Question

Используя признаки делимости докажите что дробь можно сократить и выполните сокращение :1665/6930

Answer 1

Нужно найти НОД
НОД (1665 и 6930) = 15, значит числа можно сократить на 15, то получится дробь 111/462

Answer 2

Using Divisibility Rules to Simplify a Fraction

To prove that a fraction can be simplified, we can use the divisibility rules to find the greatest common divisor (GCD) of the numerator and the denominator. Once we find the GCD, we can divide both the numerator and the denominator by this common divisor to simplify the fraction.

Divisibility Rules for 1665 and 6930

Let's start by examining the divisibility rules for 1665 and 6930 to find their GCD.

- 1665: The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. In the case of 1665, the sum of its digits is 1 + 6 + 6 + 5 = 18, which is divisible by 3. Therefore, 1665 is divisible by 3. - 6930: Similarly, applying the divisibility rule for 3 to 6930, we find that the sum of its digits is 6 + 9 + 3 + 0 = 18, which is also divisible by 3. Therefore, 6930 is divisible by 3.

Finding the Greatest Common Divisor (GCD)

Since both 1665 and 6930 are divisible by 3, we can divide them by 3 to simplify the fraction.

Simplifying the Fraction

Let's perform the simplification: 1665 ÷ 3 = 555 6930 ÷ 3 = 2310

Therefore, the fraction 1665/6930 can be simplified to 555/2310 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

So, the simplified fraction is 555/2310.