First, the classification of primary school students' knowledge of mathematical laws
(1) Write down three digits for the addition of two digits.
1, aligned with the same number;
2. Starting from the unit;
3. When the number of digits reaches 10, enter 1 into ten digits.
(2) Do a two-digit subtraction with a pen, and remember three things.
1, aligned with the same number;
2. Reduce from one place;
3. If the number of digits is not enough, subtract 1 from the number of digits, add 10 to the number of digits and then subtract.
(3) Calculation rules of mixed operation
1, in the formula without brackets, only addition and subtraction or multiplication and division can be performed from left to right;
2. In the formula without brackets, if there are multiplication and division and addition and subtraction, the multiplication and division should be calculated first, and then the addition and subtraction should be calculated;
3. If there are brackets in the formula, count the brackets first.
(D) four-digit reading method
1, read in order from the high order, thousands, hundreds, and so on;
2. There is a zero or two zeros in the middle, and one zero is read-only;
No matter how many zeros there are, don't read the last number.
(5) Four-digit writing
1, written in order from the high order;
2. Write thousands, hundreds, and so on. If there is no one in the middle or at the end, write 0 on which one.
(6) Four-digit subtraction should also pay attention to three items.
1, aligned with the same number;
2. Reduce from one place;
3. Which figure is not enough to reduce? Retract 1 from the previous position, add 10 to the standard position, and then subtract.
(7) the law of one-digit multiplication by multi-digit multiplication
1, starting from the unit, multiply each digit in multiple digits by one digit in turn;
Whoever gets the highest score will be promoted several times.
(8) Divider is the division rule of single digits.
1. Divide the dividend by the first digit of the dividend every time starting from the high digit of the dividend. If it is less than the divisor, try the division of the first two digits again.
2. Write the quotient where the divisor is divided;
3. For each quotient, the remainder must be less than the divisor.
(9) The multiplication rule that a factor is a two-digit number.
1, first multiply the number on the two-digit number by another factor, and the last digit of the number is aligned with the two-digit number;
2. Multiply the number on the ten-digit number by another factor to get that the last digit of the number is aligned with the ten-digit number;
3. Then add up the multiplied numbers twice.
(10) The divisor is the division rule of two digits.
1. Starting from the high order of the dividend, try to divide the first two digits of the dividend by the divisor. If it is less than the divisor,
2. Write the business on any one except the bonus;
3. For each quotient, the remainder must be less than the divisor.
(eleven) the reading rules of ten thousand books.
1, read ten thousand levels first, and then read one level;
2, ten thousand series should be read according to the reading method of level one, and then add a ten thousand word at the back;
3. Don't read the last digit of each level, no matter how many zeros there are. Other numbers have a zero or read only a zero and several zeros in succession.
(12) Multi-digit reading rules
1, starting from the high position and reading down one level at a time;
2. When reading 100 million or 10,000 levels, read according to a series of reading methods, and then add 100 million or 10,000 words at the back;
3. Don't read the zero at the end of each level, other numbers have a zero, or read only one zero for several consecutive zeros.
(XIII) Comparison of decimal dimensions
Compare the sizes of two decimals, first look at their integer parts. The number with large integer parts is large, so is the number with large integer parts, the number with large decimal places is large, the number with large decimal places is also large, and so on.
(14) decimal addition and subtraction operation rules
To calculate decimal addition and subtraction, first align the decimal point (that is, align the numbers on the same digit), then calculate by integer addition and subtraction, and finally align the decimal point position on the horizontal line and point the decimal point.
Calculation Rules of (15) Decimal Multiplication
To calculate decimal multiplication, first calculate the product according to the multiplication law, then look at the decimal places in the factor, count the decimal places from the right side of the product and point to the decimal point.
(16) divisor is the law of integer division.
Dividers are fractional divisions of integers. Divide according to the law of integer division. The decimal point of quotient should be aligned with the decimal point of dividend. If there is a remainder at the end of the dividend, add 0 to the remainder and continue the division.
(17) Division algorithm with divisor as decimal.
Divider is the division of decimals. First, move the divisor decimal point to make it an integer. The decimal point of the divisor is shifted to the right by several digits, and the decimal point of the dividend is also shifted to the right by several digits (the digits are not enough to make up the 0 at the end of the dividend), and then it is calculated by fractional division with the divisor as an integer.
