Four algorithms and their simple operations
Operation sequence of the first and fourth operations
1, in the formula without brackets, if there is only addition, subtraction or multiplication and division, it should be calculated from left to right.
2. There are addition, subtraction, multiplication and division in the formula without brackets, so multiply and divide first, then add and subtract.
3. If there are brackets in the formula, calculate the inner side of brackets first, and then calculate the outer side of brackets; The calculation order of the formulas in brackets follows the above calculation order.
Second, about the operation of "0":
1 and "0" are inseparable;
2, a Lou plus 0 or minus 0, finally equal to the original number.
3. The minuend is equal to the minuend, and the difference is 0.
4. Multiply 0 by any number or divide 0 by any number to get 0.
Third, the operation method and simple operation
Law of addition:
1, two addends are exchanged, and the sum is unchanged. This is called additive commutative law. Alphabetic formula: a+b=b+a
2. Add the first two numbers, or add the last two numbers first; And invariance, which is called additive associative law.
Alphabetic formula: (a+b)+c=a+(b+c)
(2) Multiplication algorithm
1, exchange the positions of two factors, and the product remains the same. This is called multiplicative commutative law. Alphabetic formula: a_b=b_a
2. Multiply the first two numbers, or multiply the last two numbers first, and the product remains unchanged. This is the so-called law of multiplication and association.
Alphabetic formula: (a_b)_c=a_(b_c)
3. When the sum of two numbers is multiplied by a number, you can multiply it first and then add it. This is the law of multiplication and distribution.
Alphabetic formula: (a+b)_c=a_c+b_c or a _ (b+c) = a _ b+a _ c.
Extended formula: (a-b)_c=a_c- b_c or a _ (b-c) = a _ b-a _ c.
(3) Simple subtraction operation:
1, a number subtracts two numbers continuously, and you can subtract the sum of these two numbers with this number.
Expressed in letters: a-b-c=a-(b+c)
2. One number subtracts two numbers continuously. You can use this number to subtract the last number and then subtract the previous number.
Expressed in letters: A-B A-B-C = A-C-B C-B.
(4) Simple division operation
1, a number is continuously divided by two numbers, and this number can be divided by the product of these two numbers.
Expressed in letters: a? b？ c=a？ (b x c)
2. A number is continuously divided by two numbers. You can divide this number by the last number, and then divide the previous number.
Expressed in letters: a? b？ c=a？ c？ b
The first one is to observe the final characteristics of numbers by using additive commutative law sum association law, and turn them into integers for simple calculation.
Such as:123+45+55 74+86+26+14163+78+22+37.
Type 2: Most of the figures in the formula are close to whole ten, whole hundred and whole thousand, and are calculated according to the principle of "add and subtract". For example, take 199 as 200-1199+299+399 99+198+97+699+999 999.
The third type: only add two numbers, one of which is close to the whole ten, the whole hundred, the whole thousand ... according to the principle of "adding more and subtracting, adding less".
For example, adding 99 is regarded as adding100-1; Adding 103 is considered as adding 100+3.
First, subtraction.
Type 1: Subtracting two or more numbers in a row is equivalent to subtracting their sum.
The second category: only two numbers meet, in which the subtrahend is close to the integer of ten, the integer of one hundred, and the integer of one thousand ... According to the principle of "adding back what is reduced" and "subtracting what is reduced",
For example, negative 99 is regarded as negative100+1; Subtracting 104 is regarded as subtracting 100-4 (which belongs to the same type of topic as addition type 3).
Second, add and subtract mixed calculation
Type 1: Move the number, and the symbol is followed by the symbol. The symbols of the first number are all plus signs. For example, in 632- 143-32, the symbol of 632 is a plus sign, the symbol of 143 is a minus sign, and the symbol of 32 is a minus sign. The purpose of moving is that subtraction can eliminate mantissa and addition can be rounded.
The second type: add brackets and remove brackets to achieve the purpose of eliminating mantissa by subtraction and rounding by addition. The principle is: add brackets after MINUS sign, remove brackets, and change the sign inside brackets; Add parentheses after the plus sign, remove the parentheses, and keep the symbols in parentheses.
Third, the multiplication formula 1:
The multiplicative commutative law and associative law 25 _ 4 =100125 _ 8 =1000 are used for calculation.
Type 2: Divide by 25 _ 4 = 100, 125 _ 8 = 1000. 25, 125 appears in the title, and the 4 and 8 you need to find are hidden in another factor.
The third category: the specific application of the law of multiplication and distribution.
(1) Forward operation of the formula, (a+b)c= ac+bc a(b+c)=ab+ac (positive sign can also be changed to negative sign).
(2) Inverse operation of the formula: ac+bc=(a+b)c ab+ac= a(b+c) (positive sign can also be changed to negative sign).
(3) Multiply two numbers, where one factor is close to whole ten, whole hundred, whole thousand ..., and then rewrite it and calculate it by the law of multiplication and distribution. Watch the brackets! Such as102as (100+2); 8 1 as (80+1); 99 as( 100- 1)； 79 as (80- 1)。
(4) When a single number appears, it should be regarded as 1 and then calculated by multiplication and division. For example, 83 is regarded as 83_ 1.
From simple operation, we can extend to another knowledge point and calculate quickly. What are the knowledge points about quick calculation? Let's have a look.
1. Two digits times two digits.
1 .10 times 10: formula: head joint, tail to tail, tail to tail.
2. The heads are the same and the tails are complementary (the sum of the tails is equal to 10): Formula: after a head is added with 1, the head is multiplied by the head and the tail is multiplied by the tail.
3. The first multiplier is complementary, and the other multiplier has the same number: formula: after a head is added with 1, the head is multiplied by the head and the tail is multiplied by the tail.
4. Dozens of eleven times dozens of eleven: formula: head to head, head to head, tail to tail.
More than ten times any number:
Formula: The first digit of the second multiplier does not drop, the single digit of the first factor multiplies each digit after the second factor, and then drops.
Suxiao No.2 prescription
First of all, add some reasons:
Where the single digit of the number to be squared is 1, and this number is greater than the power of 10 or the multiple of 10, adding the multiple of 10 to the last digit of 10 is the root of this number.
Return to convention:
When the single digit of an open number is 1 and this number is less than the power of 10 or the multiple of 10, the root of this number is to subtract the multiple of 10 from the last digit.
Plus five theorem:
The number of units of a square is 5. When this number is greater than the power of 10 or the multiple of 10, the root of this number is 10 or the multiple of 10 plus the last digit of 5.
Add two and eight theorems:
If the single digit of the root sign is 4, and this number is greater than the power of 10 or the power multiple of 10, then if there is little difference between the multiple of 10 and 10, add 2; If the difference is large, add 8 or 10 to the multiple of 0, which is the root of this number.
Add three and eight theorems:
If the number of digits is 9, and this number is greater than the power of 10 or the multiple of 10, if there is little difference, add 3; If the difference is large, add 7 to the multiple of 10 or 10, which is the root of this number.
Every six plus six theorem:
If the single digit of the number of roots is 6, and this number is greater than the power of 10 or the multiple of 10, then the number of roots plus the multiple of 10 is the number of roots.
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