The blue word i primary school math is of interest
After school, information, pre-learning
Part one numbers and algebras
(i) awareness of numbers
Integer
Neither does one object, expressed in 0. Zero and one, two, three... Are natural and integer
2. The smallest natural number is 0, and the number of natural numbers is unlimited and not the largest natural number。
3 and 0 are neither positive nor negative. All positives are greater than 0 and all negatives are less than 0。
Integers include positive, zero and negative integers. Examples are: 3, 17, 0, 90, 6 etc。
5. Integer reading and writing: multidigital numbers start from place to place, with each of the four places divided into levels of one, 10,000, and billion. When reading a number, it starts at the top and is read at the first level. Levels 10,000 and billion are read in a single reading, followed by a name. None of the zeros at the end of each level, and none of the other digits, either zero or several consecutive zeros, read only one “zeros”。
6. Integers: when writing, determine which number is the highest, which number is the highest, and then from the top, the first level goes down, and none of the last one does not。
Seven, ten, hundreds, thousands, thousands, 100,000, millions, millions, billions, billions, billions, billions..
The whole number is one unit, 10, 100, thousands, 100,000, millions, millions, billions, billions, billions..
Large numbers of redrafting: the number of a number is changed to the number of units expressed as “millions” or “billions”, provided that the decimal point is on the right point of 10,000 or billion places, and that the word “tens” or “billions” is added after the number。
The number rewrited as required, without changing the size of the original number, is the correct number of the original number and is recoverable as required. For example: 974. 8 million = 974. 8 million and 453. 2 million。
9. To seek the approximation of a single number (usually rounded): to retain a single number integer, one decimal, two decimals, three decimals ... May also be described as precise to a single place, to a decile, to a percentage, to a thousand
For example, renumber 8745603 as "millions" and omit the end number after "millions" (to 10,000s)
8745603 = 8745. 603 ≈ 8. 75 million
10, integer size comparison: if the number of digits is different, the number of digits is larger; if the number of digits is the same, the number of places above the highest is the number of places above the highest, the number of places above the highest is the same, the number of numbers above the lower upper is the same, and if the number is still the same, the comparison continues, so push up until it is larger。
Decimals
Scores of 10, 100, 1000... May be expressed in decimals. One decimal means a few cents, two decimals a few percent, three decimals a thousand..
Integers and decimals are expressed in decimal numbers, each, ten, hundred and one tenth, and one per cent. The rate of progress is 10 per neighbouring two units。
3. Move decimals one, two and three to the right 10, 100 and 1,000 times the original number, respectively
Move decimals one, two and three to the left 10 times the original number, 100 times the original number, 1,000 times the original number
4. The location of each unit of account is called digits. The digits are in a certain order。
5. Decimal reading: integer parts are still read as integers, and integer parts are read as “zero”, decimals are read as “points”, decimals are read in the order in which each decimal is read from the left to the right, and zeros of decimals are read。
6-decimal writing: integer parts are written in the form of integers, integer parts are written “0”, decimal points are written at the bottom right of the integers, and decimal parts are written consecutively on each number。
7. Basic nature of decimals: add "0" at the end of decimals or delete "0" and the size of decimals remains unchanged。
Depending on the nature of the decimals, it is generally possible to remove the "0" at the end of the decimals and to simplify them。
9 the method for comparing decimals is to compare the number of integers and, in turn, the number of deciles of the integers, the number of points in the percentage, the number of points in the thousands, from the left to the right, and the number of decimals, if any。
10. General approach to the approximation of decimals:
(1) first, the number of decimals to be retained
(2) to determine, as necessary, which number to look at
(3) results are obtained by rounding。
Score
An average of several copies of unit “1” indicates that such a number or numbers are called fractions. Is the fraction of this fraction。
As can be seen from the meaning of decimals and fractions, decimals are actually the denominators of 10, 100, 1,000 ..。
4. Scores can be divided into true and false scores。
The fraction of molecules smaller than the denominator is called the true fraction. The true score is less than 1。
6. The fraction of the molecule greater than or equal to the denominator is called a false fraction. The false score is greater than or equal to 1. The false fraction of the molecule that is the denominator is actually the whole number。
7. Only the fractions of the public factor 1 are called the simplest。
Basic nature of fractions: the molecule and denominator of fractions are multiplied or divided by the same number (except zero), and the size of the fractions remains unchanged。
The basic nature of the applied fractions is that they can be divided in permeable and approximate。
Approximate fractions: the process of dividing molecules and denominators by their maximum public factor into a minimum fraction。
A process of converting several different denominators into fractions of the same denominator equal to the original fractions, which is called permutation, depending on the basic nature of the fractions。
10 last: the product is a two-digit penultimate of one. The countdown of 1 is 0, no countdown。
Percentage
One, the number indicating a number is called a percentage. It's called percentage or percentage
2. Scores versus percentages:
Different
Same point
Score