(18) Steps to Solve Application Problems
1, find out the meaning of the problem, find out the known conditions and problems, analyze the quantitative relationship in the problem, and determine what to calculate first, then what to calculate, and finally what to calculate;
2. Determine how to calculate each step, list formulas and work out numbers;
3. Test and write the answers.
(nineteen) the general steps of solving application problems with column equations
1, find out the meaning of the problem, find out the unknown, and express it with x;
2. Find out the equal relationship between the quantities in the application problem and make an equation;
3. Solve the equation;
4. Test and write the answers.
(20) Addition and subtraction of fractions with the same denominator
Add and subtract fractions with the denominator, the denominator remains the same, and only the numerator is added and subtracted.
(twenty-one) the addition and subtraction rules of the same denominator and the same fraction.
To add and subtract fractions, first add and subtract the integer part and the fraction part respectively, and then combine the obtained numbers.
(22) Addition and subtraction of fractions with different denominators
The addition and subtraction of fractions with different denominators are divided first, and then calculated according to the addition and subtraction law of fractions with the same denominator.
(twenty-three) the calculation rules of the score multiplied by the integer.
Multiply a fraction by an integer, and use the product of the numerator of the fraction multiplied by the integer as the numerator, with the denominator unchanged.
(twenty-four) the calculation rules of the score multiplied by the score.
Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.
(twenty-five) a number divided by a fraction of the calculation rules.
A number divided by a fraction is equal to the number multiplied by the reciprocal of the divisor.
(26) Methods of converting decimals into percentages and converting percentages into decimals.
To convert decimals into percentages, just move the decimal point two places to the right, followed by hundreds of semicolons;
Convert percentages to decimals, remove the percent sign, and move the decimal point two places to the left.
(27) Methods of converting fractions into percentages and converting percentages into component numbers.
To turn a fraction into a percentage, usually first turn the fraction into a decimal (except for three decimal places), and then turn the decimal into a percentage;
Convert percentages to decimals. First, rewrite the percentage into a fraction with the initials 100, and make a quotation that can be turned into the simplest fraction.
Second, the classification of oral definitions of primary school mathematics
1. What is the circumference of the graph?
The sum of all the edges of a figure is the perimeter of the figure.
2. What is the area?
The size of the surface of an object or the plane figure surrounded by it is called their area.
3, the relationship between the parts of addition:
One addend = and-the other addend.
4, the relationship between the parts of subtraction:
Minus = Minus-Difference Minus = Minus+Difference
5, the relationship between the parts of multiplication:
One factor = the product of another factor.
6, the relationship between the parts:
Divider = dividend quotient dividend = quotient divisor
7. Angle
(1) What is an angle?
A figure composed of two rays drawn from a point is called an angle.
(2) What is the vertex of an angle?
The endpoint of an angle is called a vertex.
(3) What is the edge of a corner?
The rays that form an angle are called the edges of the angle.
(4) What is a right angle?
An angle of 90 degrees is a right angle.
(5) What is a right angle?
The two sides of an angle are on a straight line, and such an angle is called a right angle.
(6) What is an acute angle?
An angle less than 90 is an acute angle.
(7) What is an obtuse angle?
An angle greater than 90 and less than180 is an obtuse angle.
(8) What is a fillet?
The light rotates around its endpoint. The angle of Zhou Suocheng is called a fillet, and the fillet is equal to 360 degrees.
8.( 1) What is vertical? What is a vertical line? What is a drooping foot?
When two lines intersect at right angles, they are perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two lines is called the vertical foot.
(2) What is the distance from a point to a straight line?
Draw a vertical line from a point outside the line, and the distance between the point and the vertical foot is called the distance from the point to the line.
9. Triangle
(1) What is a triangle?
A figure surrounded by three line segments is called a triangle.
(2) What sides does a triangle have?
Each line segment forming a triangle is called an edge of the triangle.
(3) What is the vertex of a triangle?
The intersection of every two line segments is called the vertex of a triangle.
(4) What is an acute triangle?
A triangle with three acute angles is called an acute triangle.
