Division Quick Calculation Skills, Division Quick Calculation Skills

Multiplication and division to quickly calculate formulas.

1. A dozen times a dozen:

Formula: head by head, tail by tail, tail by tail.

Example: 12 14=?

Solution: 1 1=1

Note: Multiply the single digits, and use 0 to occupy the place if the two digits are not enough.

2. The head is the same, and the tail is complementary (the sum of the tails is equal to 10):

Formula: After adding 1 to a head, the head is multiplied by the head, and the tail is multiplied by the tail.

Example: 23 27=?

Solution: 2 1 3

Note: Multiply the single digits, and use 0 to occupy the place if the two digits are not enough.

3. The first multiplier is complementary, and the other multiplier number is the same:

Formula: After adding 1 to a head, the head is multiplied by the head, and the tail is multiplied by the tail.

Example: 37 44=?

Solution: 3+1=4

Note: Multiply the single digits, and use 0 to occupy the place if the two digits are not enough.

4. Dozens of one times dozens of one:

Formula: head by head, head by head, tail by tail.

Example: 21 41=?

Solution: 2 4=8

Multiply by any number: formula: the end does not move down, and the sum of the middle pulls down.

Example: 11 23125=?

Solution: 2+3=5

2 and 5 are at the beginning and end respectively.

Note: and full ten to one.

6. Multiply any number by a dozen times:

Example: 13 326=?

Solution: 13 digits are 3

Note: and full ten to one.

Even division can be calculated from left to right, but this method is often cumbersome to calculate. It's much easier to use "the nature of division" for questions like this one. Nature of Division:

A number is divided by several numbers consecutively, and this number can be divided by the product of all the divisors, and the quotient does not change. Represented by letters: a b c = a (b c).

In addition to the simplicity of calculating with the "nature of division", even division can also be the knowledge of reciprocal, that is, dividing by a number will also multiply the reciprocal of the number, and even division will become a continuous multiplication. The advantage of multiplication is that if the factors can be divided between them, they can be divided first and then calculated.

According to the above example problem, calculate this problem with the nature of division, and feel whether it is really simple.

Dividing becomes multiplication, dividing first, and then calculating. Suggestion: 25 4 = 100, 125 4 = 500, 125 8 = 1000 and so on, it is best to memorize it, so that it is convenient to use.

After changing the division to multiplication, the division will be divided first, and then calculated.

Try it with the nature of division and see which method you prefer.

Isn't it really easy to calculate the decimal division method with "the nature of division" in this question, so let's try it.

1. The single digit is "1".

Quick calculation formula: head multiply head, head plus head, tail is 1 (head plus head if more than 10 to carry).

2. The ten-digit number is "hall 1.""。

Quick calculation formula: the head is 1, the tail is added to the tail, and the tail is multiplied by the tail (more than 10 to be carried).

3. The single digit stool is "9".

Quick calculation formula: add 1 to each head, multiply and multiply by 10, subtract the additive, and then put 1.

4. Ten digits are both"9”。

5. The head is the same, and the tail is complementary (the mantissa adds up to 10).

Quick calculation formula: the head multiplies "head plus 1", and the tail multiplies the tail by 2 digits.

6. Complementary, the tail is the same.

Quick calculation formula: the head is multiplied by the head, and the tail is multiplied by the tail to account for 2 places.

7. Multiply the number of complementary numbers.

Quick calculation formula Zaoyan: the head plus 1 and then multiply the head, and the tail multiplies the tail to occupy 2 places.

8. One of them is 11.

Quick calculation formula: don't move from beginning to end, add and put in the middle.

The calculation tips for division are as follows:1. Decimal digits:

Where the dividend contains a multiple of the divisor, the method is as follows:

1. The dividend contains 1 times the quotient: the complement is added once from the base.

2. The difference between the dividend and the quotient is 2 times: the complement is added twice from the base.

3. The dividend contains 3 times the quotient: add the complement three times from the base.

Second, the middle array:

Where the dividend contains a multiple of the divisor, the method is as follows:

1. The dividend contains 4 times the quotient: half of the complement is added to the previous position, and the complement is subtracted once from the standard.

2. The dividend contains 5 times the quotient: half of the previous number is added to the complement, and the standard does not move.

3. The dividend contains 6 times of the quotient macro skin: half of the complement is added to the front position, and the complement is added once to the standard.

3. Large arrays:

Where the dividend contains a multiple of the divisor, the method is as follows:

1. The dividend contains 9 times the quotient: the first place is added once, and the base is subtracted once.

2. The dividend contains 8 times the quotient: the first digit is added once, and the base digit is subtracted twice.

3. The dividend contains 7 times the quotient: the first position is added once, and the base is subtracted by the chain complement three times.

