Digit puluhan naik satu angka x digit puluhan yang
tidak naik
2. Satuan x satuan
3. Hasil langkah 1 diimpitkan dengan hasil langkah 2
Contoh soal :
1. 15^2 = .... 2. 35^2 = .... 3. 125^2 = ....
1. 15^2 = .... 2. 35^2 = .... 3. 125^2 = ....
Pembahasan 1. 15^2 =15 x 15
!------!
2 x 1 = 2 -----> langkah 1
!------! ]
langkah 1& 2 diimpitkan 5 x 5 = 25 ----> langkah 2
!------!
2 x 1 = 2 -----> langkah 1
!------! ]
langkah 1& 2 diimpitkan 5 x 5 = 25 ----> langkah 2
Cara menghitungnya :
Langkah 1, 2 x 1 = 2
Langkah 2, 5 x 5 = 25, kemudian hasil langkah 1, 2
diimpitkan dengan 2, 25 jadi 225, maka 15 x 15 = 225
diimpitkan dengan 2, 25 jadi 225, maka 15 x 15 = 225
Pembahasan 2. 35^2 = 35 x 35
Cara menghitungnya :
1. 4 x 3 = 12
2. 5 x 5 = 25, hasil langkah 1, 12 diimpitkan dengan
hasil langkah 2, 25 jadi 225, maka 35 x 35 = 1225
hasil langkah 2, 25 jadi 225, maka 35 x 35 = 1225
Pembahasan 3. 125^2 =125 x 125
Cara menghitungnya :
1. 13 x 12 = 156
2. 5 x 5 = 25, hasil langkah 1, 156 diimpitkan dengan
hasil langkah 2, 25 jadi 15625,
maka 125 x 125 = 15625
hasil langkah 2, 25 jadi 15625,
maka 125 x 125 = 15625
B. Bilangan dengan digit puluhannya angka 5
dan satuannya sama
Cara Menghitungnya :
1. (5 x 5) + satuan
2. Satuan x satuan,
3. Impitkan hasil langkah 1 dengan hasil langkah 2.
Catatan : Jika hasil perkalian satuan x satuan
kurang dari sepuluh, didepannya impitkan angka 0
Seperti, 1. 52 x 52 = .... 2. 54 x 54 = ....
Pembahasan 1. 52 ^2 = 52 x 52 = ...
1. (5 x 5) + 2 = 27
2. Satuan x satuan = 2 x 2 = 4, impitkan didepannya
dengan 0, jadi 04
3. Hasil langkah 1, 27 diimpitkan dengan
hasil langkah 2, 04, jadi 2704
maka 52^2 = 52 x 52 = 2704
Pembahasan 2. 54^2 = 54 x 54 = ...
1. (5 x 5) + 4 = 29
2. 4 x 4 =16
3. Hasil langkah 1, 29 diimpitkan dengan
hasil langkah 2, 16 jadi 2916,
maka 54^2 = 54 x 54 = 2916
C. Pangkat Mendekati 10
1. Perkalian pangkat di bawah 10
Cara Menghitungnya :
a. Menjumlahkan bilangan yang dikalikan
dengan angka teman
b. teman x teman,
Hasil langkah a diimpitkan dengan hasil b
Cara ini berlaku untuk teman x teman kurang
dari 10
Contoh 1. 9 x 9 = ...
9 temannya -1
a. 9 + (-1) = 8
b. -1 x -1 = 1, hasil langkah a, 8 diimpitkan
dengan hasil langkah b, 1 jadi 81 maka
9 x 9 = 81
Contoh 2. 8 x 8 = ...
8 temennya -2
a. 8 + (-2) = 6
b. -2 x -2 = 4, hasil langkah a, 6 diimpitkan
dengan hasil langkah b, 4, jadi 64 maka
8 x 8 = 64
Jika teman x teman sama dengan 10 atau lebih
Cara Menghitung :
a. teman x teman, ditulis satuan, puluhan
disimpan
b. angka yang dikalikan + teman, kemudian +
angka puluhan yang disimpan, hasilnya
diimpit dengan hasil langkah a
satuannya saja.
Contoh 1. 6 x 6 = ....