(5) What is a right triangle?
A triangle with a right angle is called a right triangle.
(6) What is an obtuse triangle?
A triangle with an obtuse angle is called an obtuse triangle.
(7) What is an isosceles triangle?
A triangle with two equal sides is called an isosceles triangle.
(8) What is the waist of an isosceles triangle?
In an isosceles triangle, two equal sides are called the waist of the isosceles triangle.
(9) What is the vertex of an isosceles triangle?
The intersection of two waists is called the vertex of an isosceles triangle.
(10) What is the base of an isosceles triangle?
In an isosceles triangle, the side that is not equal to the other two sides is called the base of the isosceles triangle.
(1 1) What is the base angle of an isosceles triangle?
The two equal angles on the base are called the base angles of an isosceles triangle.
(12) What is an equilateral triangle?
A triangle with three equilateral sides is called an equilateral triangle, also called a regular triangle.
(13) What is the height of the triangle? What is the base of a triangle?
Draw a vertical line from the vertex of a triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle, and the opposite side of the vertex is called the bottom of the triangle.
What is the sum of the internal angles of a triangle (14)?
The sum of the internal angles of a triangle is 180.
10, quadrilateral
(1) What is a quadrilateral?
A figure surrounded by four line segments is called a quadrilateral.
(2) What is equilateral?
Two groups of parallelograms with parallel opposite sides are called parallelograms.
(3) What is the height of the parallelogram?
Draw a vertical line from one point on one side of the parallelogram to the other. The line segment between this point and the vertical foot is called the height of the quadrilateral.
(4) What is a trapezoid?
A quadrilateral with only one set of parallel sides is called a trapezoid.
(5) What is the bottom of the trapezoid?
A set of mutually equal sides in a trapezoid is called the bottom of the trapezoid (usually the shorter bottom is called the upper bottom and the longer bottom is called the lower bottom).
(6) What is a trapezoidal waist?
In a trapezoid, an unequal set of opposite sides is called the waist of the trapezoid.
(7) What is the height of the trapezoid?
Draw a vertical line from a point on the upper bottom to the lower bottom. The line segment between this point and the vertical foot is called the height of the trapezoid.
(8) What is an isosceles trapezoid?
An isosceles trapezoid is called an isosceles trapezoid.
1 1. What is a natural number?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are used to indicate that the number of objects are all natural numbers (natural numbers are all integers).
12, what is rounding?
When finding the divisor of a number, look at the number on the mantissa. If it is 4 or less, the mantissa is discarded. If it is 5 or more, after removing the mantissa, add 1 to the previous number. This method of finding approximate value is called rounding.
13, meaning of addition and arithmetic.
(1) What is addition?
The operation of combining two numbers into one number is called addition.
(2) What is addend?
The addition of two numbers is called addend.
(3) What is harmony?
The result of adding addends is called sum.
(4) What is additive commutative law?
When two numbers are added and the positions of addends are exchanged, their sum remains the same. This is called additive commutative law.
What is subtraction?
Given two numbers and one addend, the operation of finding the other addend is called subtraction.
15, what is the minuend? What is subtraction? What is the difference?
In subtraction, the known sum is called the minuend, the subtracted known number is called subtraction, and the obtained unknown number is called the difference.
16, the relationship between the addition parts:
Sum = addend+addend = and-another addend
17, subtract the relationship between the parts:
Difference = minuend-minuend = minuend-difference = minuend+difference
18, multiplication
(1) What is multiplication?
The simple operation of finding the sum of several identical addends is called multiplication.
(2) What is a factor?
Multiplying two numbers is called a factor.
(3) What is a product?
The number obtained by multiplying the factor is called the product.
(4) What is the multiplicative commutative law?
When two factors are multiplied, the positions of the factors are reversed and their products remain unchanged. This is called multiplicative commutative law.
(5) What is the law of multiplicative association?
When multiplying three numbers, multiply the first two numbers and then the third number, or multiply the last two numbers and then the first number, and the product remains unchanged. This is the so-called law of multiplication and association.
19 branch
(1) What is division?
Given the product of two factors and one of them, the operation of finding the other factor is called division.
(2) What is dividend?
In division, the known product is called dividend.
(3) What is a divisor?
