Here's another way to solve this problem:

There is a common factor of 45 in the numerator and denominator; those divide out to equal 1. Then we have (16*67)/(65+67*65).

Although there is a 67 in both the numerator and denominator, this is NOT a common factor, because there is something else added to the product in the denominator. So we have to leave it as is and do some multiplication. 16*67 = 1072, and 67*65 = 4355, then we add the 65 to get 4420.

Now, our fraction is 1072/4420. If you know the rules for divisibility
by 4 (if the last two digits of a number are a number that is a multiple of 4,
then the entire number is a multiple of 4. *[see below the answer for
an explanation of why that works.]*

Well, 72 = 4*18, so 1072 has a factor of 4. (We also know that's true
because one of the factors was 16, or 4*4.) 20 = 4*5, so 4420 also is
divisible by 4. 1072 = 4*268 and 4420=4*1105, so **the simplified
fraction = 268/1105**. This fraction doesn't simplify further
because 268=2*2*67 and 1105=5*221.

*Now, why does the divisibility rule for 4's work?
Obviously, if a two-digit number is divisible by 4, that takes care of the
divisibility of that part of the number. 100 is divisible by 4 (e.g., 4
quarters = $1.00); therefore, any multiple of 100--including 1,000 (10^3),
10^4, etc.--will be divisible by 4.*

To find the value of 16*67*45/45(65+67*65), use the proper precedence of operations.

First evaluate what is within the brackets. Remember that multiplication is done before addition

65 + 67*65 = 65 + 4355 = 4420

16*67*45/45(65+67*65)

=> 16*67*45/45*4420

cancel 45 which is common in the numerator and denominator

=> 16*67/4420

=> 4*67/1105

=> 268/1105

**The required result is 268/1105**

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