Amillionaire leaves 4/17 of his estate to his son, 7/13 to his wife, 2/3 to his daughter and the remaining 2 million to his dog, what was the total of his estate?

Comment
I'm going to do this two ways, one using a calculator and one not.
Let the total amount of his estate be x.

Equation and Solution
If you have a calculator with an a b/c key on it you can do this problem easily, or at least the fractional part will be easy.

First: develop the  equation
(4/17) x + (7/13)x + 2/3 x + 2 000 000  

Solve the equation
Use the a b/c key on your calculator if you have one. If not go down the second solution part. Put a fraction in as follows.
4 a b/c 17 + 7 a b/c 13 + 2 a b/c 3 = 
You should get 1 r 16 r 51 
What this translates into is 1 292 / 663 of x
or 955/663 x + 2000000

So the total of fhis estate is
(955/663) x + 2000000 <<<< answer In decimal form you get
1,44 x + 2000000 <<<< answer in decimal.

Note: you cannot solve this to the exact amount of his estate because the fractional amount exceeds x which assumed to be the total amount of his estate.

By hand
Find the ;lowest common denominator of 13 17 and 3. Since all of them are prime numbers the lowest common denominator is 13 * 17 * 3 = 663
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Next set up the 3 fracttions so the denominator = 663
4 / 17 =( 4 * 13 * 3) / 663 = 156 / 663

7/13 = 7 * 17*3 / 663 = 357 / 663

2/3 = 2*13 * 17 / 663 = 442 / 663

Now add these up 156/663 + 357/663 + 442/663 = 955 / 663 This is irreducible
This fraction is over 1 so it cannot represent the total amount in his estate. It is too large.    

(955/663)x + 2000000 <<<<<< fractional answer
1.44x + 2000000 < decimal answer.

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