In division, a known factor is called divisor.
(4) What is business?
In division, the unknown factor is called quotient.
20, the relationship between the parts of multiplication:
Product = factor One factor = another factor of product
2 1 and (1);
Quotient = Divider = Divider Quotient
(2) the relationship between each part of division and the remainder:
Dividend = quotient divisor+remainder
22. What is a name number?
Usually, the sum of the measured number and the unit name is called the nominal number.
23. What is a single number?
A number with only one company name is called a single number.
24. What is a composite number?
Numbers with two or more unit names are called composite numbers.
25. What is a decimal?
Imitate the writing of integers, write them on the right side of integer digits, and separate them with dots. The numbers used to represent ten, percent and thousandth are called decimals.
26. What are the basic properties of decimals?
Adding or removing zeros at the end of decimals to keep the size of decimals unchanged is the basic nature of decimals.
27. What is a finite decimal?
The number of decimal places is limited. A decimal is called a finite decimal.
28. What is an infinite decimal?
Decimals with infinite digits are called infinite decimals.
29. What is a circular festival?
A number in which each part of the cyclic decimal system repeats in turn is called the cyclic part of this number.
30. What is a pure cyclic decimal?
The cyclic segment starting from the first decimal place is called pure cyclic decimal.
3 1, what is a mixed cyclic decimal?
Loop segments that do not start with the first decimal part are called mixed loop decimals.
32. What are the four operations?
We call the four operations of addition, subtraction, multiplication and division four operations.
33. What is an equation?
Equations with unknowns are called equations.
34. What is solving an equation?
The process of solving equations is called solving equations.
35. What is a multiple? What is a divisor?
If A is divisible by B, A is a multiple of B, and B is called a divisor of A (or a factor of A).
36. What kind of number is divisible by 2?
Numbers with 0, 2, 4, 6 and 8 in a unit can be divisible by 2.
37. What is an even number?
A number divisible by 2 is called an even number.
38. What is an odd number?
Numbers that are not divisible by 2 are called odd numbers.
39. What kind of number is divisible by 5?
A number with a unit of 0 or 5 can be divisible by 5.
40. What number is divisible by 3?
The sum of digits of a number can be divisible by 3, and so can this number.
4 1, what is a prime number (or prime number)?
If a number has only 1 and its two divisors, such a number is called a prime number.
42. What is a composite number?
A number has other divisors besides 1 and itself. Such numbers are called composite numbers.
43. What is a prime factor?
Every composite number can be written as the product of several prime numbers. Every prime number is a factor of this composite number, which is called the prime factor of this composite number.
44. What is a factorization prime factor?
Multiplying a prime factor by a composite number to represent it is called prime factor decomposition.
45. What is a common divisor? What is a common divisor?
The common divisor of several numbers is called the common divisor. One of them is called common divisor.
46. What is a prime number?
Two numbers whose common divisor is only 1 are called prime numbers.
47. What is a common multiple? What is the least common multiple?
The common multiple of several numbers is called the common multiple of these numbers. The smallest one is called the least common multiple of these numbers.
48. Score
(1) What is a score?
Divide the unit 1 into several parts on average, and the number representing such a part or parts is called a fraction.
(2) What is a fractional line?
The horizontal line in the middle of the score is called the fractional line.
(3) What is the denominator?
The part below the fractional line is called the denominator.
(4) What is a molecule?
The part above the fractional line is called the numerator.
(5) What is a decimal unit?
Divide the unit 1 into several parts, indicating that some of them are called decimal units.
49. What's the score?
(1) For two fractions with the same denominator, the fraction with larger numerator is larger.
(2) For two fractions with the same numerator, the numerator with smaller denominator is larger.
(3) What is a true score?
Fractions with numerator less than denominator are called true fractions.
(4) What is a false score?
Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions.
(5) What is a score?
A number consisting of an integral fraction and a true fraction is usually called a fraction.
(6) What is the basic nature of the score?
The numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains the same, which is the basic property of the fraction.
(7) What is approximate score?
Turning a fraction into a number equal to it, but with smaller numerator and denominator, is called divisor.
(8) What is the simplest score?
A fraction whose numerator and denominator are prime numbers is called simplest fraction.