What is the law of change between the dividend, divisor, quotient, and remainder?

Because of the dividend.

Divisor = quotient + remainder.

So when the dividend and the divisor are expanded by the same multiple at the same time, the quotient does not change, and the remainder expands by the same multiple as the divisor and the dividend.

Extended information: Dividend, a mathematical term, is a number that is divided by another number in a division operation, such as 24 8 = 3, where 24 is the dividend, and the formula is the dividend divisor = quotient ......Remainder.

Related algorithms.

1.Dividend Divisor = Quotient (......Remainder.

2.(Dividend - Remainder) Quotient = Divisor;

3.divisor quotient + remainder = dividend;

4.Quotient = (Dividend - Remainder) Divisor.

The law of the quotient with the dividend and the divisor.

1.The quotient of the dividend and the divisor multiplied or divided by a non-zero number at the same time does not change;

2.The dividend is enlarged (or reduced) several times, and the divisor remains unchanged, and the quotient expands (or decreases) several times;

3.The dividend remains unchanged, the divisor expands (or shrinks) several times, and the quotient shrinks (or expands) several times;

4.If the dividend is enlarged by a fold and the divisor is reduced by a fold, the quotient is expanded by a b times.

In the division formula, the change law of the dividend, divisor, quotient and remainder is explained in detail.

The dividend and the divisor increase to ten times at the same time, the quotient remains unchanged, and the remainder becomes ten times the original.

The dividend and the divisor are expanded by the same multiple at the same time, the quotient remains unchanged, and the remainder is restored.

Divisor vs. Dividend.

The two zeros are removed, the quotient remains unchanged, and the remainder is remainder.

100 times smaller.

So 100 times the later remainder is equal to the original remainder.

So the remainder is reduced by 297, so the later remainder = 297 99 = 3 so the original remainder = 3 100 = 300

In the first volume of primary mathematics for the fourth grade, the divisor and the divisor are removed at the same time to find the remainder.

The divisor and the divisor remove two zeros at the same timeThe remainder should also be stripped of two zeros.

Explain the remainder, 99 less than the original.

3x100=300

It turns out that the remainder is 300

Calculation rules for integer multiplication:

1) Digit alignment, from the right, use the number on each of the second factor to multiply the first factor, multiply to which digit you want, and the end of the number will be aligned with which digit of the second factor.

2) Then add up the numbers that you have multiplied several times.

Multiply the number with 0 at the end of the integer: you can first multiply the numbers before 0, and then see how many zeros there are at the end of each factor, and add a few zeros to the end of the multiplied number).

If the divisor and the dividend are removed from two zeros at the same time, the divisor and the dividend are reduced by 100 times at the same time, so the remainder is also reduced by 100 times at the same time.

Therefore, the reduced remainder is 297 (100-1)=3, and the original remainder is 3 100=300

A number divided by 500, using the law of quotient invariance, the divisor and the dividend are removed from two zeros at the same time, and the remainder is reduced by 297, what is the original remainder?

Solution: a 500 = b......c

Using the law of invariant quotient, a 100 5 = b......(c-297), the remainder should also be stripped of two zeros, c 100 = c-297

c=300, so the original remainder is 300

1.Dividend.

At the same time as the divisor, expand (or shrink) several times (non-0 multiples, the same below), the quotient remains unchanged, and the remainder.

Expand (or shrink) by the same multiple with both the dividend and the divisor;

2.The dividend is enlarged (or reduced) several times, and the divisor remains unchanged, and the quotient expands (or decreases) several times;

3.If the dividend remains unchanged, the divisor expands (or shrinks) several times, and the old state business shrinks (or expands) several times;

4.If the dividend is enlarged by a fold and the divisor is reduced by a fold, the quotient is expanded by a b times.

a÷b=c ..d is (a-d) b=c rule.

a-d) (2b) = c is enlarged (or reduced) several times when it is divided by the same cherry blossom, the quotient remains unchanged, and the remainder contains the expansion (contraction) of several times.

a-d) b=2c is enlarged (or reduced) by several times, and the quotient and remainder are likewise enlarged or shrunk by several times.

3. (a-d) (2b) = In addition to expanding (or shrinking) several times, the quotient is also shrinking (or expanding) several times.