6 temannya -4
a. -4 x -4 = 16, ditulis 6, puluhan 1 disimpan
b. 6 + (-4) = 2, kemudian + 1 = 3, hasil akhirnya
diimpitkan dengan hasil langkah a, 6, jadi 36,
maka 6 x 6 = 36
2. Perkalian pangkat di atas 10
Jika teman x teman kurang dari 10
Cara Menghitungnya :
a. Menjumlahkan bilangan yang
akan dikalikan dengan angka teman
b. teman x teman, hasil langkah a
diimpitkan dengan hasil langkah b
Contoh 1. 13 x 13
13 temannya 3
a. 13 + 3 = 16
b. 3 x 3 = 9, hasil lagkah a, 16 diimpitkan
dengan hasil langkah b, 9 maka 13 x 13 = 169
Jika teman x teman = 10 atau lebih
Cara menghitungnya :
1. teman x teman, tulis satuannya, puluhannya disimpan
2. angka yang dikalikan ditambah dengan teman,
hasilnya ditambah angka yang disimpan langkah 1
3. hasil langkah 2, diimpitkan dengan satuan langkah 1.
Contoh, 14 x 14 = ...
14 temannya 4
1. teman x teman, 4 x 4 = 16, ditulis 6, 1 disimpan
2. (14 + 4) + 1 = 19
3. 19 diimpitkan dengan 6, jadi 196 maka 14x14=196
D. Pangkat Mendekati 100
1. Perkalian Pangkat di bawah 100
Cara Menghitungnya :
a. Angka yang akan dikalikan dijumlah
dengan angka teman
b. Teman x teman, jika hasilnya kurang dari 10,
hasilnya didepannya diimpitkan dengan 0,
kemudian hasil langkah a diimpitkan dengan
hasil langkah b
Contoh 1. 99 x 99 = ...
99 temannya -1
a. 99 + (-1) = 98
b. -1 x -1 = 1, karena kurang 10, ditulis 01,
hasil langkah a diimpitkan dengan
hasil langkah b, 01, jadi 9801
maka 99 x 99 = 9801
Contoh 2. 96 x 96 = ...
96 temannya -4
a. 96 + (-4) = 92
b. -4 x -4 = 16, hasil langkah a, 92 diimpitkan
dengan hasil langkah b, 16, jadi 9216
maka 96 x 96 = 9216
2. Perkalian Pangkat di Atas 100
Cara Menghitungnya :
a. Angka yang akan dikalikan ditambah dengan teman
b. teman x teman, jika hasilnya kurang dari 10,
impitkan sebelumnya dengan 0 kemudian
hasil langkah a impitkan dengan hasil langkah b
Contoh 1. 103 x 103 = ....
103 temannya 3
a. 103 + 3 = 106
b. 3 x 3 = 9, karena kurang 10, ditulis 09 kemudian
hasil langkah a, 106 diimpitkan dengan
hasil langkah b, 09, jadi 10609
maka 103 x 103 = 10609
E. Pangkat Mendekati 1000
1. Perkalian Pangkat di Bawah 1000
Cara Perhitungannya
a. Angka yang dikali dijumlah dengan angka teman
b. Teman x teman, jika hasilnya kurang dari 10,
didepannya ditambah dengan 00 kemudian
hasil langkah a diimpitkan dengan hasil langkah b.
Jika teman x teman, lebih besar atau
sama dengan 10 didepannya diimpitkan 0
Contoh 1. 999 x 999 = ....
999 temannya -1
a. 999 + (-1) = 998
b. -1 x -1 = 1, karena kurang dari 10 ditulis 001,
hasil langkah a diimpitkan dengan
hasil langkah b, 998001, maka 999 x 999 = 998001
Contoh 2. 996 x 996 = ....
996 temannya -4
a. 996 + (-4) = 992
b. -4 x -4 = 16, hasil a, 992 diimpitkan dengan
hasil langkah b, 16 jadi 992016
maka 996 x 996 = 992016
2. Perkalian Pangkat Di atas 1000
Cara Perhitungannya :
a. Angka yang akan dikalikan ditambah teman
b. Teman x teman, jika hasilnya kurang dari 10,
diimpitkan dengan 00. Jika hasilnya lebih atau
sama dengan 10, diimpitkan dengan 0
Contoh 1. 1003 x 1003 = ....
1003 temannya 3
a. 1003 + 3 = 1006
b. 3 x 3 = 9, ditulis 009 kemudian hasil langkah a, 1006
diimpitkan dengan hasil langkah b, 009, jadi 1006009
maka 1003 x 1003 = 1006009
F. Pangkat Dengan Satuannya 1, seperti 11, 21, 31, dst
Cara menghitungnya :
1. Bilangan sebelumnya dikalikan dengan
bilangan setelahnya
2. Hasil langkah 1 ditambah dengan 1
Contoh 1. 11 x 11 = ...
Angka 11 berada diantara bilangan 10 dan 12
Bilangan sebelum 11, 10
Bilangan setelah 11, 12
Cara menghitungnya :
11 x 11 = (10 x 12) + 1 = 121
Contoh 2. 21 x 21 = ...
