Question

[Trịnh Quỳnh Hoa]

Exer 1: There is a division with the quotient is 6 and the remainder is 3. The sum of dividend, divisor and remainder are 195. Find the dividend are divisor.

Exer 2: Prove that: Amoney three consecutive natural numbers, there is one only one the number which divisibles by 3.

Exer 3: Given natural number, n = \(\overline{1ab1}\). Let m be the natural number which is written the opposite respectively of n. Prove that the different of n and m divisibles by 90.

Answer 1

[Aoko-chan]

Exer 1:

Trả lời:

The sum of dividend and divisor are:

195 - 3 = 192

Because the quotient is 6.

The divisor is:

(192-3) : (6+1) = 27

The dividend is:

192 - 27 = 165

Exer 2:

Trả lời:

Let three unknow numbers be: n, n + 1, n + 2.

Because n has three forms: 3k, 3k + 1, 3k + 2.

+) If n

Answer 2

[Aoko-chan]

Xin lỗi, mình vẫn chưa viết xong, rồi mình viết tiếp đây:

+) If n = 3k then there is only n divisibles by 3.

+) If n = 3k + 1 then there is only n + 2 divisibles by 3.

+) If n = 3k + 2 then there is only n + 1 divisibles by 3.

Thus, amoney three consecutive natural numbers, there is one only one the number which divisibles by 3.

Exer 3:

Trả lời:

When we written the opposite respectively of n, we obtain \(\overline{1ba1}\).

We have:

\(\overline{1ab1}\) + \(\overline{1ba1}\) = (1000 + 100a + 10b + 1) - (1000 + 100b + 10a + 1)

= 90a - 90b

= 90(a - b)\(⋮\) 90

Thus, the difference of n and m which divisibles by 90.