4. m(a-d) nb=(m n)c is the same as 2,

Dividend = Divisor Quotient + Remainder.

Dividend - Remainder = Divisor Quotient.

The dividend remains unchanged, the divisor expands to n times the original, and the quotient becomes the original 1 n.

The dividend remains unchanged, the divisor shrinks to 1 n, and the quotient becomes n times the original.

Literal expression for division: Dividend Divisor = quotient.

The dividend remains unchanged, the divisor expands to n times the original, and the literal expression: dividend (divisor n) = dividend divisor n = quotient n.

The dividend does not change, the divisor is reduced to the original 1 n, and the literal expression: dividend (divisor 1 n) = quotient n.

Definition. Two numbers a, b(b≠0), are known and require division by a number q, so that the product of q and b is equal to a, this operation is called division, denoted as a b=q or a b=q, read as a divided by b equals q, or a is equal to q than b, a is called the dividend, b is called the divisor, q is called the quotient of a and b, and the symbol " " or " "

Division can be defined as: the operation of knowing the product of two numbers and one of the factors, and finding the other factor. Therefore, division is also the inverse of multiplication, and division can also be seen as an algorithm that continuously subtracts the number of divisions from the dividend, and subtracts the number of times the number of divisions is calculated.

When the dividend is constant, the relationship between the divisor and the quotient is inversely proportional, and the larger the divisor, the smaller the quotient. The smaller the divisor, the greater the quotient.

The dividend is unchanged, and since the divisor is inversely proportional to the quotient, the greater the divisor, the smaller the quotient, and the smaller the divisor, the greater the quotient.

Method 1. Solution: From the meaning of the question, it can be seen that the quotient of the two zeros at the end of the dividend and the divisor at the same time remains unchanged, but the remainder is reduced by 100 times, that is, the original remainder = 100 new remainder.

Original remainder - new remainder = 100 new remainder - new remainder = 9999 new remainder = 99

New remainder = 1 original remainder = 100 1 = 100

Method two. Solution: Let the new remainder be x, and the original remainder = 100x100x-x = 99 from the meaning of the title

x = 1 original remainder = 100 1 = 100

The remainder becomes 99 (100 1) 1

A: The original remainder was 100.

Dividend. , divisor, quotient relationship change law formula is the dividend and the divisor multiplied at the same time or divided by the same number that is not 0, the quotient does not change. The dividend remains the same, the divisor expands by a factor of how many times, and the quotient shrinks by the same multiple. How many times the divisor is reduced, and the quotient is expanded by the same multiple.

The divisor remains the same, how many times the dividend is enlarged, the quotient is expanded by the same multiple, the dividend is reduced by many times, and the quotient is reduced by the same multiple.

The law of change of dividend, divisor, and quotient

The multiples of the dividend and the divisor are the same, the dividend is unchanged, the divisor is expanded by several times, and the quotient is reduced by several times. The divisor remains the same, the divisor shrinks by a factor of several times, and the quotient expands by a factor of several times. That is to say, the dividend is constant, the divisor is multiplied by a few, the quotient is divided by a few, the dividend is unchanged, the divisor is divided by a few, the quotient is multiplied by a few, and the divisor cannot be 0.

If the divisor remains the same, the dividend expands several times, the quotient expands by several times, and the divisor remains the same, and the dividend shrinks by several times, and the quotient shrinks by several times. That is to say, the divisor does not change, the dividend is multiplied by a few, the quotient is multiplied, the divisor is unchanged, the dividend is divided by a few quotients, and the divisor cannot be 0.

The quotient remains unchanged, and the divisor is expanded several times by the Wang wax state, and the divisor is expanded several times. The quotient does not change, the dividend is reduced by several times, and the divisor is reduced by several times, and the source of the dilemma is that the quotient is unchanged, and the dividend is multiplied by a few times, and the divisor is multiplied by a few. The quotient does not change, the dividend is divided by a few, the divisor is divided by the number of local rows, and the divisor cannot be 0.

When the dividend is constant, the quotient changes with the change of the divisor, and when the divisor does not change, the quotient changes with the change of the dividend.

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 for the two numbers A and B divided by 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, and B is divided by the remainder of C (or the remainder of this product divided by C) respectively. 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 remainder of the remainder divided by the remainder. 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.

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