I do not understand how to decide which method would you use to determine whether this proportion is true or false? 19/6=4/27

Answer 1

here is a neat trick:

write down the two fractions without any "sign" between them

19/6 4/27
first write down the cross-product from topleft to bottomright

459
leave a space then write down the crossproduct from topright to bottomleft
459 36

Place the correct relationship sign, = > or <, between them AND the original fraction.

since 459 > 36
19/6 > 4/27 , so the proportion is false.

another example

17/24 4/5

65 96

since 65< 96
17/24 < 4/8

another

9/12 36/48

432 432

since 432 = 432
9/12 = 36/48

Answer 2

As a general point, before you resort to any actual math at all it's always a good idea to just LOOK at the equation for a few seconds and see if anything leaps out at you - because the more complicated an equation is, the more time a flash of inspiration can save you. In this instance the only thing you need to spot to save yourself the trouble of multiplying it out is that the first fraction is bigger than one, whereas the second one is smaller than one - so obviously they can't be equal. You will however now need to decide which of the methods you've been told about for deciding whether or not the proposition is true or not encompasses the discovery you've just made (and I don't know what those methods are, because they're not listed here).