All the concepts of rational numbers in the first year of junior high school!! Please write it to me

1. Rational numbers can be divided into integers and fractions can also be divided into three types: one; positive, two; 0,three; Negative number. Real numbers other than infinite non-cyclic decimals are collectively referred to as rational numbers.

The different signs are added to take the sign with the larger absolute value, and subtract the smaller absolute value from the larger absolute value. (2) The law of subtraction of rational numbers: subtracting a number is equal to adding the opposite number of the number.

3) The rule of multiplication of rational numbers: multiply two numbers with the same sign to get a positive number, multiply two numbers with different signs to get a negative number, and multiply the absolute value. Multiplying any number by 0 gives 0

Several numbers that are not equal to 0 are multiplied, and the sign of the product is determined by the number of negative factors. When there is an odd number of negative factors, the product is negative; When the negative factor has an even number, the product is positive. and multiply their absolute values.

4) The rule of division of rational numbers: dividing by a number is equal to multiplying the reciprocal of this number. (Note:.)

0 has no reciprocal) divide the two numbers, with the same sign being positive and the different sign negative, and dividing the absolute value. 0 divided by any number that is not equal to 0 is equal to not being able to do a divisor under any conditions. (5) Rational number mixture operation rule:

Multiply first, then multiply and divide, and finally add and subtract, when there are parentheses, you must first count the parentheses.

If there is a negative sign in front of it, it must be the opposite number.

In fact, it stands to reason that a negative number is the opposite of the positive number to which it corresponds.

At this time, it is a negative number, generally speaking, it is a negative number with parentheses, and it is an opposite number without parentheses, you will know it when you encounter a power, but sometimes the parentheses will be omitted.

However, for example, (-50) is a negative number, but it is actually the opposite of 50, so generally opposite numbers and negative numbers are interchangeable.

1) In order to represent some quantities with opposite meanings, one meaning is defined as positive, and another quantity with the opposite meaning is specified as negative, and positive and negative numbers are generated

2) Positive and negative numbers are used to express quantities with opposite meanings, which are exactly what can be arbitrarily chosen, but it is customary to stipulate "forward, rising, income, above zero temperature" and so on as positive, and "backward, falling, expending, sub-zero temperature" and so on as negative

2 The concept of positive and negative numbers.

1) A number greater than 0 is called a positive number;

2) The number with the " " sign in front of the positive number is called a negative number, and the negative number is smaller than 0;

3) Zero is neither positive nor negative, zero represents the boundary between positive and negative numbers

3 Concepts of rational numbers.

1) Rational numbers: integers and fractions are collectively referred to as rational numbers;

2) Integers include positive integers, zeros, and negative integers;

3) Scores include both positive and negative scores

4) Classification of rational numbers:

Classification by the positive and negative of numbers:

Classified by the definition of rational numbers:

5) Positive numbers and 0s are usually referred to as non-negative numbers; Negative numbers and 0s are collectively referred to as non-positive numbers; Positive integers and 0s are called non-negative integers (also called natural numbers); Negative integers and 0s are collectively referred to as non-positive integers

4 The concept of the number line.

1) Definition: Draw a horizontal straight line, take a point on the straight line, indicate 0 (called the origin) and select a certain length as the unit length, and specify that the right direction on the straight line is the positive direction, and a number axis is obtained

The simple definition is: a straight line that specifies the origin, positive direction, and unit length is called the number axis

2) The number axis is a straight line, which can be extended infinitely to both sides; The origin, positive direction, and unit length are the three elements of the number axis, and all of them are indispensable; The selection of the "three elements" is based on actual needs

5 How to draw the number line.

1) Draw a straight line (generally horizontal) and mark a point as the origin 0

2) The direction from the origin to the right is positive, and the direction to the left is negative.

3) Select the appropriate length unit as the unit length.

6 The relationship between a point on a number line and a rational number.

Is it enough?

Rest assured, children will have multiple-choice questions at most if they have rational numbers, and they will not account for many points.

Rational numbers: Rational numbers are a collective term for integers and fractions, and all rational numbers can be converted into fractions.

Integer: (3) (4) (6) (8) (13).

Fractions: (1) (2) (5) (9) (10) (11) (12) Positive: (2) (3) (5) (8) (10) (12) [7) is positive but not rational].

Non-positive numbers: (1) (4) (6) (9) (11) (13) [(4) not rational numbers] Positive fractions: (2) (5) (10) (12).

Positive rational numbers: (2) (3) (5) (8) (10) (12) Non-negative numbers: (2) (3) (5) (8) (10) (12) (13) [7) is positive but not rational].

Natural numbers: (3) (8) (13).

Integer: (3) (4) (6) (8) (13).