Expand your knowledge: 1. Algorithm of division:

Knowing the product of two factors and one of the factors, the operation of finding the other factor is called division. The division of two numbers is also called the ratio of two numbers. If ab=c(b≠0), the operation of finding another factor a using the product c and the factor b is division, written as c b, which is read as c divided by b (or b divided by c).

Second, the law of division:

1. The divisor is a few digits, first look at the first few digits of the dividend, the first few are not enough to divide, look at one more, divide to which digit, the quotient is written on which digit, not enough quotient one, 0 occupancy. The remainder is smaller than the divisor, and if the quotient is a decimal, the decimal point of the quotient should be aligned with the decimal point of the dividend; If the divisor is a decimal, it is calculated by dividing the divisor as an integer.

2. Quotient invariant property: the dividend and the divisor are multiplied or divided by a non-zero natural number at the same time, and the quotient is invariant.

Multi-digit division quick calculation skills: The purpose of division is to find the quotient, but fromDividendWhen you suddenly can't see how much quotient it contains, you can use the method of trying the quotient and estimating the quotient to see how many divisors the highest digits of the multiplier contain (that is, how many times the quotient is contained), and then add the number to the base several times, and the number obtained is the quotient.

1.Decimals:

1 times: add the complement once from the base.

The dividend contains quotient by 2 times: add the complement twice from the base.

3 times: add three times from the base.

Example: 7995 65 = 123, (the complement of 65 is 35).

Arithmetic sequence: The first two digits of the dividend, 79, contain 65 times the divisor, and add the complement once (35) to get 1-1495 (dash.

The front is the quotient, and the dash is followed by the divisor of the Lee, the same below);

The multiplier 149 contains two times the divisor, and the complement is added twice (35*2=70) to obtain 12-195;

The dividend of 195 contains three times the divisor, and the complement is added three times (35*3=105) to obtain 123 (quotient).

2.Medium array: Whenever the divisor contains a multiple of the divisor, the method is:

4 times: half of the complement is added to the previous position, and the complement is subtracted once by the base.

The dividend contains 5 times the quotient: the previous digit is added to the complement by half, and the base does not move.

6 times: half of the complement is added to the front position, and the complement is added once at the base.

The multi-digit number is divided by the multi-digit number, which should be calculated vertically, and the dividend is written in the inside of the vertical division sign, and the divisor is written on the left side of the vertical bend.

First look at the divisor there are a few digits, just look at the first few digits of the dividend is greater than the divisor or smaller, if it is smaller than the divisor, you have to look at one more place to the right, try the quotient to write on this digit if the quotient is successful, and then multiply it with the quotient and the divisor, remember to multiply from the unit digit of the divisor, the unit digit of the product obtained and the digits of the dividend are on the same as the quotient, and then subtract and write the difference which Hui potato is written below the corresponding digit, and then move the next digit of the dividend down and then divide, which digit is not enough quotient to write zero in the position of this quotient.

until it is divided to the unit of the dividend, if divisible.

It is the quotient of the income, if there is a remainder.

Just after the quotient, dot six dots and write the remainder.

If the number in the same digit of the dividend and the divisor is larger, the quotient is written directly on the corresponding digit of the dividend. The following is divided by the same method as above. Remember to write the quotient after the division horizontal formula at the end.

The quick calculation tips for multi-digit division are as follows:

1. The division rule of integers.

1. Start from the quotient of the dividend, first see how many digits there are in the divisor, and then use the divisor to try to divide the first few digits of the dividend, if it is smaller than the divisor, try to divide one more digit; 2. Divide to which digit of the dividend, write the quotient on that one; 3. The remaining number after each division must be smaller than the divisor.

Second, the divisor is the decimal division rule of an integer:

1. According to the law of integer division, the decimal point of the quotient should be aligned with the decimal point of the dividend; 2. If there is still a remainder at the end of the dividend, add zero after the remainder, and then continue to divide.

3. The divisor is the decimal division of the decimal number of the law of the hole:

1. First look at how many decimal places there are in the divisor, move the decimal point of the dividend to the right by a few places, and make up for the insufficient digits with zero; 2. Then divide according to the decimal division where the divisor is an integer.

4. The division of fractions:

1. Multiply the numerator of the dividend by the denominator of the divisor as the numerator; 2. Multiply the denominator of the dividend by the numerator of the divisor as the denominator.

Supplement: division rule: the divisor is a few digits, first look at the first few digits of the dividend, the first few are not enough to divide, look at one more, divide to which digit, the quotient is written on which digit, not enough quotient one, 0 occupancy.

