1, in the formula without brackets, if there is only addition, subtraction or multiplication and division, it should be calculated from left to right. (Operation at the same level goes from left to right, without brackets)
2. There are multiplication, division, addition and subtraction in the formula without brackets. You should calculate multiplication and division first, and then add and subtract. (Addition, subtraction, multiplication and division, multiplication and division before addition and subtraction, without brackets)
3. There are brackets in the formula. You should count the inside of the brackets first, and then count the outside.
4. Addition, subtraction, multiplication and division are called four operations.
5. Operation on zero: a number plus 0 returns the original number, the minuend is equal to the subtrahend is 0, a number multiplied by 0 returns 0, and 0 is divided by a non-zero number, and 0 cannot be divided.
Unit 2: Position and Direction
1, the method of drawing the plan: first determine the direction, then determine the distance, and you can use the scale when determining the distance.
2. The position is relative, the direction is opposite, the degree is the same, and the distance is the same. For example, A is 40 southwest of B, then B is 40 northeast of A. ..
3. Drawing method of simple circuit diagram: first determine the starting point, and then set the direction and distance for drawing; Then choose the second starting point as the center point, then set the direction and distance of drawing ... and so on. (Where to go, where to put the sign)
4. Steps of drawing the plan: orientation, distance, name and angle.
5. Generally speaking, it goes up north and down south, left west and right east.
Unit 3: Algorithms and Simple Calculations
(A) the addition algorithm
1, additive commutative law: Add two numbers, exchange the positions of two addends, and the sum remains unchanged.
Expressed in letters: a+b = b+a.
2, the law of addition and association: three numbers are added, first add the first two numbers, or add the last two numbers first, and the sum is unchanged. Expressed in letters: a+b+c= a +( b+c)
(2) Multiplication algorithm
1, multiplication method of substitution: two numbers are multiplied, and the positions of two factors are exchanged, and the product remains unchanged.
Expressed in letters: a× b = b× a.
2. Multiplication and association law: when three numbers are multiplied, the first two numbers are multiplied first, or the last two numbers are multiplied first, and the product remains unchanged. Expressed in letters: a×b×c= a×(b×c)
3. Multiplication and distribution law: the sum of two numbers is multiplied by one number. You can multiply these two numbers by this number first, and then add them up. Expressed in letters: (a+b) × c = a× c+b× c.
The law of multiplication and distribution is still used to multiply the difference between two numbers by a number: (a-b) × c = a× c-b× c.
(3) Simple calculation
1, additive commutative law and the law of addition, such as 63+56+37=63+37+56 or 56+(63+37).
2. Multiplicative commutative law and multiplicative associative law, such as 15×7×2= 15×2×7 or 7×( 15×2).
3. Continuous reduction, variable reduction and summation (the nature of subtraction). Expressed in letters: a-b-c=a-(b+c)
4. Reduction and continuous reduction, such as 567-(167+254) = 567-167-254.
5. Classification by product (nature of classification). Expressed in letters as a \b \c = a \b×c
6,25× 4 =100, so when you see 25, you think of 4.
(1) multiplicative commutative law or multiplicative associative law, such as 25× 17×4.
(2) Multiplicative splitting method, such as 25×32=25×(4×8)=25×4×8.
(3) Addition resolution method, such as 25×14 = 25× (10+4) = 25×10+25× 4.
(4) multiply 100 by 4, such as 36×25=36× 100÷4.
(5) Divide by 100 times 4, such as 3200÷25=3200÷ 100×4.
7, 125×8= 1000, so when you see 125, you think of 8.
(1) multiplicative commutative law or multiplicative associative law, such as125×17× 8 =125× 8×17 or
17×( 125×8)
(2) Multiplicative splitting method, such as125× 32 = 25× (4× 8) =125× 8× 4.
(3) additive resolution method, such as125×18 =125× (10+8) =125×/kloc-0+.
(4) Multiply 1000 by 8, such as 24× 125=24× 1000÷8.
(5) Divide by 1000 times 8, such as 32000125 = 320001000× 8.
8. In multiplication, addition and subtraction operations, if there are * * * identical factors in two multiplication formulas, you can use the multiplication distribution law for simple calculation. Namely:
a×c+b×c = (a+b)×c
a×c-b×c = (a-b)×c
9. Omit the form of × 1, such as 34× 99+34 = 34× 99+34×1= 34× (99+1).
Or 34×101-34 = 34×1-34×1= 34× (101-/kloc-
Special cases such as 10,99 and 10 1,
(1) changes the distribution law by splitting, such as 76×99=76×( 100- 1).
Or 76×101= 76× (100+1).
(2) More and less, such as 346+199 = 346+(200-1) = 346+200-1.
(3) Add a few more, such as 346-199 = 346-(200-1) = 346-200+1.
(4) subtract the integer first and then the mantissa (subtraction and continuous subtraction), such as 700-402=700-(400+2)=700-400-2.
1 1, subtraction becomes one minus one plus, for example.
Addition before subtraction: 967-(421-233) = 967-421+233 = 967+233-421.
Subtract first and then add: 967-(567-235)=967-567+235.
Unit 4: the meaning and nature of decimals
1, decimal counting units are: 0. 1 (or one tenth), 0.0 1 (or one hundredth), 0.00 1 (or one thousandth) ... The corresponding figures are decimal, percentile and thousandth respectively. ...
2. Decimal reading: the integer part is read as an integer, and the decimal part should read the numbers on each bit in order.
3. Decimal writing: the integer part is written as an integer part, the integer part is written as 0, and the decimal part writes each number in turn.