Angka 21 berada diantara 20 dan 22
Bilangan sebelum 21, 20
Bilangan setelah 21, 22
Cara menghitung 21^2 =
21 x 21 = (20 x 22) + 1 = 441
Contoh 3. 31 x 31 = ...
Angka 31 berada diantara 30 dan 32
Cara menghitung 31^2 = ...
31 x 31 = (30 x 32) + 1 = 961
2. Satuan x satuan,
3. Impitkan hasil langkah 1 dengan hasil langkah 2.
Catatan : Jika hasil perkalian satuan x satuan
kurang dari sepuluh, didepannya impitkan angka 0
Seperti, 1. 52 x 52 = .... 2. 54 x 54 = ....
Pembahasan 1. 52 ^2 = 52 x 52 = ...
1. (5 x 5) + 2 = 27
2. Satuan x satuan = 2 x 2 = 4, impitkan didepannya
dengan 0, jadi 04
3. Hasil langkah 1, 27 diimpitkan dengan
hasil langkah 2, 04, jadi 2704
maka 52^2 = 52 x 52 = 2704
Pembahasan 2. 54^2 = 54 x 54 = ...
1. (5 x 5) + 4 = 29
2. 4 x 4 =16
3. Hasil langkah 1, 29 diimpitkan dengan
hasil langkah 2, 16 jadi 2916,
maka 54^2 = 54 x 54 = 2916
C. Pangkat Mendekati 10
1. Perkalian pangkat di bawah 10
Cara Menghitungnya :
a. Menjumlahkan bilangan yang dikalikan
dengan angka teman
b. teman x teman,
Hasil langkah a diimpitkan dengan hasil b
Cara ini berlaku untuk teman x teman kurang
dari 10
Contoh 1. 9 x 9 = ...
9 temannya -1
a. 9 + (-1) = 8
b. -1 x -1 = 1, hasil langkah a, 8 diimpitkan
dengan hasil langkah b, 1 jadi 81 maka
9 x 9 = 81
Contoh 2. 8 x 8 = ...
8 temennya -2
a. 8 + (-2) = 6
b. -2 x -2 = 4, hasil langkah a, 6 diimpitkan
dengan hasil langkah b, 4, jadi 64 maka
8 x 8 = 64
Jika teman x teman sama dengan 10 atau lebih
Cara Menghitung :
a. teman x teman, ditulis satuan, puluhan
disimpan
b. angka yang dikalikan + teman, kemudian +
angka puluhan yang disimpan, hasilnya
diimpit dengan hasil langkah a
satuannya saja.
Contoh 1. 6 x 6 = ....
6 temannya -4
a. -4 x -4 = 16, ditulis 6, puluhan 1 disimpan
b. 6 + (-4) = 2, kemudian + 1 = 3, hasil akhirnya
diimpitkan dengan hasil langkah a, 6, jadi 36,
maka 6 x 6 = 36
2. Perkalian pangkat di atas 10
Jika teman x teman kurang dari 10
Cara Menghitungnya :
a. Menjumlahkan bilangan yang
akan dikalikan dengan angka teman
b. teman x teman, hasil langkah a
diimpitkan dengan hasil langkah b
Contoh 1. 13 x 13
13 temannya 3
a. 13 + 3 = 16
b. 3 x 3 = 9, hasil lagkah a, 16 diimpitkan
dengan hasil langkah b, 9 maka 13 x 13 = 169
Jika teman x teman = 10 atau lebih
Cara menghitungnya :
1. teman x teman, tulis satuannya, puluhannya disimpan
2. angka yang dikalikan ditambah dengan teman,
hasilnya ditambah angka yang disimpan langkah 1
3. hasil langkah 2, diimpitkan dengan satuan langkah 1.
Contoh, 14 x 14 = ...
14 temannya 4
1. teman x teman, 4 x 4 = 16, ditulis 6, 1 disimpan
2. (14 + 4) + 1 = 19
3. 19 diimpitkan dengan 6, jadi 196 maka 14x14=196
D. Pangkat Mendekati 100
1. Perkalian Pangkat di bawah 100
Cara Menghitungnya :
a. Angka yang akan dikalikan dijumlah
dengan angka teman
b. Teman x teman, jika hasilnya kurang dari 10,
hasilnya didepannya diimpitkan dengan 0,
kemudian hasil langkah a diimpitkan dengan
hasil langkah b
Contoh 1. 99 x 99 = ...
99 temannya -1
a. 99 + (-1) = 98
b. -1 x -1 = 1, karena kurang 10, ditulis 01,
hasil langkah a diimpitkan dengan
hasil langkah b, 01, jadi 9801
maka 99 x 99 = 9801
Contoh 2. 96 x 96 = ...
