static/uploads/YC/2022 1 1 18/3 DAA ABC 9 1449 Fe 272 c 457 abca ad 756839 . png " width = " 484 " height = " 300 "/>
Xiao Shengchu's Math Exercises and Answers Analysis
1. Write 2005 natural numbers from 1 to 2005, and get a multi-digit 123456789...2005. What is the remainder of this multi-digit divided by 9?
Solution:
Firstly, the characteristics of numbers divisible by 9 are studied: if the sum of numbers on each digit can be divisible by 9, then this number can also be divisible by 9; If the sum of each number is not divisible by 9, then the remainder is the remainder obtained by dividing this number by 9.
Problem solving:1+2+3+4+5+6+7+8+9 = 45; 45 is divisible by 9.
And so on: the sum of digits in the number 1~ 1999 can be divisible by 9. The decimal digits of these numbers are 10~ 19, 20 ~ 29...90 ~ 99 all appear 10 times, so the sum of the decimal digits is 65449.
Similarly, the sum of hundreds of digits from 100 to 900 is 4500, which can also be divisible by 9.
That is to say, the sum of the digits of each of these continuous natural numbers (1~999) can be divisible by 9;
Similarly, the sum of hundreds, tens and single digits of these continuous natural numbers (1000~ 1999) can be divisible by 9 ("1" in thousands is not considered here, and we are short of 2000200 1200320042005).
The sum of a * * * 999 "1"from 1000 to 1999 is 999, which can also be divisible;
The sum of digits of 200020012002200320042005 is 27, which is exactly divisible.
The final answer is that the remainder is 0.
2.a and B are two nonzero different natural numbers less than 100. Find the value of A-B in a+b ...
Solution:
(A-B)/(A+B)=(A+B-2B)/(A+B)= 1-2 _ _ B/(A+B)
The previous 1 will not change, only the minimum value at the back is needed, and at this time, (A-B)/(A+B).
When B/(A+B) is the minimum, (A+B)/B is the minimum.
The problem is transformed into finding the value of (a+b)/b.
(A+B)/B= 1+A/B, and the possibility is A/B=99/ 1.
(A+B)/B= 100
The value of (A-B)/(A+B) is 98/ 100.
3. It is known that A.B.C are all non-zero natural numbers, and the approximate value of A/2+B/4+C/ 16 is 6.4, so what is its accurate value?
The answer is 6.375 or 6.4375.
Because a/2+b/4+c/16 = 8a+4b+c/16 ≈ 6.4,
So 8A+4B+C≈ 102.4, because a, b and c are non-zero natural numbers, and 8A+4B+C is an integer, which may be 102 or 103.
When it is 102, 102/ 16=6.375.
When it is 103, 103/ 16=6.4375.
4. The sum of three digits is 17. Ten digits are greater than one digit 1. If the hundred digits of this three-digit number are switched with the single digits to get a new three-digit number, the new three-digit number is larger than the original three-digit number 198. Find the original number.
The answer is 476.
Solution: If the original digit is a, then the decimal digit is a+ 1 and the hundredth digit is 16-2a.
According to the equation100a+10a+16-2a-100 (16-2a)-10a-a =198.
If a=6, then a+ 1=7 16-2a=4.
A: The original number was 476.
5. Write 3 in front of a two-digit number, and the three-digit number is 7 times the original two-digit number by 24. Find the original two digits.
The answer is 24.
Solution: let two digits be a, then three digits are 300+a.
7a+24=300+a
a=24
A: The two-digit number is 24.
6. After exchanging a two-digit unit with a ten-digit number, a new number is obtained. When it is added to the original number, the sum is exactly the square of the natural number. What's the total?
The answer is 12 1.
Solution: Let the original two digits be 10a+b, then the new two digits are10B+A.
Their sum is10a+b+10b+a =11(a+b).
Because this sum is a square number, it can be determined that a+b= 1 1.
So this sum is1/kloc-0 /×11=121.
A: Their total is 12 1.
7. The last digit of six figures is 2. If you move 2 to the first place, the original number is three times the new number. Find the original number.
The answer is 857 14.
Solution: Let the original six digits be abcde2 and the new six digits be 2abcde (you can't put a horizontal line on the letters, please treat the whole as six digits).
Let abcde (five digits) be x, then the original six digits are 10x+2, and the new six digits are 200000+x.
According to the meaning of the question, (200000+x)×3= 10x+2.
The solution is x=857 14.
So the original number is 857 142.
Answer: The original number was 857 142.
8. There is a four-digit number, the sum of single digits and hundredths is 12, and the sum of tens and thousands is 9. If one digit is exchanged with a hundred digits, and thousand digits are exchanged with ten digits, the new number will increase by 2376. Find the original number.
