Improper fractions - grade 6 

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If the fraction is greater than 12 then it would look like 12+a/b where a and b are natural numbers (positive integers).

The improper fraction would be (12b+a)/b. The numerator 12b+a is 10 more than the denominator b, so 12b+a=b+10. Therefore 11b+a=10. The smallest value for b=1, so 11+a=10, making a=10-11=-1. But a has to be a positive integer, so this is a contradiction. If b>1, we have a=10-11b, which would make a even more negative, so there can be no such fraction a/b and therefore no improper fraction (12b+a)/b satisfying the requirement that the mixed number is greater than 12.

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