Dsanders

Well the last problem makes sense now. Thanks for the help. Is the "multiply by numerator and divide by denominator" rule applicable for simplifying any multiplication problem involving a fraction and whole number? For example, would the same method work if it was 5/9(67)? That would equal 37.2 and that would be correct right?

Multiplication is just a list of factors. Some of those factors can be inverses (or parts of a whole). The denominator of a fraction usually collects all those inverses under the division bar, and all the non-inverted numbers (wholes) over the bar. So 5/9×67 is (5)(/9)(67). And as long as multiplication is commutative, you can reorder those factors whatever you please, eg. shift all inverses to the end of the list: (5)(67)(/9), which is 5×67/9.

67 is prime, so you cannot factor it any further, and the fraction 5×67/9 or 335/9 is irreducible. But 9 fits into it 37 whole times, so you can put it as (9×37 + 2)/9 and then split as 9×37/9 + 2/9 which is the same as 37×9/9 + 2/9, and this simplifies to 37 + 2/9 (37 wholes and 2 ninth parts of the remainder). If it were 2/10, then you could write 37.2, but since it's 2/9, it is actually 37.222222... or 37.(2) (a repeating decimal).