Question

1/2+13/26+103/206+1008/2016​

Answer 1

Ответ: 1/2 + 13/26 + 103/206 + 1008/2016 = 2.

Пошаговое объяснение:

Заметим, что дроби 13/26, 103/206 и 1008/2016 можно сократить на число, стоящее в числителе каждой дроби; после чего каждая из дробей станет равной 1/2.

После сокращения получим:

1/2 + 13/26 + 103/206 + 1008/2016 = 1/2 + 1/2 + 1/2 + 1/2 = 1 + 1 = 2.

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Answer 2

To add the fractions 1/2, 13/26, 103/206, and 1008/2016, we need to find a common denominator and then add the numerators. Let's break down the steps:

Finding the Common Denominator:

The common denominator is the least common multiple (LCM) of the denominators. In this case, the denominators are 2, 26, 206, and 2016. To find the LCM, we can use the prime factorization method or the division method.

Using the prime factorization method: - The prime factorization of 2 is 2. - The prime factorization of 26 is 2 * 13. - The prime factorization of 206 is 2 * 103. - The prime factorization of 2016 is 2^5 * 3^2 * 7.

To find the LCM, we take the highest power of each prime factor: - The LCM of 2, 26, 206, and 2016 is 2^5 * 3^2 * 7 * 13 = 32 * 9 * 7 * 13 = 36288.

Adding the Fractions:

Now that we have the common denominator, we can add the fractions by adding the numerators and keeping the common denominator.

1/2 + 13/26 + 103/206 + 1008/2016 = (1 * 18144 + 13 * 14016 + 103 * 176 + 1008 * 18) / 36288

Simplifying the numerator: = (18144 + 182208 + 18008 + 18144) / 36288 = 236504 / 36288

Simplifying the fraction: = 118252 / 18144

Therefore, the sum of the fractions 1/2, 13/26, 103/206, and 1008/2016 is 118252/18144.

Please note that the above calculations were done using the given fractions and their respective denominators.