The answer is 3963.
Solution: If the original four digits are abcd, the new digits are cdab, d+b= 12, and a+c=9.
According to "the new number is 2376 more than the original number", it can be known that abcd+2376=cdab, and the vertical column is convenient for observation.
Speed up the receiving and delivery system
2376
cdab
According to d+b= 12, we can know that d and b may be 3 and 9; 4、8; 5、7; 6、6。
Looking at the unit of vertical position again, we can know that only when d=3 and b=9; Or d=8 and b=4.
Take d=3, b=9, and substitute it into the vertical hundreds, and you can determine that the tenth digit has carry.
According to a+c=9, we can know that A and C may be 1 and 8; 2、7; 3、6; 4、5。
Looking at the ten digits in the vertical form again, we can see that it only holds when c=6 and a=3.
Then substitute the vertical thousand, and it will be established.
Get: abcd=3963
Then take d=8 and b=4 and substitute them into the vertical decimal places, so we can't find a number suitable for the vertical decimal places, so it doesn't hold.
9. There is a two-digit number. If you divide it by one digit, the quotient is 9 and the remainder is 6. If you divide two digits by the sum of one digit and ten digits, the quotient is 5 and the remainder is 3. Find this two-digit number.
Solution: Let this two-digit number be ab.
10a+b=9b+6
10a+b=5(a+b)+3
The simplified result is the same: 5a+4b=3.
Because a and b are both one-digit integers,
Get a=3 or 7 and b=3 or 8.
The original number was 33 or 78.
10. If it is10,21in the morning, what time is it after 28799 ... 99 (a * * * has 20 9s)?
The answer is 10: 20.
Solution:
(28799 ... 9 (20 9s)+1)/60/24 is divisible, that is to say, just after an integer day, the time is still 10: 2 1, because the previous calculation added1minute, so now.
Junior high school mathematics required test type
1, approximate value, where "10,000" and "100,000,000" are rewritten as units or the mantissa or "rounding" after "10,000,000" is omitted and the composition of numbers.
2. Median, mode or average
3. Factor multiples (focus on prime number, composite number, even number, odd number, prime number, greatest common factor and least common multiple)
4, quantity and measurement
5. Exchange of fractions, decimals, percentages and ratios.
6. Scale
The chicken and the rabbit are in the same cage.
8. pigeon nest principle
9. Calculate the relationship between the current price and the original price (focusing on the discount)
10, find each copy and score it.
Answering methods of mathematics problems in Xiaoshengchu
1, operational skills survey
2. Geometric intuitive observation
3. Investigation on reasoning and deductive ability
Induction of key knowledge points in primary school mathematics
(1) Write down three digits for the addition of two digits.
1, aligned with the same number;
2. Starting from the unit;
3. When the number of digits reaches 10, enter 1 into ten digits.
(2) Do a two-digit subtraction with a pen, and remember three things.
1, aligned with the same number;
2. Reduce from one place;
3. If the number of digits is not enough, subtract 1 from the number of digits, add 10 to the number of digits and then subtract.
(3) Calculation rules of mixed operation
1, in the formula without brackets, only addition and subtraction or multiplication and division can be performed from left to right;
2. In the formula without brackets, if there are multiplication and division and addition and subtraction, the multiplication and division should be calculated first, and then the addition and subtraction should be calculated;
3. If there are brackets in the formula, count the brackets first.
(D) four-digit reading method
1, read in order from the high order, thousands, hundreds, and so on;
2. There is a zero or two zeros in the middle, and only one "zero" is read;
No matter how many zeros there are, don't read the last number.
(5) Four-digit writing
1, written in order from the high order;
2. Write a few words in thousands, a few words in hundreds, and so on. Write "0" in the middle or at the end.
(6) Four-digit subtraction should also pay attention to three items.
1, aligned with the same number;
2. Reduce from one place;
3. Which figure is not enough to reduce? Retract 1 from the previous position, add 10 to the standard position, and then subtract.
(7) the law of one-digit multiplication by multi-digit multiplication
1, starting from the unit, multiply each digit in multiple digits by one digit in turn;
Whoever gets the highest score will be promoted several times.
(8) Divider is the division rule of single digits.
1. Divide the dividend by the first digit of the dividend every time starting from the high digit of the dividend. If it is less than the divisor, try the division of the first two digits again.
2. Write the quotient where the divisor is divided;
3. For each quotient, the remainder must be less than the divisor.
(9) The multiplication rule that a factor is a two-digit number.
