1. Divide the unit "1" into several parts on average, and the number representing such a part or several points is called a fraction.

2. Divide the unit "1" into several parts, indicating the number of these parts, which means decimal unit. A score consists of several fractional units.

3. Scoring rate: divide the unit "1" into several shares on average, and find the scores of other quantities in the total shares.

Single quantity: total quantity ÷ quantity = single quantity (expressed in fractions)

(The denominator of a single quantity and score is the total number of average scores)

4. The relationship between fraction and divisor:

Frequency divider/frequency divider = frequency divider/frequency divider A/B = A/B (b ≠ 0)

5. Unit conversion: When changing the name of a low-level unit to the name of a high-level unit, if the number on the low-level unit is not divisible by the advancing rate, the quotient can be expressed by a fraction. (Result discount points)

6. Score comparison:

Two numbers with the same denominator, the number with the larger numerator is larger.

Two numbers with the same numerator, the number with the smaller denominator is larger.

7. Fractions with numerator less than denominator are called true fractions. Features: True score is less than 1.

Fractions with numerator greater than or equal to denominator are called false fractions. Features: False score is greater than 1 or equal to 1.

8. Method of turning a false score into an integer or a fraction: turn a false score into an integer or a fraction, and divide the numerator by the denominator. If it is divisible, the quotient is an integer. The numerator is divided by the denominator, the integer that cannot be divided is the quotient, the remainder is the numerator, and the denominator remains the same.

The method of changing a fraction into a false fraction: integer multiplied by denominator, numerator as denominator, denominator unchanged.

9. The basic nature of the score:

1. Both the numerator and denominator of the fraction are multiplied or divided by the same number (except 0), and the size of the fraction remains the same.

2. The denominator of the fraction remains the same, and the molecular magnification is several times, so is the size of the fraction. If the numerator remains the same, the denominator is enlarged several times, but the fraction is reduced by the same multiple.

10. Meaning of common factor and greatest common factor: The common factor of several numbers is called the common factor of these numbers. The greatest common factor of several numbers is called the greatest common factor of these numbers.

1 1. The meaning of reduction: to change a fraction into a fraction equal to it, but the numerator and denominator are relatively small, which is called reduction.

12. simplest fraction: The numerator and denominator have only one common factor 1, which is called simplest fraction.

13. prime factor decomposition: each composite number can be obtained by multiplying several prime numbers.

14. Prime number: Only two numbers with a factor of 1 are called prime numbers.

15. When two numbers are multiples, their greatest common factor is smaller and their smallest common multiple is larger.

16. When two numbers are coprime, their greatest common factor is 1, and their least common multiple is their product.

17. Common multiple and minimum common multiple: the multiple shared by several numbers is called the common multiple of these numbers. The least common multiple of several numbers is called the least common multiple of these numbers.

18. The meaning of the total score: it is called the total score when the scores of different denominators are replaced by the scores of the same denominator.

19. Decimal method: Decimal method. There are some small trees. Just write a few zeros after 1 as the denominator and remove the decimal point of the original decimal as the numerator. After dividing them into components, you can lower the discount points.

20. Decimalization method of decimals: Decimalization requires numerator-denominator, and several decimal places can be reserved according to rounding.

2 1. Method for judging whether a simplest fraction can be converted into a finite decimal: If the denominator contains no other prime factors except 2 and 5, the simplest fraction can be converted into a finite decimal.

22, commonly used fractions and decimals (Cai Ying 9 1 page)