4. Nature of decimals: The decimal ends with "0" or is removed, and the size of the decimal remains unchanged.
5. Method of comparing decimal sizes: first compare the integer parts; If the integer parts are the same, compare decimals; If the deciles are the same, compare the percentiles; If the percentile is the same, compare the thousandth ... and so on.
6, mobile decimal point method:
(1) If the decimal point moves one place to the right, the decimal point will be expanded to 10 times the original number; If the decimal point is moved two places to the right, it will be expanded to 100 times of the original number; If the decimal point is moved three places to the right, it will be expanded to 1000 times the original number.
(2) If the decimal point is moved one place to the left, the decimal point will be reduced to one tenth of the original number; If the decimal point moves two places to the left, the decimal point will be reduced to 1% of the original number; If the decimal point is moved three places to the left, it will be reduced to one thousandth of the original number.
(3) Pay attention when moving the decimal point. When moving the decimal point to the left, if there are not enough integer digits, add "0" to the left of the number and add the decimal point. Such as: 2 reduced to one tenth of it is 0.2; When the decimal point moves to the left, the "0" after the decimal point should be removed, for example, 350 is reduced to its 3.5%.
7. Name rewriting step: (1) Judge which unit is larger and which unit is smaller; (2) judging whether to rewrite the large unit number into the small unit number or rewrite the small unit number into the large unit number; (3) Determine the progress between units, and then determine whether to use multiplication or division (small units are divided into large units, and large units are divided into small units by multiplication).
8. In order to find an approximate value of a decimal, we usually use the "rounding" method. (1) Keep an integer, indicating that it is accurate to one place, depending on the number of the tenth place; (2) Keep one place after the decimal point, indicating that it is accurate to ten places, depending on the number in the percentile; (3) Keep two decimal places, indicating that it is accurate to one percent, depending on the number on one thousandth; ..... and so on. Finally, according to the rounding method to decide whether to give up or enter.
9. How to rewrite an integer "10,000" or "100 million" into a number in units of "10,000" or "100 million": put a decimal point in the lower right corner of "10,000" or "100 million" and add the words "10,000" or "100 million" after the number. Note: Remove the "0" at the end after rewriting.
Unit 5: Triangle
1, a triangle is a figure surrounded by three line segments, which has three sides, three angles and three vertices. The sum of any two sides of a triangle is greater than the third side. Triangles are stable.
Draw a vertical line from the vertex of the triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle. This opposite side is called the base of a triangle.
3. Triangle can be divided into acute triangle, right triangle and obtuse triangle according to angle. To judge what a triangle is, just look at the largest angle in the triangle. The largest angle is an acute angle, which is an acute triangle. The largest angle is a right angle, which is a right triangle; The largest angle is an obtuse angle or an obtuse triangle.
According to the sides, it can be divided into equilateral triangle, isosceles triangle and equilateral triangle (equilateral triangle is a special isosceles triangle). Isosceles triangle: two waists are equal and two base angles are equal; Equilateral triangle: All three internal angles are equal, all equal to 60.
4. The sum of the internal angles of the triangle is equal to 180, regardless of the size and shape of the triangle.
5. You can spell a rectangle with at least two identical right triangles; At least three identical equilateral triangles can be used to form a trapezoid; At least two identical equilateral triangles can be used to form a parallelogram.
Unit 6: addition and subtraction of decimals
1, methods to be paid attention to when calculating decimal addition and subtraction:
(1) The decimal points should be aligned, that is, the same numbers should be aligned.
(2) When calculating, count from the rightmost side. When adding, pay attention to which digit adds up to 10, and enter 1 in the previous digit. When subtracting, pay attention to which digit is not enough, and subtract one from the previous digit.
(3) There is "0" in the calculation result, which should be generally removed.
2. Decimal addition and subtraction mixed operation and integer addition and subtraction mixed operation are in the same order:
(1) In the formula without brackets, only addition and subtraction are calculated from left to right;
(2) If there are brackets in the formula, calculate the formula in brackets first, and then calculate the formula outside brackets.
3. The simple calculation of additive commutative law, additive associative law and continuous subtraction is also applicable to the simple calculation of decimal addition and subtraction.
Unit 7: Statistics
The methods of making statistical charts of broken lines: one chart (point), two links (line segment) and three marks (data).
The characteristics of broken-line statistical chart: it can reflect the change of data more clearly.
Unit 8: Mathematical Wide Angle
When solving the problem of planting trees, we must first analyze the route of planting trees:
Interval number = total length ÷ plant spacing
1, when trees are planted at both ends of the unclosed route, the number of intervals = number of trees-1.
Given the total length and plant spacing, the number of trees = total length ÷ plant spacing+1;
Given the plant spacing and the number of plants, the total length = plant spacing × (plant number-1) = plant spacing × interval number.
Given the total length and number of plants, plant spacing = total length ÷ (number of plants-1) = total length ÷ number of intervals.
2. When there are no trees planted at both ends of the unclosed route, the interval number = number of trees+1.
Given the total length and plant spacing, the number of trees = total length ÷ plant spacing-1 = interval number-1;
Given the number of trees and plant spacing, the total length = plant spacing × plant spacing = plant spacing × (number of trees+1).
Given the total length and the number of trees, plant spacing = total length ÷ interval number = plant spacing × (number of trees+1).
3. When trees are planted at one end of the unclosed route and not at the other end, the number of trees = the number of intervals;
4. In the case of planting trees on the closed route, the number of trees = the number of intervals.