Hebei Education Edition Seventh Grade Mathematics Volume 1

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"Positive and Negative Numbers" PPT courseware

Self-introduction: My name is Liu Qing, I am 1.6cm tall, 30 years old, and weigh 51.5kg.

The boys in our class have….

Which numbers appeared in the introduction just now? Can you classify them according to the number classification methods you have learned before?

Whole numbers and fractions

Are there other numbers besides this in life?

In life, production, and scientific research, we often encounter problems with number representation and number operations. For example,

1. The weather forecast shows that the temperature in Beijing on a certain day in November 2003 is -3~3. C, what exactly does it mean? What is the temperature difference in Beijing on this day?

The highest temperature today is 3 degrees above zero. C, the lowest temperature is minus 3. C, the temperature difference is 6. C.

2. In a football match involving three teams, the red team beats the yellow team (4:1), the yellow team beats the blue team (1:0), and the blue team beats the red team (1:0). How to determine the scores of the three teams? Goal difference and ranking order?

Goal difference and ranking order: When two teams compete, the team with higher points will be ranked first; both teams have the same points, and the team with more goal difference will be ranked first; both teams have the same points and goal difference; the team with more goals will be ranked first. ranked first;

A new number appears here:

-3 means minus 3 degrees Celsius,

-2 means a net loss of 2 goals,

-0.5 means 0.5mm smaller than the design size

and

3 means 3 degrees Celsius above zero,

2 means a 2 goal difference,

+0.5 means 0.5mm larger than the design size

Numbers like -3, -2, -0.5, ... (that is, numbers other than 0 that we have learned before are preceded by a negative sign "-" are called negative numbers.

The numbers other than "0" that we learned in elementary school are all called positive numbers.

example

(1) Within one month, Xiao Ming’s weight increased by 2 kg, Xiao Hua’s weight decreased by 1 kg, and Xiao Qiang’s weight remained unchanged. Write down their weight gain values ​​this month;

(2) The changes in the total import and export volume of goods in the following countries in 2001 compared with the previous year are:

The United States decreased by 6.4%, and Germany increased by 1.3%.

France decreased by 2.4%, and the United Kingdom decreased by 3.5%.

Italy grew by 0.2% and China by 7.5%.

Write the growth rate of the total merchandise imports and exports of these countries in 2001.

Solution: (1) This month, Xiao Ming’s weight has increased by 2kg, Xiaohua’s weight has increased by -1kg, and Xiaoqiang’s weight has increased by 0kg.

(2) Growth rate of total merchandise exports of six countries in 2001:

United States -6.4%, Germany 1.3%,

France -2.4%, UK -3.5%,

Italy 0.2% and China 7.5%.

Class exercises

1. (1) If 5°C above zero is recorded as +5°C, then what is recorded as -3°C below zero?

(2) East and west are two opposite directions. If -4 meters means an object moves 4 meters westward, what does +2 meters mean? What do you remember when an object stays put?

(3) 7.5 tons of flour shipped into a warehouse is recorded as +7.5 tons, so what should be recorded as 3.8 tons shipped out?

Summary: (1) Positive numbers and negative numbers represent quantities with opposite meanings;

(2) Zero is neither a positive number nor a negative number.

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Update Time: 2024-10-02

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