You can specify the number, you can have the name of the unit
It's a relationship between two numbers
Percentage
No specific number, no unit name
3 discounts: when a commodity is sold, it is often sold at a “discount”, or, in short, a discount of 10 per cent or a percentage of dozens. For example: 80 per cent of the original price is sold at a discount and 65 per cent at a discount。
Current prices = discount
4. Interoperable fractions, decimals, percentages。
(1) split the fraction into decimals, dividing the denominator by the molecule of the fraction。
(2) the number of decimal ingredients is first recast by the parent of the component to be 10, 100, 1000 and then approximately the minimum fraction。
(3) the decimal shall be converted to a percentage, with two decimal points moved to the right and a percentage number added。
(4) the percentage shall be reduced to decimals, the percentage number shall be removed and the decimal point shall then be moved two times to the left。
(5) the fractions shall be converted into percentages, first into decimals (three decimals shall normally be retained, i. E., one decimal before the percentage number), and then into decimals。
(6) the percentage has been reduced to the number of components, with the percentage having first been rewritten to 100 points for the parent of the component, with the offer of approximately points being approximately the simplest。
5. A few percent more (less) than the other one is a few percent more (less) than the other。
"1" for more or less units
6. Interest = principal x interest rate x time
Factor(s) and multiplier(s) [premature(mass), plural, odd, even]
1, 4x3 = 12, 12 is a multiple of 4 and 12 is a multiple of 3 and factors of 12。
2. The smallest number of multiples is itself, not the largest. A multiple is infinite。
The single smallest factor is 1 and the largest factor is itself. One factor is limited。
Characteristics of multiples of 4, 5 and 5: the number of places is 5 or 0。
Characteristics of multiples of 2: 2, 4, 6, 8 or 0 per bit. Two multiples are even。
Characteristics of the multiple of three: the number above you must be three。
The number of five and two is called even. It's not a double number called an odd number。
6 a number, if there are only one and two factors per se, is called a prime (or prime)。
7. A number, if there are factors other than one and itself, is called a combination。
Of these, 1-20:
Numbers: 2, 3, 5, 7, 11, 13, 17, 19。
Totals: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20。
One is neither a prime nor a single
The smallest odd number is one, the smallest even number is zero, the smallest prime number is two and the smallest compound is four。
10. If the two numbers are multiples, the large is the smallest common multiple and the small is the largest public factor。
11 if the two figures are only the public factor 1, the maximum public factor is 1 and the smallest common factor is their product。
Only two of the public factors of 1 are:
(1) two natural numbers adjacent to each other
(2) prime and prime
(3) prime and compound (but not multiple of prime)
(ii) operations of numbers
Method of calculation [integer, decimal, fraction]
1 integer plus minus equal digits shall be equalized from lower。
2. The decimal additions and subtractions shall be calculated by aligning decimal points and starting with lower places。
3. Decimal multiplier:
(1) the amount of the accumulation is calculated by multiplying integers, depending on the number of decimals in the factor, counting from the right side of the accumulation, with decimals。
(2) note: if the number of decimal places is not sufficient, it should be filled with zero in the front。
Decimal division:
(1) decimal points shall be aligned with the decimal points that have been divided
(2) when there is a surplus, add zero to the end and continue to be divided downwards
(3) if the number of places is less than one, write zero in the integer part of the business, point decimal places and continue to be divided。
(4) when transforming the division into an integer, several decimals of the division are moved to the right and several decimal points of the division are moved to the right。
(5) when the number of decimal places is less than the number of decimal places, zero shall be filled at the end of the dividing number。
5. Score plus minus:
(1) add to or subtract from the denominator, adding to or subtracting from the molecule and maintaining the denominator。
(2) the heterogeneity shall be increased and reduced by an incoherent fraction into a condensed fraction。
6. Comparison of fraction sizes:
(1) in comparison with the denominator, the molecule is large and small。
(2) the fractions of the heterogeneity are compared, divided and then compared; if the molecule is the same, the denominator is small。
7. Score multipliers, molecules multiplied by molecules and denominators multiplied by denominators。
8. A number divided by b (except zero) equals the penultimate number of a number multiplied by b。
Four operations
Add
One plus = and one plus
Subtract
Deducted = difference + decrease bad
Multiplication
One factor = accumulator and another factor
Division
Divided = commercial x division = division ÷ business
1 divisiond commercial constant: divided and divided by the same number (except zero) at the same time。
2. Easy to calculate
Operating law:
Law of operations
In letters
The law of exchange
A+b=b+a
The law of addition
(a+b) +c =a+ (b+c)
Multiplication exchange
Axb=bxa
Multiplication laws
(axb) xc = ax (bxc)
Multiplication law
(a+b)xc=axxc+bxc
Subtract operation patterns
A-b-c=a-(b+c)
Division mode of operation
A ÷b÷c=a÷(bxc)
2. Multiplication, division. (small technique: symbol is the opposite; two digits multiplied by 1.)
(1) a÷0. 1 = ax10
(2) a x 0. 1 = a ÷ 10
(7) a÷0. 01=ax100
(8)ax0. 01=a÷100
(3) a÷0. 2=ax5
(4) ax0. 2 = a÷5
(9) a÷0. 25=ax4
(10) ax0. 25 = a÷4
(5) a÷0. 5 = ax2
(6) ax0. 5 = a÷2
(11) a0. 0. 125=ax8
(12) a x 0. 125 = a ÷8
3. Approach to approximation。
(1) rounded. (2) insertion to one law. (3) endnote。
Comparison of sizes of accumulation and factor, factor and division:
2nd factor > 1, accumulation > factor 1
2nd factor = 1, accumulation = factor 1
2nd factor
Divide > 1, class
