If the sum of the repeating decimals 0.353535…+0.252525…   is written as a fraction in lowest terms, the product of the numerator and denominator is:

# If the sum of the repeating decimals   is written as a fraction in lowest terms, the product of the numerator and denominator is:

1. A
2475
2. B
680
3. C
670
4. D
660

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### Solution:

Concep- We will first write   and   in the form of   where   separately. For doing that, we will express the first term as  , then multiply with 100 as   and then express it as  . Now, again this can be written as  . Now, we can get   in the form of a fraction. In a similar manner, we will carry out this process again for the second term. Then sum these two values in fractional form. The percent we ultimately achieve will be the one we need. The needed result is then obtained by multiplying its numerator and denominator.

Numerator   and Denominator
Their product
Hence, the correct answer is option 4.

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