96 temannya -4
a. 96 + (-4) = 92
b. -4 x -4 = 16, hasil langkah a, 92 diimpitkan
dengan hasil langkah b, 16, jadi 9216
maka 96 x 96 = 9216
2. Perkalian Pangkat di Atas 100
Cara Menghitungnya :
a. Angka yang akan dikalikan ditambah dengan teman
b. teman x teman, jika hasilnya kurang dari 10,
impitkan sebelumnya dengan 0 kemudian
hasil langkah a impitkan dengan hasil langkah b
Contoh 1. 103 x 103 = ....
103 temannya 3
a. 103 + 3 = 106
b. 3 x 3 = 9, karena kurang 10, ditulis 09 kemudian
hasil langkah a, 106 diimpitkan dengan
hasil langkah b, 09, jadi 10609
maka 103 x 103 = 10609
E. Pangkat Mendekati 1000
1. Perkalian Pangkat di Bawah 1000
Cara Perhitungannya
a. Angka yang dikali dijumlah dengan angka teman
b. Teman x teman, jika hasilnya kurang dari 10,
didepannya ditambah dengan 00 kemudian
hasil langkah a diimpitkan dengan hasil langkah b.
Jika teman x teman, lebih besar atau
sama dengan 10 didepannya diimpitkan 0
Contoh 1. 999 x 999 = ....
999 temannya -1
a. 999 + (-1) = 998
b. -1 x -1 = 1, karena kurang dari 10 ditulis 001,
hasil langkah a diimpitkan dengan
hasil langkah b, 998001, maka 999 x 999 = 998001
Contoh 2. 996 x 996 = ....
996 temannya -4
a. 996 + (-4) = 992
b. -4 x -4 = 16, hasil a, 992 diimpitkan dengan
hasil langkah b, 16 jadi 992016
maka 996 x 996 = 992016
2. Perkalian Pangkat Di atas 1000
Cara Perhitungannya :
a. Angka yang akan dikalikan ditambah teman
b. Teman x teman, jika hasilnya kurang dari 10,
diimpitkan dengan 00. Jika hasilnya lebih atau
sama dengan 10, diimpitkan dengan 0
Contoh 1. 1003 x 1003 = ....
1003 temannya 3
a. 1003 + 3 = 1006
b. 3 x 3 = 9, ditulis 009 kemudian hasil langkah a, 1006
diimpitkan dengan hasil langkah b, 009, jadi 1006009
maka 1003 x 1003 = 1006009
F. Pangkat Dengan Satuannya 1, seperti 11, 21, 31, dst
Cara menghitungnya :
1. Bilangan sebelumnya dikalikan dengan
bilangan setelahnya
2. Hasil langkah 1 ditambah dengan 1
Contoh 1. 11 x 11 = ...
Angka 11 berada diantara bilangan 10 dan 12
Bilangan sebelum 11, 10
Bilangan setelah 11, 12
Cara menghitungnya :
11 x 11 = (10 x 12) + 1 = 121
Contoh 2. 21 x 21 = ...
Angka 21 berada diantara 20 dan 22
Bilangan sebelum 21, 20
Bilangan setelah 21, 22
Cara menghitung 21^2 =
21 x 21 = (20 x 22) + 1 = 441
Contoh 3. 31 x 31 = ...
Angka 31 berada diantara 30 dan 32
Cara menghitung 31^2 = ...
31 x 31 = (30 x 32) + 1 = 961
Cara lain menghitung Pangkat yang bersatuan 1 (satu).
Jika suatu bilangan yang bersatuan satu dipangkatkan
dimisalkan dengan (a + 1)^2, maka pangkat nilai tersebut
sama dengan a^2 + 2a + 1.
Coba kita latih beberapa contoh soal pangkat dengan cara
seperti ketentuan di atas.
Contoh 1. 21 x 21 = ....
21 = (20 + 1), berarti nilai a = 20, maka :
21^2 = 20 x 20 + 2 x 20 + 1 = 441
Contoh 2. 31 x 31 = ....
31 = (30 + 1), berarti nilai a = 30, maka :
31^2 = 30 x 30 + 2 x 30 + 1 = 961
G. Perhitungan Pangkat, satuannya 9, seperti 9, 19, 29, 39,
89, dan seterusnya.
Di sini akan dibahas perhitungan pangkat dengan pola
mengalikan angka sebelumnya dengan angka setelahnya
kemudian ditambah 1.
