Question

используя признаки делимости сократите дроби: а). 126/318 б). 330/390

Answer 1

а)сокращаем на шесть и получаем:126/318 =21/53
б)сокращаем на 30,и получаем : 330/390=11/13

Answer 2

Simplifying Fractions Using Divisibility Rules

To simplify fractions using divisibility rules, we need to find the greatest common divisor (GCD) of the numerator and denominator and then divide both the numerator and denominator by the GCD. This will give us the simplified form of the fraction.

Let's apply this method to the given fractions:

a) 126/318

To simplify the fraction 126/318, we need to find the GCD of 126 and 318. One way to find the GCD is to factorize both numbers and identify the common factors.

The prime factorization of 126 is 2 * 3^2 * 7, and the prime factorization of 318 is 2 * 3 * 53.

To find the GCD, we take the product of the common prime factors raised to the lowest power. In this case, the common prime factors are 2 and 3. The lowest power of 2 is 1, and the lowest power of 3 is 1. Therefore, the GCD of 126 and 318 is 2 * 3 = 6.

Now, we divide both the numerator and denominator of the fraction by the GCD:

126/318 = (126 ÷ 6) / (318 ÷ 6) = 21/53

Therefore, the simplified form of 126/318 is 21/53.

b) 330/390

To simplify the fraction 330/390, we need to find the GCD of 330 and 390.

The prime factorization of 330 is 2 * 3 * 5 * 11, and the prime factorization of 390 is 2 * 3 * 5 * 13.

The common prime factors are 2, 3, and 5. The lowest power of 2 is 1, the lowest power of 3 is 1, and the lowest power of 5 is 1. Therefore, the GCD of 330 and 390 is 2 * 3 * 5 = 30.

Now, we divide both the numerator and denominator of the fraction by the GCD:

330/390 = (330 ÷ 30) / (390 ÷ 30) = 11/13

Therefore, the simplified form of 330/390 is 11/13.

In summary: - The simplified form of 126/318 is 21/53. - The simplified form of 330/390 is 11/13.

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