What are the characteristics of 7'11'13?

What are the characteristics of 7'11'13?


Characteristics of numbers divisible by 7
Method 1: a number cuts off the last digit, and then subtracts 2 times of the number cut off from the remaining number. In this way, if the final result is a multiple of 7 (including 0), then the original number must be divisible by 7. For example, the process of judging whether 133 is a multiple of 7 is as follows: 13-3 × 2 = 7, so 133 is a multiple of 7 The process of judging whether 6139 is a multiple of 7 is as follows: 613-9 × 2 = 595, 59-5 × 2 = 49, so 6139 is a multiple of 7, and so on
Method 2: if the difference between the last three digits of a multi digit number and the number before the last three digits can be divided by 7, then the multi digit number can be divided by 7
For example, the last three digits of the judgment number 280679 are 679, and the number composed of the last three digits is 280679-280 = 399399, which can be divided by 7, so 280679 can also be divided by 7. This method is also suitable for judging whether it can be divided by 11 or 13
For example, the last three digits of 283679 are 679, and the number composed of the last three digits is 283679-283 = 396396, which can be divided by 11. Therefore, 283679 can be divided by 11
For example: judge whether 383357 can be divided by 13
The last three digits of this number are 357, and the number composed of the last three digits is 383. The difference between the two numbers is: 383-357 = 26, 26 can be divisible by 13, so 383357 must be divisible by 13
Method 3. First place reduction method, in the first place or the first few places, reduce to the multiple of 7
For example, to judge whether 456669 can be divided by 7, 456669-420000 = 36669, as long as 32669 can be divided by 7. For 32669, 32669-28000 = 46694669-4200 = 469469-420 = 49, 49 can be divided by 7, so 456669 can be divided by 7
Characteristics of numbers divisible by 11
In addition to the above method 2 of divising by 7, which is applicable to 11, you can also add a number from the right to the left, the number on the odd bit and the number on the even bit, and then calculate their difference. If the difference is a multiple of 11 (including 0), then the original number must be divisible by 11. For example, judge whether 491678 can be divisible by 11
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K - → sum of odd digits 9 + 6 + 8 = 23, 4I & y.f6_ Y &; w-b6o / O &; Z0 - → sum of even digits 4 + 1 + 7 = 12, 6t / jy'ad *? 23-12 = 11
Therefore, 491678 can be divided by 11. This method is called odd even difference method
Characteristics of numbers divisible by 13
In addition to the above-mentioned method 2 of divising by 7 is applicable to 13, you can also remove the number of an integer, and then add 4 times of the number from the remaining number. If the sum is a multiple of 13, the original number can be divisible by 13. If the number is still too large to be observed directly, repeat this process
For example: to judge whether 1284322 can be divided by 13. 128432 + 2 × 4 = 128440, teacher's studio ᦇ 173; y ^ C + O j-z12844 + 0 × 4 = 128441284 + 4 × 4 = 1300, w4v / hwh01300 △ 13 = 100, teacher's studio 'NJP, e'o7s; m
Therefore, 1284322 can be divided by 13



What are the characteristics of some numbers that can be divided by 7, 11 or 13? (for example, the last digit of a number divided by 2 can be divided by 2)


The characteristic of a number divisible by 7. A number cuts off the last digit, and then subtracts 2 times of the number cut off from the remaining number. In this way, if the final result is a multiple of 7 (including 0), then the original number must be divisible by 7. For example, judge whether 6692 can be divisible by 7



What are the characteristics of divisible numbers by 2.5.4.25.8.125.7.11.13 and why?


The characteristic is to include all these factors, and the index reaches the highest power
The highest power of 2 is 3
5 to the highest third power
The others are to the power of 1
Such a number is a multiple of 8 * 125 * 7 * 11 * 13
The lower three digits are 0, and the difference between the sum of odd digits and the sum of even digits is a multiple of 11



Calculation: - (1 / 2-2 / 5) calculate the process and answer; - 8 / 9-9 / 8 absolute value calculate the process and answer
-(1 / 2-2 / 5) calculate process and answer; - 8 / 9-9 / 8 absolute value calculate process and answer


Solution:
-(1/2-2/5)
=-(1x5 / 2x5-2x2 / 2x5) (general)
=-(5/10-4/10)
=-1/10
- 8 / 9-9 / 8
=- 8x8 / 9x8-9x9 / 9x8 (general)
=- 64 / 72-81 / 72
=- 145 / 72
=145/72
The answer is over



Two and one-third minus [minus one and one-half minus (five half plus four and two-thirds)]


Original formula = 7 / 3 - [- 3 / 2 - (5 / 2 + 14 / 3)]
=7/3+14/3+3/2+5/2
=7+4
=11



-[+ (- one and half)] simplification


-[+ (- one and half)]
=-(- one and a half)
=1.5
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Simplification + {negative one and half} - (= 3.6)


+{negative one and a half} = negative one and a half
-(+3.6)=-3.6



One and a half: 0.5 is faster than (), and the ratio is () faster


One and a half: 0.5 ratio after simplification (3:1), the ratio is (3)
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What is (- 12) / (- 4) / (minus one and half) equal to?


=3÷(-1.5)
=-2
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One and a half plus how much is one


One and a half plus a negative half equals one