Why is the seventh grade math number not enough? Explain it carefully (no exercises, handouts). Help me explain this lesson.

Detailed explanation and synchronous practice of the typical example of "How many numbers are not enough"

When the seventh-grade students come into contact with rational numbers for the first time, they often can't master the relevant knowledge well. This paper analyzes several typical examples, hoping that students can gain something.

Example 1 (1) If the income 100 yuan is recorded as+100 yuan, then the expenditure 180 yuan is recorded as.

(2) If 15 degrees above zero is marked as+15℃, then minus 20 degrees is marked as.

(3) If the elevator goes up to two floors and is marked as +2, then -3 means the elevator.

Fine analysis: When using positive numbers and negative numbers to represent different quantities, it should be noted that quantities with opposite meanings should be represented by different properties. If a quantity is positive, the opposite quantity should be expressed as negative.

Answer: (1)- 180 yuan; ⑵ -20℃; (3) It dropped three floors.

Example 2, the following statement is true ()

Rational numbers are either positive or negative.

B. Rational numbers can be integers or fractions.

C rational numbers are integers, fractions, positive rational numbers, negative rational numbers and zero.

D. Rational numbers are natural numbers and negative numbers.

Specific analysis: At this time, we mainly investigate the understanding of the concept of rational numbers, that is, 0 is not positive or negative, A is wrong, C is wrong in classification, and D is not a natural number. All non-negative rational numbers are wrong.

Answer: choose B.

Example 3 Fill the following figures in the corresponding brackets:

-5,+ ,0.62,4,0,- 1. 1, ,-6.4,-7,-7 ,7。

(1) positive integer set: (…);

⑵ Negative integer set: (…);

(3) Score set: (…);

(4) Integer set: (…);

5] Set of negative rational numbers: (…);

Set of positive rational numbers: (…).

Answer:

(1) positive integer set: (4, 7 …);

⑵ Negative integer set: (-5,-7 …);

⑶ Scoring set: (+,0.62,-1. 1, -6.4,-7 …);

(4) Integer set: (-5, 4, 0, -7, 7 …);

5. Set of negative rational numbers: (-5,-1. 1, -6.4, -7,-7 …);

[6] Set of positive rational numbers: (+,0.62, 4, 7 …).

Synchronization exercise:

1. Use positive and negative numbers to represent quantities in the following questions.

(1) In the knowledge contest, adding 5 points is represented by +5, so deducting 3 points should be represented as

(2) If the loss 200 yuan is recorded as -200 yuan, then the profit 300 yuan should be recorded as

(3) In the quality spot check, if a ball exceeds the standard weight of 10g, it is marked as+10g, and then -5g indicates it.

2.( 1) A table tennis match was held in the first grade of a school. Class One won two games with a score of +2, Class Two lost three games and Class Three was unbeaten.

(2) If the 500 yuan of profit is recorded as +500 yuan, then -200 yuan said;

(3) If the clockwise rotation of 30 is marked as+30, then-45 means.

3, zero is ()

A, the smallest natural number b, the smallest integer

C, both positive and negative have D, negative

4. What is the practical significance of the following questions?

(1) The car went forward -30 meters;

(2) The difference between the reservoir water level and the normal water level is+40m;

(3) The temperature in a certain area is-5℃ on a certain day;

The altitude of a place is +400 meters.

Reference answer:

1, (1)-3 (2)+300 yuan (3) The actual weight of the ball is 5g less than the standard weight.