Question

К числителю дроби 2/3 прибавили несколько раз число 2016 а к знаменателю 2017 Можно ли получить дробь 3/5

Answer 1

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Answer 2

Problem Analysis

We are given a fraction, 2/3, and we need to add a certain number, 2016, to the numerator and a different number, 2017, to the denominator. We need to determine if it is possible to obtain the fraction 3/5 after performing these operations.

Solution

Let's solve this problem step by step:

1. Start with the fraction 2/3. 2. Add 2016 to the numerator: 2 + 2016 = 2018. 3. Add 2017 to the denominator: 3 + 2017 = 2020.

So, after performing these operations, we have the fraction 2018/2020.

To check if this fraction can be simplified to 3/5, we need to find the greatest common divisor (GCD) of the numerator and denominator and see if it is equal to 1.

The GCD of 2018 and 2020 is 2. Since the GCD is not equal to 1, the fraction 2018/2020 cannot be simplified to 3/5.

Therefore, it is not possible to obtain the fraction 3/5 by adding 2016 to the numerator and 2017 to the denominator of the fraction 2/3.

Conclusion

Adding 2016 to the numerator and 2017 to the denominator of the fraction 2/3 does not result in the fraction 3/5. The resulting fraction is 2018/2020, which cannot be simplified to 3/5 because their greatest common divisor is 2, not 1.