Rule number one: exactly equal to 0.
1999 subtract 253, add 244, then subtract 253 and add 244. ......................................................................................................................................
Answer: 195 times
Analysis: This topic seems simple, because a period is reduced by 9, and some students think that only 1999 can be divisible by 9 how many times. In fact, there is a hidden problem: if the number 1999 is at a certain point, that is, in the process of subtracting 253 and adding 244, there may be only 253 left, which is equal to 0 after subtracting 253. Let's try to see if the mentioned situation will happen.
1999-253= 1746
1746/(253-244)= 194
194+ 1= 195
As we guessed.
Detailed explanation: 1999-253= 1746.
1746/(253-244) =194 times
But the final subtraction is also an operation: 194+ 1= 195 times.
Comments: The result is as stated in the analysis, and 194+ 1 stands for the previous reduction of 253. For necessity, it is more convenient for us to subtract 253 first than to subtract 253 later.
Part II: Calculation.
(1) In the addition formula, if one addend increases by 50 and the other addend decreases by 20, how much does the sum increase or decrease?
Answer: Increase by 30.
Analysis: This question is not very difficult, but beginners will find it lacking in conditions. In fact, this has nothing to do with the values of the two addends and with itself. Because only the "increase and decrease of sum" is calculated.
If we use "a" instead of one addend, b stands for another addend, and (A+B) stands for sum.
(A+50)+(B-20)
=(A+B)+30
Comment: Some conditions of some topics are not what we need to know. It is a skill that we must learn to express these unknowns with letters or symbols.
(2) In the addition formula, if the minuend increases by 50 and the difference decreases by 20, how will the minuend change?
Answer: Increase by 70.
Analysis: Same as above. In fact, the change of meiosis has nothing to do with the value of meiosis, the sum of meiosis and the difference itself.
We use "a" to represent the minuend, b to represent the minuend, and (A-B) to represent the difference.
Subtraction = minuend-difference
=(A+50)-(A-B)-20]
=B+70
Comments: The method of using letters to represent numbers here is very appropriate. Some unknowns that don't need to be known will be cancelled during the operation, which will bring convenience to the calculation.
Chapter 3: Page number problem.
There is a 50-page book. Add up the page numbers of each page of this book, and add the page numbers of a piece of paper wrongly again, and the total is 1300. What is the extra page number in the middle?
Answer and analysis: From page 1 to page 50, the sum of page numbers is1+2+3+4+…+49+50 =1275, so the extra pages are1300-1275.
Chapter 4: Two buckets
Two buckets can hold 50 kilograms of water. If you pour the water in the first bucket into the second bucket, there is as much water in the two buckets. How many kilograms of water was originally contained in the first bucket? How many kilograms of water was originally filled in the second bucket?
Instruction: According to the known condition that "if the water in the first bucket is poured into the second bucket of 6kg, the water in the two buckets is the same", it can be judged that the weight difference of the first bucket is 6*2= 12 (kg). When two buckets are filled with 50kg of water, the weight of water in the small bucket is (50- 12)\2= 19 (kg), and that in the large bucket is 19+ 12=3 1 (kg).
Solution 1: weight of water in small bucket: (50-6*2)\2= 19 (kg)
The weight of water in the big bucket: 19+ 12=3 1 (kg)
Answer: The first barrel was originally 3 1kg water, and the second barrel was originally 19kg water.
Chapter V: Interest Groups
Students actively participate in the school's interest groups in art, calligraphy and model airplanes. Among them, there are 86 people in the art calligraphy group, 80 people in the art model group and 90 people in the calligraphy model group. How many people are there in the art, calligraphy and model airplane groups?
Note: According to 86 people in the art calligraphy group and 80 people in the art model group, we can know that their total includes the total number of two art groups, one calligraphy group and one model group. If you subtract the sum of the number of people in the calligraphy group and the model group, you can get twice the number of people in the art group.
Q: How many people are there in the art group?
(86+80-90)\2
=76\2
=38 (person)
How many people are there in the calligraphy group: 86-38=48 (people)
How many people are there in the model airplane team: 90-48=42 (people)
A: There are 38 people in the art group, 48 in the calligraphy group and 42 in the model airplane group.