Unit 1 four arithmetic operations
1, operation sequence
P5: In the formula without brackets, if there is only addition and subtraction or only multiplication and division, it must be calculated.
For example: 98-46+25 6÷3×98
= =
= =
P6: In the formula without brackets, there are multiplication, division, addition and subtraction, which must be calculated first.
For example: 36+64÷4
=
=
P 1 1: If there are brackets in the formula, it must be calculated first.
For example: 100(4+2 1)
=
=
2.P 12:, and are collectively called four operations.
3.P 13: Operation on 0
Add a number to 0 and you get the number.
Subtract 0 from a number and you get the number.
Multiply a number by 0 to get 0.
Divide 0 by a number to get 0.
0 cannot be divided completely, for example, 5÷0 does not exist and is meaningless.
4. Elementary arithmetic methods.
Look (numbers, operation symbols, thinking about the operation order. )
Draw a line (draw a line, which step is counted first, draw a horizontal line under which step, and copy if it is not counted. )
Three calculations (calculated in order of operation)
Check (check whether the operation sequence is wrong and the calculation is wrong. )
Unit 3 Algorithm and Simple Calculation
1, algorithm and formula characteristics
Characteristics of Examples of Arithmetic Formula
P28:: additive commutative law a+b=b+a 34+89+66=34+66+89.
26+47-6=26-6+47 1, only addition and subtraction.
2. Pay attention to exchange the previous "-"signs when subtracting.
3. In simple calculation, additive commutative law and additive associative law are generally used at the same time.
P29: additive associative law
a+b+c=a+(b+c)
88+ 104+96=88+( 104+96)
79+26-9=26+(79-9)
P34: Multiplicative commutative law a × b=b× a 4×58×25=4×25×58 1, only multiplication.
2. Multiplicative commutative law and multiplicative associative law are generally used at the same time in simple calculation.
3. Pay attention to finding good friends:
2×5= 10
4×25= 100
8× 125= 1000
P35: Multiplicative associative law
a×b×c
=a×(b×c)
125×67×8=67×( 125×8)
P36: division by multiplication and division: (a+b)×c
=a×c+b×c
Combination: a×b+a×c
=a×(b+c) 25×(200+4)=25×200+25×4
265×105-265× 5 = 265× (105-5)1,with multiplication and addition; Or multiplication and subtraction.
2. When disassembling, divide the number outside the bracket into two numbers inside the bracket.
3. When merging, extract the same factor and add or subtract different factors.
Pay special attention to: the difference between multiplicative associative law and multiplicative distributive law.
For example:125× (8× 20)125× (8+20)
= =
= =
= =
2. Nature of operation
The essence of continuous subtraction: if a number subtracts two numbers continuously, the sum of the two numbers can be subtracted.
Formula: a-b-c=a-(b+c)
For example:128-57-43 =128-(57+43)
Memory: decrease, increase, unchanged.
The nature of continuous division: a number divided by two numbers can be divided by the product of these two numbers.
Formula: a÷b÷c=a÷(b×c)
For example: 2000 ÷125 ÷ 8 = 2000 ÷ (125× 8)
Memory: multiplication has not changed except for change.
3. When two numbers are multiplied, one of them can be split and then simply calculated.
For example: 72× 125 23×99
=(9×8)× 125 =23×( 100- 1)
=9×(8× 125) =23× 100-23× 1
=9× 1000 =2300-23
=9000 =2277
Unit 6 Addition and Subtraction of Decimals
1 and addition and subtraction of decimals
The same numbers should be aligned, that is, aligned.
② Starting from the lowest digit, which digit adds up to 10, and the previous digit advances to1; Which one is not enough? Borrow the previous one 1.
③ Not enough, use 0 to occupy a place.
For example: 8-2.49
2. Mixed operation and simple calculation of decimals
The addition and subtraction of decimals is the same as that of integers.
Simple calculation of decimals, like simple calculation of integers, is carried out by using commutative law and associative law.
The Significance and Properties of Quaternary Decimal
1, decimal meaning: divide an object into 10, 100, 1000,,,, each of which accounts for,,,
P5 1: Fractions with denominator of 10 can be written as one decimal place, fractions with denominator of 100 can be written as two decimal places, and fractions with denominator of 1000 can be written as three decimal places.
The counting unit of decimals is one tenth, one hundredth, one thousandth,,, written as 0. 1, 0.0 1, 0.00 1,,, respectively.
The advance rate between every two adjacent counting units is.
2. Decimal digit sequence table
Decimals consist of,, and.
Numeric sequence table of decimals:
Integer part decimal part decimal part
digital ...
… …
finger
…
…
The lowest digit of the integer part is, and the highest digit of the decimal part is.
2.309, 2 in place, indicating a, 3 in place, indicating a,
9 in place, indicating a.
3.P53: Decimal reading and writing
① Read (write) the integer part first, and read (write) according to the integer reading (writing) method.
② Read (write) the decimal point again.
(3) Finally read (write) the decimal part, and read (write) the numbers on each digit in turn.
Note: If there are several zeros in the decimal part, you should read several zeros, and the zeros after the decimal point should also be read.
For example, 20.040 is pronounced as: and 407.07 is written as:.
4.P58: Properties of decimals:.
5.P60: Comparison of decimals
Look at the integer part first, and the larger the integer part, the larger the number.
(2) If the integer parts are the same, look at the decimal places, and the number with decimal places is large.
(3) If the decimals are still the same, look at the percentile again until the sizes of the two decimals are compared. . .
Note: There are not enough digits, so use 0 to fill the space.
For example: 8.11.008.101.
6.P6 1: the size change caused by the movement of the decimal point.
If the decimal point is moved one place to the right, it will double, that is,
If the decimal point is moved two places to the right, the decimal point will be doubled, that is,
If the decimal point is moved three places to the right, the decimal point will be doubled, that is,
If the decimal point is moved one place to the left, the decimal point will be doubled, that is,
If the decimal point is moved two places to the left, the decimal point will be doubled, that is,
If the decimal point is moved three places to the left, the decimal point will be doubled, that is,
For example:
7.P68: Rewriting the name (unit conversion+problem group exercise)
Find the approximate value of a decimal.
When seeking approximate value, keep integer to represent accurate to the nearest position; Keep a decimal place to indicate accuracy to the correct position; Keeping two decimal places means being accurate to the right place.
Please note that 0 after the decimal point cannot be omitted when representing approximate values.
Finding the approximate number of decimals is similar to finding the approximate number of integers.
For example: 8.392≈ (accurate to 1%)
P74: Rewritten as a number in units of "ten thousand" or "hundred million"
(1) shall be graded first, starting with one digit, and every four digits shall be one level.
② The decimal point is at the right end of the 10,000 (billion)-digit number, and the exact number can be obtained by adding 10,000 (billion) words after the number.
③ Find out the approximate figures as required. Finally, pay attention to the unit.
For example, keep one decimal place: 6 4850 0000 =
≈