Untuk angka 9 kuadratnya = 9 x 9, angka sebelum 9 adalah
8, sedangkan angka setelah 9 adalah 10,
kemudian selisih 9 - 8 = 1, atau 10 - 9 = 1dapat dihitung
dengan cara (8 x 10) + 1 = 81
Untuk angka 19 kuadratnya = 19 x 19, bisa dihitung
dengan cara (18 x 20) + 1 = 361
Untuk angka 29 kuadratnya = 29 x 29, bisa dihitung
dengan cara (28 x 30) + 1 = 841
Untuk angka 39 kuadratnya = 39 x 39, bisa dihitung
dengan cara (38 x 40) + 1 = 1421
Cara di atas untuk soal 9 x 9 sebenarnya mirip dengan
Pola Pendekatan 10.
9 temannya -1
9 temannya -1
___________ x
8 diimpitkan dengan 1
Tahapan perhitungannya :
1. 9 + (-1) = 8
2. -1 x -1 = 1, langkah 1 diimpitkan dengan langkah 2,
jadi 81, maka 9 x 9 = 81
Cara lain dengan menggunakan rumus : a^2 - 2a + 1
Rumus di atas hasil pemangkatan dari (a -1)^2
Untuk pangkat dari 9 dihitung dengan merubah 9
menjadi = (10 - 1), berarti nilai a = 10,
maka 9^2 = (10 - 1)^2 = 10^2 - 2x10 + 1 = 100-20+1=81
Pangkat 19 menjadi 19 = (20 -1), nilai a = 20,
19^2 = (20 - 1)^2 = 20^2 - 2x20 + 1 = 461
Pangkat 29 menjadi 29 = (30 - 1), nilai a = 30,
29^2 = (30 - 1)^2 = 30^2 - 2x30 + 1 = 841
Pangkat 39 menjadi 39 = (40 -1), nilai a = 40,
39^2 = (40 - 1)^2 = 40^2 - 2x40 + 1 = 1521
H. Pangkat dengan satuan 2, seperti 12, 22, 32, 42, dan seterusnya
Cara cepatnya,
1. Dua angka di belakangnya x dua angka setelahnya
2. Selisihnya dikuadratkan
3. Hasil langkah 1 + hasil langkah 2
Contoh 1. 12^2 = 12 x 12 = ...
1. Dua angka sebelum 12, 10 x dua angka setelah 12, 14 ; 10 x 14 = 140
2. Selisihnya, 12 - 10 = 2, dikuadratkan = 4
3. 140 + 4 = 144
Cara hitungnya:
(10 x 14) + 2^2 = 140 + 4 = 144
Contoh 2. 22^2 = 22 x 22 = ...
1. Dua angka sebelum 22, 20 x dua angka setelah 22, 24 ; 20 x 24 = 480
2. Selisihnya, 22 - 20 = 2, dikuadratkan = 4
3. 480 + 4 =484
Cara hitungnya :
(20 x 24) + 2^2 = 480 + 4 = 484
Contoh 3. 32^2 = 32 x 32 = ...
Dua angka sebelum 32, 30
Dua angka setelah 32, 34
Selisihnya 32 - 30 = 2
Cara hitungnya :
(30 x 34) + 2^2 = 1024
Contoh 4. 42^2 = 42 x 42 = ...
Dua angka sebelum 42, 40
Dua angka setelah 42, 44
Selisihnya 42 - 40 = 2
Cara hitungnya :
(40 x 44) + 2^2 = 1744
I. Pangkat dengan satuan 8, seperti 8, 18, 28, 38 dan seterusnya
Cara Menghitung Cepatnya :
1. Dua angka sebelumnya x dua angka setelahnya
2. Selisihnya dikuadratkan
3. Hasil langkah 1 + hasil langkah 2
Contoh 1. 8^2 = 8 x 8 = ...
Dua angka sebelum 8, 6
Dua angka setelah 8, 10
Selisihnya, 8 - 6 = 2 atau 10 - 8 = 2, dikuadratkan
Cara hitungnya :
(6 x 10) + 2x2 = 64
Contoh 2. 18^2 = 18 x 18
Dua angka sebelum 18, 16
Dua angka setelah 18, 20
Selisihnya, 18 - 16 = 2 atau 20 - 18 = 2, kemudian
dikuadratkan, 2 x 2 = 4
Cara hitungnya :
(16 x 20) + 4 = 324
Contoh 3. 28^2 = 28 x 28
Dua angka sebelum 28, 26
Dua angka setelah 28, 30
Selisihnya, 28 - 26 = 2 atau 30 - 28 = 2
kemudian dikuadratkan, 2 x 2 = 4
Cara hitungnya :
(26 x 30) + 4 = 784
Posted by Ir. H. Hanafi at 7:19 AM 1 comments
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