The original translation uses the divisibility rule to illustrate whether the following numbers can be divisible by 2, 3, 5, 6, 10:

1.39 2.82 3. 157 4.56

Solving the so-called divisibility rule probably refers to such a rule:

The necessary and sufficient conditions for an integer to be divisible by 2 are: the single digit is one of 0, 2, 4, 6 and 8;

The necessary and sufficient condition for an integer to be divisible by 3 is that the sum of the numbers on each digit can be divisible by 3;

The necessary and sufficient condition for an integer to be divisible by 4 is that the last two digits are divisible by 4;

The necessary and sufficient conditions for an integer to be divisible by 5 are: the single digit is 0 or 5;

The necessary and sufficient condition for an integer to be divisible by 6 is that it can be divisible by both 2 and 3;

The necessary and sufficient condition for an integer to be divisible by 8 is that the last three digits can be divisible by 8;

The necessary and sufficient condition for an integer to be divisible by 9 is that the sum of the numbers on each digit can be divisible by 9;

A necessary and sufficient condition for an integer to be divisible by 10 is that the unit number is 0.

Explain 3 and 9 a little bit. The sum of the numbers on each digit, such as the number 3 12, is 3+ 1+2, which is 6. (And the number 3 12 can be regarded as the abbreviation of 300+ 10+2. The decimal three digits written in abc form represent the number100a+10b+C. If the sum of the digits on each digit is still a large number, you can continue the same operation until you know exactly whether the last digit can be divisible by 3 (or 9). For example, to judge whether 57943 is divisible by 3, calculate 5+7+9+4+3 first, and get 28. If you know that 28 is not divisible by 3, you will soon know that 57943 can also be divisible by 3. If you don't know whether 28 is divisible by 3, you can of course try to divide it, or continue to work out 2+8= 10 by our rules and 1 = 1. Finally, we know that 1 cannot be divisible by 3, so neither can 10, nor can 28. Divided by 9 is similar.

These are enough to solve this problem.

According to the rules, we can easily get the following answer: (For convenience, the following is omitted. The order of "can" after each number is arranged in the order of "can it be divisible by 2, 3, 5, 6, 10".

1.39 No, no, no.

2. Can you, can you, can't you?

3. 157 no, no, no, no.

4. Can you, can you, can't you?

the second question

The following products are written in exponential form:

1.2*2*2*3*3*7 2.2*3*3*7*7*7* 1 1

Is the solution easy to translate? The exponential form is the abbreviation of serial multiplication, just as multiplication is the abbreviation of serial addition. Just count and write the same factor as 1, and write its number in the upper right corner. A word related to exponent is called power, the one in the upper right corner is called exponent, the one in the normal position is called base, and the whole one is called power.

1.2 (a small three in the upper right corner) *3 (a small two in the upper right corner) *7 is 2? *3? *7

2.2*3 (a small two in the upper right corner) *7 (a small three in the upper right corner) * 1 1, which means 2*3? *7? * 1 1

Third question

Write the following powers as the product of the same factor:

1.x (a small seven in the upper right corner) 2. (-2) (a small four in the upper right corner)

Solving this problem is just the opposite of the last one.

1. Just multiply by 7 x's, that is, x*x*x*x*x*x*x * X *.

2. Multiply four (-2), that is, (-2)*(-2)*(-2)*(-2)

The fourth question

Judge whether the following expressions are monomials and explain the reasons.

1.2 1abc 2。 -3(x+y) 3。 4n-7 4。 -5 12

Solving the classification of monomial and polynomial is to prepare for studying basic algebra, equation and linear algebra in the future.

Single judgment may be a bit cumbersome for beginners:

First of all, in algebraic expressions, we have letters (used to represent an uncertain number, usually called variables), numbers (constants), four operations of addition, subtraction, multiplication and division, and power operations. Parentheses are used to specify the operation order. Because of the distribution law of multiplication and addition, any algebraic expression (algebraic expression without letters in denominator) can be written in the form of b ... c, but there is no addition or subtraction in A, B, C, and so on. Such A, B, C and so on are monomials, and the results of addition or subtraction between them are integer polynomials. Specifically, what is a monomial? The monomial must meet the following conditions: it does not contain addition and subtraction operations (that is, only multiplication, division and power operations) and if there are letters, the letters cannot be on the denominator.

1.2 1abc is.

2.-3(x+y) is not because of addition.

3.4n-7 is not because of subtraction.

4.-5 12 is (note: odd numbers are also monomials, and the number of letters is not specified in the conditions to be met by monomials. If there are no letters or multiple letters (such as 2 1abc), it can be a monomial; Secondly, the negative sign is not a subtraction operation, and the addition, subtraction, multiplication and division operations are all binary, that is, they have to act on two terms.