SOLUTION: The sum of two mixed numbers is 6. what might the two mixed numbers be? show as many different solutions as you can. Explain your strategy.

Question 1121485: The sum of two mixed numbers is 6. what might the two mixed numbers be? show as many different solutions as you can. Explain your strategy.

Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
A question like this has too many possible answers. You can choose any denominator you want. "Show as many different solutions as you can." This can be never ending.

Just one example.

--

Maybe better:
Let some natural number d, be used as denominator. For NUMERATOR of 1,
These examples will work:

or

but this example will not work according to your description:
, because one of the numbers is not a mixed number.

You could also take this a make it more general than "numerator of 1".
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

If one mixed number is "x", then the other mixed number is 6 - x. In this way, taking any mixed number as "x", you obtain the other mixed number 6-x so that their sum is 6. There are infinitely many solutions. For example, these pairs (5,1), (4,2), (,), (7,-1), (-2,8), and so on . . .

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

There are an infinite number of solutions; so I can't "show as many different solutions as I can".

A strategy for finding pairs of mixed numbers whose sum is 6 might be

3+n and 3-n

where n is any real number that is not an integer.

A few examples....

n=1/2 --> 3 1/2 and 2 1/2
n=3/7 --> 3 3/7 and 2 4/7
n=1 2/11 --> 4 2/11 and 1 9/11
n=5 2/5 --> 8 2/5 and -2 2/5
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