My discovery
Students, have you made some casual discoveries in math study like me? Now I will introduce some of my findings.
If you want to calculate a multi-digit multiplied by 5, do you want to calculate it vertically? But I can do it with my mouth, because I found a little trick. Do you want to know? Let me tell you: calculate the product of 48532×5, first find this number 485320, and then divide it by 2. Can I take it orally? 242660 This is the product of 48532×5. Do you know why? I first expanded the original number by 10 times, and then reduced it by 2 times. Is it equivalent to expanding five times? Have you mastered this little trick?
I also found the same thing: multiplying a number by 1.5 only needs to add half to itself. (think about why? How about a number multiplied by 15? Use the method just now to add one more step-you have already thought of it, and then expand it by 10 times!
I also found a multi-digit, and the last two digits meet this requirement: ten digits are odd, and one digit is 5. Multiplied by 5, the last two digits of the product must be 75. I think why is this? Because the unit of multiple digits is multiplied by 5 to get 25, the unit of product is 5, which is the tenth power of 2, and the odd number of ten is multiplied by 5 to get 15. This 5 must be added with the 5 to be written on the ten, so the product must be the tenth power of 7 and the tenth power of 5. In the same way, it is not difficult for you to deduce that a multi-digit number is even in ten digits and 5 in one digit. It is multiplied by 5, and the last two digits of the product must be 25.
Can this discovery be explained by an ingenious algorithm of multiplying numbers by 5 that I mentioned earlier? Think about it, they are the same, because after this number is expanded by 10 times, the last two digits are 50, and then divided by 2, there may be a remainder of 1 in the hundreds, and when combined with 50, 150÷2=75 is the last two digits, or there may be no/kloc-0 in the hundreds.
Students, is my little discovery insignificant? But I am very proud, this is the result of my own observation and thinking. Aren't great discoveries made up of these bits and pieces? Students, let's be a diligent thinker and discoverer!
Understanding of zero
Zero looks monotonous, but it is not. In fact, it is very rich and hides a lot. Zero is special in mathematics. No matter what you do, you should consider zero.
"0" is often used as a symbol in geometry.
The uniqueness of "0" comes from some concepts or problems. For example, every rational number has a reciprocal, while "0" does not. Rational numbers are divided into positive numbers and negative numbers. "0", a number is divided into one category, isn't this special? In divisor, only zero cannot be divided. Zero is the dividend. No matter what number you divide (except "0"), you will get zero.
We often ignore zero, but it plays an important role. Like what's the problem? Some people can't think of "0". When counting, some people will forget zero. For example, how many integers are there that are not greater than 5 and not less than -5? Someone will have eight. Actually, there are still 0. For example, which numbers are not bigger in absolute value than themselves? That's positive numbers and zeros (also called non-negative numbers).
Zero is more colorful in life. At the parent-teacher conference after the semester, when the teacher showed the wrong textbook to parents, we all hoped that our boxes would be marked with "0", indicating that we had not made any mistakes, and our parents were happy and we were happy. But we don't want to see this number or an integer close to this number on paper, otherwise the day of going home will be sad. Nobody wants to get "0" in the competition.
Zero is money. I think zero is a trap in the problem, and everyone should consider zero when doing problems in the future. Zero can also change people's mood on different occasions. It's wonderful and rich.
Understanding of 0
0 is a wonderful number and an "old friend" that middle school students often meet. You have to satisfy all the calculations and concepts.
First of all, 0 means nothing, which can be called "desert" in numbers. 0 is also a strange number. In all units such as volume, area, weight, speed and distance, it doesn't mean time, a person's age, the starting point and the starting point of a game.
Among the natural numbers in the digital library of the mathematical kingdom, the number 0 is definitely the smallest. Without 0, there is no natural number, because 0 is the starting point of natural number.
In calculation, when 0 is multiplied by any number, including negative number, fraction and zero, the absolute value of 0 is also equal to 0. Among rational numbers, its absolute value is the smallest. When 0 is divided by any number, 0 plus a number still gets that number, for example: 0+ 1 = 1, 0+ 1. Subtract a number from 0 to get its reciprocal, for example: 0- 1=- 1, 0-87=-87.
On the number axis, 0 is the origin and boundary line. Why does 0 wonderfully separate positive numbers from negative numbers? Because 0 is neither positive nor negative, it is just an integer. When 0 and positive numbers are together, it is called non-negative, and when negative numbers are together, it is called non-positive. On the number axis, 0 provides great convenience for us to judge the size of positive and negative numbers. The right side is positive, the left side is negative, the number on the right side is always greater than the left side, which means that the positive number is greater than the negative number, and 0 is greater than the negative number, but less than the positive number.
In geometry, an angle of 0 degrees means a ray, which has no angle and no degree. 0 square meters means no area, and 0 meters long means no height. A weight of 0 kg means no mass, and a weight of 0 m3 means no volume.
In topography, 0 means sea level, above 0 means above sea level, below 0 means below sea level. Xinjiang in China has a basin with an altitude of155m, and Tibet in China has Mount Everest with an altitude of 8848m.
At noon today, in order to measure the size of chopsticks more accurately, I asked my father to take a slender measuring cylinder from the chemistry room. The scale unit is smaller, and each unit is only 1 cubic centimeter. At this point, I seem to feel victory beckoning to me. I really have everything except hands-on experiments.
First of all, I drew a dividing line on disposable chopsticks with a pencil, divided the chopsticks into two sections evenly, and soaked them in water to avoid washing them when measuring. Then, insert the chopsticks into the measuring cylinder, drop water into the measuring cylinder with a dropper, let the water in the measuring cylinder rise to the dividing line of the chopsticks, take the chopsticks out of the measuring cylinder after recording the water level scale (38 ml), and then record the water level scale (34.5 ml) in the measuring cylinder. The difference between the two water level gauges is the volume of this part of chopsticks, which is 3.5 cubic centimeters. In the same way, I measured the volume of the other part of the chopsticks to be 5 cubic centimeters. When the two measurements are added together, the volume of the chopsticks is 8.5 cubic centimeters. When I got the result, I cried excitedly. How proud and proud I am at this time!
Then, according to the situation that each person uses three pairs every day, I calculated the disposable chopsticks consumption of our school (1500 people) and the whole country (1200 million people) for one year, which are 13.96 cubic meters and169000 cubic meters respectively. The result surprised me. What a pity to waste so many wooden disposable chopsticks every year! I hereby appeal to the students at school, no! It is the people of the whole country, and it is not! Everyone in the world should stop using disposable chopsticks. Only in this way can we protect our forest resources, make our earth environment better and let everyone on the earth breathe clean and fresh air.