1, the expression of the equation is called equality.
2. An equation with an unknown number is an equation.
3. Equation must be an equation; An equation is not necessarily an equation. Equation > equation
4. Adding or subtracting the same number on both sides of the equation at the same time results in an equation. This is the essence of the equation.
When both sides of an equation are multiplied or divided by the same number that is not equal to 0, the result is still an equation. This is also the nature of the equation.
5. The process of finding the unknown quantity in the equation is called solving the equation.
Common relations in solving equations:
One addend = sum-another addend = minuend-difference = minuend+difference.
One factor = product/divisor = dividend/quotient dividend = quotient × divisor
Note: After solving the equation, you should form a good habit of testing.
6. The sum of five consecutive natural numbers (or consecutive odd numbers and consecutive even numbers) is equal to five times the median number. The sum of odd consecutive natural numbers (or even consecutive odd numbers) is equal to the middle number.
7. The sum of four consecutive natural numbers (or consecutive odd numbers or even numbers) is equal to the sum of the middle two numbers or the first two numbers × number ÷2 (Gaussian sum formula).
8. enumerate the ideas of solving application problems by equations: a. examine the problems and understand the known conditions and problems of the problems. B, clear the equal relationship of the topic. C, set an unknown number, and the number that is generally found is represented by X. D, list equation E, solve equation F, test G and answer according to the equivalence relation.
The second unit determines the position
1. When determining the position, the vertical rows are called columns and the horizontal rows are called rows. Determine which column is generally counted from left to right and which row is generally counted from front to back.
2.Number pair (x, y) The 1 th number indicates which column (x) and the second number indicates which row (y). When writing a number pair, write the number of columns first, then the number of rows.
3. Seen from the globe, it is the meridian connecting the North Pole and the South Pole, and the ring perpendicular to the meridian is the latitude. Longitude and latitude are arranged in a certain order, indicating "longitude" and "latitude" respectively, and both "longitude" and "latitude" are expressed in degrees (), minutes (') and seconds (").
4. Move a point to the left and right by several squares, except that the number on column (X) changes, decreases to the left and increases to the right, while the number on row (Y) remains unchanged. For example, the position of point (6, 3) is (8, 3) after being shifted to the right by 2 units, and column 6+2 = 8; The position of the point (6,3) is (4,3) after being shifted to the left by 2 units, and the column 6-2=4.
5. Move a point up and down a few squares, except that the number on the row (Y) has changed, and the number on the column (X) has not changed. For example, the position of point (6, 3) is (6, 5) after moving up by 2 units, and line 3+2 = 5; When the point (6,3) moves down by 2 units, the position is (6, 1), and the column 3-2= 1.
Unit 3 Common Multiples and Common Factors
1, the smallest factor is 1, the largest factor is itself, and the number of a number factor is limited.
The minimum multiple of a number is itself, and there is no maximum multiple. The multiple of a number is infinite.
The largest factor of a number is equal to the smallest multiple of this number.
2. The common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers, with the symbol =40,(5,8)= 1
The greatest common factor of two adjacent numbers is 1, and the least common multiple is their product. =72,(9,8)= 1
Numbers with special relationships (both are composite numbers, one is odd and the other is even, but there is only one common factor between them 1), such as 4 and 9, 4 and 15, 10 and 2 1, and the greatest common factor is 1.
For two numbers in general relation, the greatest common factor is found by enumeration or short division, and the least common multiple is found by large number doubling or short division. (See page 3 1 in the textbook for details.)
Numbers and information
1, China's current postal code is "four levels and six yards". The first and second representatives are provinces (autonomous regions and municipalities directly under the Central Government), the third represents postal districts, the fourth represents county (city) post offices, and the last two are delivery bureau (district) numbers.
2. ID card coding rules: 1-6 digits are administrative division codes, of which 1 and 2 digits are provincial government codes, 3 and 4 digits are prefecture-level government codes, and 5 and 6 digits are county-level government codes. 7- 14 digit is your date of birth, where 7- 10 digit is the year of birth (4 digits),1-12 digit is the month of birth, 13- 14. 18 is the check code, which is calculated by the numbering unit according to the unified formula, and the value range is 0- 10. When the value is equal to 10, it is represented by the Roman numeral symbol χ.