The remainder is smaller than the divisor, and if the quotient is a decimal, the decimal point of the quotient should be aligned with the decimal point of the dividend; If the quotient is a decimal, it is calculated by dividing the divisor as an integer. After secondary school, the division sign is usually omitted as a score line.

Subtraction quick calculation techniques include borrowing method, complement method, decomposition method, and reverse order subtraction.

1. Borrowing method to search for grandchildren: borrow the single digit of the subtracted number to the tenth digit, and then subtract the corresponding number from the subtracted number. (as shown in the image below).

2. Complement method: make up the subtraction into an easy-to-calculate number, such as using 10 to complement the number, that is, add a number to the subtracted number to make it become and so on, and then subtract the subtraction from it. (as shown in the image below).

3. Decomposition method: decompose the subtraction into smaller numbers for calculation, for example, when subtracting a number, split it into two numbers and subtract the sail chain. (as shown in the image below).

4. Reverse subtraction: reverse the order of the subtraction and the subtraction, and then use addition to calculate the difference between them. (as shown in the image below).

The Importance of Mathematics in Primary Schools:

1. Develop logical thinking ability: Mathematics is a discipline that trains logical thinking, and primary school mathematics education can help children cultivate logical thinking ability and improve their ability to analyze and solve problems.

2. Improve mathematical literacy: Primary mathematics education is very important for improving children's mathematical literacy, which can help children master basic mathematical knowledge, skills and thinking methods, and lay a solid foundation for more in-depth learning in the future.

3. Cultivating practical ability: Primary school mathematics education also involves a lot of calculation and application problems related to daily life, which helps children develop practical skills in real life, such as calculation ability, measurement ability and problem-solving ability.

Subtraction quick calculation techniques include borrowing method, complement method, decomposition method, and reverse order subtraction.

1. Borrowing method.

Borrowing method: borrow the unit digit of the minus number to the ten digit, and then subtract the corresponding number from the trillion belt socks in the subtracted number.

The premise of the borrowing method is that it does not need to be subtracted within 20 without the help of formulas. Therefore, like 14-9, it is necessary to know that the way of things is equal to 5 without the help of a formula.

2. Complement method.

Example: The complement of 3 is 7 because 3+7=10 (plus 7 is 10).

3. Decomposition method.

Decomposition method: Break down the subtraction into smaller numbers for calculation, for example, when subtracting a number, split it into two numbers and subtract them.

1. Mastering the decomposition within 10 is the basis for mastering skills.

2. Memorize the mantra.

For example, minus nine plus one; minus eight plus two; Subtract seven plus three, and so on.

4. Reverse subtraction.

Reverse the order of the subtracted and subtracted numbers, and then use addition to calculate their differences.

For example: 868-52-48=868(52+48).

Division Calculation Method].

In the division of integers, there are only two cases: divisible and indivisible. When it is not divisible, remainders are generated, so the remainder problem is very important in elementary school mathematics.

1) The absolute value of the difference between the remainder and the divisor should be less than the absolute value of the divisor (applicable to the field of real numbers);

2) Dividend = Divisor Quotient + Remainder;

divisor = (dividend - remainder) quotient;

quotient = (dividend - remainder) divisor;

Remainder = Dividend - Divisor Quotient.

3) If the remainder of a, b divided by c is the same, then the difference between a and b is divisible by c. For example, the remainder of 17 and 11 divided by 3 is 2, so 17-11 is divisible by 3.

4) The remainder of the sum of A and B divided by C (except in the absence of a remainder of the two numbers A and B divided by the skewer C) is equal to the sum of the remainders of A and B divided by C respectively (or the remainder of this sum divided by C). For example, the remainders of 23,16 divided by 5 are 3 and 1, respectively, so the remainder of (23+16) divided by 5 is equal to. Note:

When the sum of the remainders is greater than the divisor, the remainder is equal to the sum of the remainders divided by the remainder of c. For example, the remainders of 23,19 divided by 5 are 3 and 4, respectively, so the remainder of (23+19) divided by 5 is equal to the remainder of (3+4) divided by 5.

5) The product of a and b divided by the remainder of c is equal to the product of a, b divided by the remainder of c (or the remainder of this product divided by c). For example, the remainders of 23,16 divided by 5 are 3 and 1, respectively, so the remainder of (23+16) divided by 5 is equal to. Note:

When the product of the remainder is greater than the divisor, the remainder is equal to the product of the remainder divided by the remainder of c. For example, the remainders of 23,19 divided by 5 are 3 and 4, respectively, so the remainder of (23 19) hand not divided by 5 is equal to the remainder of (3 4) divided by 5.

Properties (4) and (5) can be generalized to the case of multiple natural numbers.