1, first multiply the number on the two-digit number by another factor, and the last digit of the number is aligned with the two-digit number;
2. Multiply the number on the ten-digit number by another factor to get that the last digit of the number is aligned with the ten-digit number;
3. Then add up the multiplied numbers twice.
(10) The divisor is the division rule of two digits.
1. Starting from the high order of the dividend, try to divide the first two digits of the dividend by the divisor. If it is less than the divisor,
2. Write the business on any one except the bonus;
3. For each quotient, the remainder must be less than the divisor.
(eleven) the reading rules of ten thousand books.
1, read ten thousand levels first, and then read one level;
2, 10,000-level numbers should be read according to the ten-level reading method, and then add a word "10,000" at the back;
3. Don't read the last digit of each level, no matter how many zeros there are. Other numbers have a read-only "zero" with one zero or several consecutive zeros.
(12) Multi-digit reading rules
1, starting from the high position and reading down one level at a time;
2. When reading 100 million or 10,000 levels, read according to a series of reading methods, and then add the words "100 million" or "10,000" at the back;
3. Don't read the zero at the end of each level, other numbers have a zero, or read only one zero for several consecutive zeros.
(XIII) Comparison of decimal dimensions
Compare the sizes of two decimals, first look at their integer parts. The number with large integer parts is large, so is the number with large integer parts, the number with large decimal places is large, the number with large decimal places is also large, and so on.
(14) decimal addition and subtraction operation rules
To calculate decimal addition and subtraction, first align the decimal point (that is, align the numbers on the same digit), then calculate by integer addition and subtraction, and finally align the decimal point position on the horizontal line and point the decimal point.
Calculation Rules of (15) Decimal Multiplication
To calculate decimal multiplication, first calculate the product according to the multiplication law, then look at the decimal places in the factor, count the decimal places from the right side of the product and point to the decimal point.
(16) divisor is the law of integer division.
Dividers are fractional divisions of integers. Divide according to the law of integer division. The decimal point of quotient should be aligned with the decimal point of dividend. If there is a remainder at the end of the dividend, add 0 to the remainder and continue the division.
(17) Division algorithm with divisor as decimal.
Divider is the division of decimals. First, move the divisor decimal point to make it an integer. The decimal point of the divisor is shifted to the right by several digits, and the decimal point of the dividend is also shifted to the right by several digits (the digits are not enough to make up the 0 at the end of the dividend), and then it is calculated by fractional division with the divisor as an integer.
(18) Steps to Solve Application Problems
1, find out the meaning of the problem, find out the known conditions and problems, analyze the quantitative relationship in the problem, and determine what to calculate first, then what to calculate, and finally what to calculate;
2. Determine how to calculate each step, list formulas and work out numbers;
3. Test and write the answers.
(nineteen) the general steps of solving application problems with column equations
1, find out the meaning of the problem, find out the unknown, and express it with x;
2. Find out the equal relationship between quantity and quantity in the application problem and make the equation;
3. Solve the equation;
4. Test and write the answers.
(20) Addition and subtraction of fractions with the same denominator
Add and subtract fractions with the denominator, the denominator remains the same, and only the numerator is added and subtracted.
What methods are there to improve primary school math scores?
First of all, listen to the teacher carefully.
This is the main reason for getting good grades. Listen attentively, follow the teacher's thinking, don't be distracted, and don't listen at the same time. Secondly, we should pay attention to every word the teacher says, because mathematics is famous for its rigor, and there are serious differences between words, and there are infinite mysteries hidden between words. Pay attention to taking notes when listening to the lecture. Please raise your hand to speak actively in class. Raise your hand to speak has many advantages: ① It can consolidate the knowledge learned in class. (2) Exercise your eloquence. Those vague ideas and mistakes can be taught by teachers. It's killing three birds with one stone. In short, listening should be done with hands, mouth, eyes, ears and heart.
Second, extracurricular exercises.
Confucius said, "Learn from time to time". Homework after class is also an important part of learning and consolidating mathematics. I pay great attention to the accuracy and speed of solving problems. Accuracy means accuracy, concentrate on completing your homework independently, strive to be accurate once, and correct any mistakes in time. And speed is to exercise your concentration and sense of urgency. You can set an alarm clock at the beginning of your homework and put it out of sight, which will help improve the speed of your homework. I won't be nervous during the exam, and I won't lose sight of one thing.
Third, review and preview.
Math review can be arranged every night. After finishing my homework that day, I will briefly look at the new knowledge I will learn the next day, and then recall what the teacher said. When I sleep in bed, I will "watch" the teacher's class in my mind like watching a movie. If there is any problem, I can turn over the books until I understand them. Every Sunday, I will summarize, review and preview the week's homework. This is good for learning mathematics, and you won't forget it if you master it firmly.