How many different ways can you write a fraction that has a numerator of 2 as a sum of fractions
1 answer:
Infinitely many ways!
Suppose you have the fraction 2/d.
<span>Pick </span>any<span> pair of integers a and b where b ≠ 0.</span>
Then 2b-ad is and integer, as is bd so that (2b - ad)/bd is a fraction.
Consider the fractions a/b and (2b - ad)/bd
<span>Their sum is </span>
a/b + (2b-ad)/bd = ad/bd + (2b-ad)/bd = 2b/bd = 2/d - as required.
<span>Since a and b were chosen arbitrarily, there are infinitely many possible answers to the question.</span>
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