Mathematical manuscripts for traveling

1. Commutative law of addition: When two numbers are added, the positions of the addends are exchanged, and the sum remains unchanged. a+b=b+a

2. Associative law of addition: Three numbers To add, add the first two numbers first, or add the last two numbers first, and then add them to the third number. The sum remains unchanged. a+b+c=a+(b+c)

3. Commutative law of multiplication: When two numbers are multiplied, the positions of the factors are exchanged, and the product remains unchanged. A×B=B×A　

4. Associative law of multiplication: When three numbers are multiplied, Multiply the first two numbers first, or multiply the last two numbers first, and then multiply them by the third number. Their product remains unchanged. A×B×C=(A×B)×C　

5. The distributive law of multiplication: when two numbers are multiplied by the same number, you can multiply the two addends by the number respectively, and then add the two products, the result remains unchanged. For example: (2 +4)×5=2×5+4×5.

6. Properties of division: In division, the dividend and the divisor expand (or shrink) by the same multiple at the same time, and the quotient remains unchanged. Any number that is not 0 is 0.

7. Equality: The formula in which the value on the left side of the equal sign is equal to the value on the right side of the equal sign is called an equation. The basic properties of the equation: both sides of the equation If multiplied (or divided) by the same number at the same time, the equation still holds.

8. Equation: An equation containing unknown numbers is called an equation.

9. A linear equation of one variable: An equation that contains an unknown number and the degree of the unknown number is first degree is called a linear equation of one variable. N yuan - N unknown numbers; M degree - the highest power of the unknown number

10. Fraction: put the unit "1" A number that is equally divided into several parts and represents such a part or fractions is called a fraction. 11. Rules for addition, subtraction, multiplication and division of fractions:

To add and subtract fractions with the same denominator, only add and subtract the numerators. The denominator remains unchanged.

To add and subtract fractions with different denominators, first combine the fractions, then add and subtract.

The rule of multiplication of fractions: use the product of the numerator as the numerator, and use the product of the denominator as the numerator. The product is used as the denominator.

The rule of division of fractions: dividing by a number is equal to multiplying by the reciprocal of the number.

12. Comparison of fractions: Comparing fractions with the same denominator, the numerator The bigger one is bigger and the smaller numerator is smaller. When comparing fractions with different denominators, first divide them together and then compare them; if the numerators are the same, the one with the larger denominator will be smaller.

13. When multiplying a fraction by an integer, use the numerator of the fraction. The product multiplied by the integer is used as the numerator, and the denominator remains unchanged.

14. When multiplying fractions by fractions, the product multiplied by the numerators is used as the numerator, and the product multiplied by the denominators is used as the denominator.

15. A fraction divided by an integer (except 0) is equal to the fraction multiplied by the reciprocal of the integer.

16. Proper fraction: The fraction whose numerator is smaller than the denominator is called a proper fraction.

17 .Improper fractions: A fraction whose numerator is greater than its denominator or whose numerator and denominator are equal is called an improper fraction. An improper fraction is greater than or equal to 1.

18. Mixed numbers: Writing improper fractions in the form of integers and proper fractions is called Mixed numbers.

19. The basic properties of fractions: when the numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, the size of the fraction remains unchanged.

20 .Dividing a number by a fraction is equal to the number times the reciprocal of the fraction.

21. Dividing number A by number B (except 0) is equal to number A times the reciprocal of number B.