(1) The relationship between the parts of multiplication:

Factor × factor = product One factor = product ÷ another factor.

(2) the relationship between the parts:

Know the product of two factors and one of them, find the other factor and divide it.

Division without remainder: Division with remainder:

Dividend = quotient× divisor Dividend = quotient× divisor+remainder

Divider = divider/quotient divider = (divider-remainder)/quotient

Quotient = divider/divider quotient = (divider-remainder)/divider

(3) the relationship between multiplication and division:

Division is the inverse of multiplication. Note: 0 cannot be divided.

(4) divisibility: an integer is divisible by another integer that is not zero, and the quotient is an integer without a remainder, so we say that one number can be divisible by another number. If 6÷2=3, that is, 6 is divisible by 2, or 2 is divisible by 6.

Note: to judge whether a number can be divisible by another number, we should first look at whether the dividend, divisor (divisor is not 0) and quotient are integers, and then look at whether there is a remainder. Any one is a decimal or an inseparable fraction. . For example, 60÷2=30, we say that 60 is divisible by 2 or 2 is divisible by 60. If a÷b(b≠0)=c, A is divisible by B, and B is divisible by A. ..

(2), the multiplication algorithm

1, exchange the positions of two factors, and the product is unchanged. This is the so-called multiplication commutative law.

Alphabetic formula: a×b=b×a

2. Multiply the first two numbers, or multiply the last two numbers, and the product remains unchanged. This is the so-called law of multiplication and association.

Letter formula: (a×b)×c=a×(b×c)

3. When the sum of two numbers is multiplied by a number, you can multiply it separately and then add it. This is the so-called law of multiplication and division.

Use the letter formula: (a+b)×c=a×c+b×c or a× (b+c) = a× b+a× c.

Generalization of the laws of multiplication and distribution;

The difference between two numbers is multiplied by a number, which can be multiplied by the subtracted two numbers respectively, and then the product is subtracted. Expressed in letters as:

(a-b)×c=a×c-b×c a×c-b×c=(a-b)×c

(3) Simple operation of subtraction:

1, a number subtracts two numbers continuously, and you can subtract the sum of these two numbers with this number.

Expressed in letters: a-b-c=a-(b+c)

2. One number subtracts two numbers continuously. You can use this number to subtract the last number and then subtract the previous number.

Expressed in letters: A-B A-B-C = A-C-B C-B.

(4) Simple operation of division:

1, a number is continuously divided by two numbers, and this number can be divided by the product of these two numbers.

Expressed in letters: a÷b÷c=a÷(b×c)

2. A number is continuously divided by two numbers. You can divide this number by the last number, and then divide the previous number.

Expressed in letters: a \b \c = a \c \b

(5), the change law of products

① One factor is reduced (expanded) several times, and the other factor is expanded (reduced) by the same multiple, and the product remains unchanged.

(2) If one factor shrinks (or expands several times) and the other factor remains unchanged, the product will also shrink (or expand) several times.

③ One factor is magnified m times, the other factor is magnified n times, and the product is magnified m×n times;

One factor MINUS m times, another factor MINUS n times, and the product MINUS m×n times;

One factor is expanded (reduced) by m times, another factor is reduced (expanded) by n times, and the product is expanded or reduced by m÷n times.

(6), the changing law of quotient

Dividend is reduced (expanded) several times, divisor is expanded (reduced) by the same times, and the quotient remains unchanged.

Dividend is reduced (expanded) several times, and quotient is reduced (expanded) several times by the same factor.

The dividend is constant, the divisor is reduced (expanded) several times, and the quotient is also expanded (or reduced) several times.

(7), to solve the problem:

1, encountered a problem.

Meeting distance = speed × meeting time

Meeting time = meeting distance/speed and

Speed Sum = Meeting Distance/Meeting Time

2. Distance problem (same direction)

Distance = speed difference × time interval

Time interval = distance interval ÷ speed difference

Speed difference = distance/time interval

3. Engineering problems

Work efficiency × working hours = total workload.

Total amount of work ÷ work efficiency = working hours

Total workload ÷ working time = working efficiency

4. Most and least problems

At least as many people as possible buy expensive ones, and at least as many people as possible buy cheap ones.

5. Cost-effective shopping and travel.

Calculate first and then compare.