by Guest » Sat Jan 25, 2020 12:04 pm
An interesting approach is this: ask how 5/8 compares with 62/100, say.
Write 5/8 ?? 62/100, where ?? stands for the unknown inequality.
Now we can operate on expressions like this using operations that leave true statements true and false statements false. For example we can multiply both sides by any positive number (negative ones, on the other hand, reverse inequalities, so would not be legitimate), such as 800, which is what we will do.
This gives
500 ?? 496, and it is clear that ?? stands for >. Hence we have 5/8 > 62/100.
I'm not saying this is easier than some of the other approaches, but it's worth thinking how such an approach might be used in wider contexts.
An interesting approach is this: ask how 5/8 compares with 62/100, say.
Write 5/8 ?? 62/100, where ?? stands for the unknown inequality.
Now we can operate on expressions like this using operations that leave true statements true and false statements false. For example we can multiply both sides by any positive number (negative ones, on the other hand, reverse inequalities, so would not be legitimate), such as 800, which is what we will do.
This gives
500 ?? 496, and it is clear that ?? stands for >. Hence we have 5/8 > 62/100.
I'm not saying this is easier than some of the other approaches, but it's worth thinking how such an approach might be used in wider contexts.