Toán tiếng Anh 6, các phép toán trên số nguyên (2)

  • UEE|
  • ASP|
  • JMS|
18 Sep 2013
  • sum: tổng, 
  • product: tích
  • difference: hiệu
  • consecutive integers: số nguyên liên tiếp

Các bài toán trang 11, 12 sách NCPT toán 6, Vũ Hữu Bình

Ví dụ 1. Find two integers given that their sum is five times their positive difference, and their product is 24 times their positive difference.

Ví dụ 2. Let $a,b$ be two integers whose product is $6210$. If one of the two numbers is reduced by 7 units, the resulting product is $5265$. Find the value of $a,b$.

Ví dụ 3. (Bài 25 trang 11) Prove that the following difference can be written as product of two equal integers.

Ví dụ 4. (Bài 28 trang 11) Show with proof that each of the following numbers can be written as product of two consecutive whole numbers. 

$$111222,\;\; \; 444222.$$

Ví dụ 5. The 19th of August 2002 is Monday, what day is it on 19th of August of 1945?

Ví dụ 6. Let $A=3+3^2+3^3+\cdots+3^{100}$. Find the value of whole number $n$ such that $2A+3=3^n$.

Ví dụ 7. Find the value of 

$$A=\frac{72^3\times 54^2}{108^4},\;\; B=\frac{3^{10}\times 11+3^{10}\times 5}{3^9\times 2^4},\; \; C=\frac{2^{10}\times 13+2^{10}\times 65}{2^8\times 104}.$$

Ví dụ 8. (Bài 44 trang 13, sách NCPT toán 6) Find a three digit number $\overline{abc}$ given that the positive difference of this number and a number $\overline{cba}$ formed by the same three digits written in reverse order is $495$ and that the product of the leftmost and rightmost number is equal to the square of the ones digit, $b^2=ac$.

Ví dụ 9. Given a whole number $123456789$, a new number results from a combination of the addition or subtaction is performed among its digits or groups of digits. For example, $12+3+4+5-6-7-8+9=24-21+9=12$. Find such a combination such that the resulting number is $100$.