Score: 1 2 5 9 10 11 12 Positive: 2 3 5 7 8 10 12 Non-positive:

1 4 6 9 11 13 4 Positive Score: 2 5 10 12

Positive rational numbers: 2 3 5 8 10 12 Non-negative numbers: 2 3 5 7 8 10 12 13 Natural numbers: 3 8 13

There is still controversy as to whether zero is a natural number, but it can be counted as a natural number for now.

The number is the serial number.

Integer: (3), (4), (6), (8), (13) Fractions: (1), (2), (5), (9), (10), (11), (12), (14).

Positive integers: (3), (8).

Non-positive numbers: (1), (4), (6), (9) (11) (14) Positive fractions: (2) (5) (10) (12).

Positive rational numbers: 2 3 5 8 10 12 Non-negative numbers: 2 3 5 7 8 10 12 13 Natural numbers: 3 8 13

It should be ......= -

Equal ratio of the book Wang number series sum, the common ratio q=1 Shenzi brother 2, a1=1 2.

sn=a1(1-q^n)/1-q

So the upstream attack is equal to 1-1 2 n

The content is combined with the original question, please read it carefully, hoping to understand the meaning. Zhu has a good time studying!!

The absolute value of a positive number is a positive number, the absolute value of a negative number is also a positive number, and 0 is the absolute value of 0, so why does it happen that when a is a positive number, the absolute value of a is a, and when a is a negative number, the absolute value of a is -a [the meaning of negative a]? Doesn't it mean that the absolute value of a negative number is positive?

a is the opposite of a.

Since a is a negative number, the opposite of a is a positive number (absolute value definition: the distance from a number to the origin is called the absolute value of this number).

If the absolute value of x is equal to 5, then x = plus or minus 5

A set of two numbers that are opposites of each other are equal distances from the origin).

If -x [negative x means] = 3

then x=-3-x is the opposite of x).

Knowing that the absolute value of a = 2, the absolute value of b = 3, and a is a negative number, find the values of a and b.

a|=2a=plus/minus 2

And because a is a negative number.

So a=-2

b|=3b=plus/minus 3

It is important to remember that removing the absolute value sign will result in a positive or negative (except for 0).

The second question is divided into 6 situations:

1、a>0,b>0,c>0。The answer is 1+1+1=3;

2、a>0,b>0,c<；

3、a>0,b<0,c<；

4、a<0,b<0,c<0.-1-1-1=-3；

5、a<0,b<0,c>0.-1-1+1=-1；

6、a<0,b>0,c>0.-1+1+1=1；

To sum up, the answer is 3,1,-1,3

The third question is analyzed as above, and the final answer is 1/2 (the second and fifth cases are appropriate).

1。The cube of a number is negative, and the square of this number is (positive).

2。An odd number with an absolute value greater than 1 and less than 5 and 1/2 is ).

3。The smallest positive integer divided by 32, 36, 48 and 15 is (303).

4。The product of a negative integer and -540 is a perfect square number, then the maximum negative integer that satisfies the condition is (15), and this perfect square number is (8100).

Two. Multiple choice questions

1.If the sum of two prime numbers is 49, then the opposite of the reciprocal sum of these two prime numbers is (b).

94 b. minus 49/94 49 d. 86/45

2.The reciprocal of a number is greater than minus 3 and smaller than 2, then this number (c).

a。larger than minus 1/3 and smaller than 1/2; b。More than 1/2 c. Larger than 1/2 and smaller than minus 3/1. does not exist.

3.An integer greater than negative and less than (a).

a。There are 8 numbers, and their sum is minus 4 b。There are 7 numbers, and their sum is minus 4 c。There are 7 numbers, and their sum is 0

c。There are 8 numbers, and their sum is 0

4.The sum of the absolute value equal to 2/3 of the number and the reciprocal of minus 7/2 is equal to (d).

a。minus 6/17 20 or minus 8/21 c. minus 6 days 25 days. 25/6 or minus 17/6

1.The square of any non-zero rational number is positive.

36 = 2 2 * 3 2, 48 = 2 4 * 3, the least common multiple is 2 5 * 3 2 = 288, 288 + 15 = 303

Therefore, the maximum negative integer that satisfies the condition is -3*5=-15, and the perfect square number is 8100

The inverse of the reciprocal sum is -(1 a+1 b)=-(a+b) ab, which can only be -49 94,b

Of course, you don't need to do this for this problem, because the prime numbers except 2 are all odd numbers, and one of the two prime numbers that add up to an odd number must be 2, so the other is 47

2.This one... It should be larger than 1/2 or smaller than minus 3, and it looks like it should be written in C loosely.

3.From -4 to 3, a, d